source: vis_dev/vis-2.3/src/img/imgLinear.c @ 99

/**CFile***********************************************************************

  FileName    [imgLinear.c]

  PackageName [img]

  Synopsis    [Routines for image computation using Linear Arrangement
   published in TACAS02.]

  Description []

  SeeAlso     []

  Author      [HoonSang Jin]

  Copyright   [Copyright (c) 1994-1996 The Regents of the Univ. of Colorado.
  All rights reserved.

  Permission is hereby granted, without written agreement and without license
  or royalty fees, to use, copy, modify, and distribute this software and its
  documentation for any purpose, provided that the above copyright notice and
  the following two paragraphs appear in all copies of this software.

  IN NO EVENT SHALL THE UNIVERSITY OF COLORADO BE LIABLE TO ANY PARTY FOR
  DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES ARISING OUT
  OF THE USE OF THIS SOFTWARE AND ITS DOCUMENTATION, EVEN IF THE UNIVERSITY OF
  COLORADO HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

  THE UNIVERSITY OF COLORADO SPECIFICALLY DISCLAIMS ANY WARRANTIES,
  INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
  FITNESS FOR A PARTICULAR PURPOSE.  THE SOFTWARE PROVIDED HEREUNDER IS ON AN
  "AS IS" BASIS, AND THE UNIVERSITY OF COLORADO HAS NO OBLIGATION TO PROVIDE
  MAINTENANCE, SUPPORT, UPDATES, ENHANCEMENTS, OR MODIFICATIONS.]

******************************************************************************/
#include "imgInt.h"
#include "fsm.h"
#include "heap.h"

static char rcsid[] UNUSED = "$Id: imgLinear.c,v 1.18 2010/04/10 00:37:06 fabio Exp $";
static char linearVarString[] = "TCNI";


/*---------------------------------------------------------------------------*/
/* Constant declarations                                                     */
/*---------------------------------------------------------------------------*/

/*---------------------------------------------------------------------------*/
/* Type declarations                                                         */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Structure declarations                                                    */
/*---------------------------------------------------------------------------*/


/*---------------------------------------------------------------------------*/
/* Variable declarations                                                     */
/*---------------------------------------------------------------------------*/

Cluster_t *__clu;

/*---------------------------------------------------------------------------*/
/* Macro declarations                                                        */
/*---------------------------------------------------------------------------*/

#define BACKWARD_REDUCTION_RATE 0.5
#define FORWARD_REDUCTION_RATE 0.5

/**AutomaticStart*************************************************************/

/*---------------------------------------------------------------------------*/
/* Static function prototypes                                                */
/*---------------------------------------------------------------------------*/

static void ImgLinearUpdateVariableArrayWithId(Relation_t *head, int cindex, int id);
static int ImgLinearQuantifyVariablesFromConjunct(Relation_t *head, Conjunct_t *conjunct, array_t *smoothVarBddArray, int *bModified);
static void ImgLinearConjunctRefine(Relation_t *head, Conjunct_t *conjunct);
static void ImgLinearVariableArrayQuit(Relation_t *head);
static void ImgLinearConjunctQuit(Conjunct_t *conjunct);
static Conjunct_t ** ImgLinearAddConjunctIntoArray(Conjunct_t **array, int *nArray, Conjunct_t *con);
static void ImgLinearFindSameSupportConjuncts(Relation_t *head, int from, int to);
static void ImgLinearClusterSameSupportSet(Relation_t *head);
static void ImgLinearExpandSameSupportSet(Relation_t *head);
static int ImgLinearIsSameConjunct(Relation_t *head, Conjunct_t *con1, Conjunct_t *con2);
static bdd_t * ImgLinearClusteringSmooth(Relation_t *head, Cluster_t *clu, int **failureHistory, int andExistLimit, int bddLimit);
static int ImgLinearClusterUsingHeap(Relation_t *head, double affinityLimit, int andExistLimit, int varLimit, Img_OptimizeType optDir, int rangeFlag, int (*compare_func)(const void *, const void *));
static void ImgLinearPrintTransitionInfo(Relation_t *head);
static void ImgLinearComputeLifeTime(Relation_t *head, double *paal, double *patl);
static void ImgLinearFreeSmoothArray(array_t *smoothVarBddArray);
static void ImgLinearPrintMatrixFull(Relation_t *head, int matrixIndex);
static void ImgLinearPrintMatrix(Relation_t *head);
static void ImgLinearCAPOReadVariableOrder(Relation_t *head, char *baseName, int includeNS);
static void ImgLinearCAPOInterfaceVariablePl(Relation_t *head, char *baseName, int includeNS);
static void ImgLinearCAPOInterfaceVariableScl(Relation_t *head, char *baseName);
static void ImgLinearCAPOInterfaceVariableNet(Relation_t *head, char *baseName, int includeNS);
static void ImgLinearCAPOInterfaceVariableNodes(Relation_t *head, char *baseName, int includeNS);
static void ImgLinearVariableOrder(Relation_t *head, char *baseName, int includeNS);
static void ImgLinearCAPOReadConjunctOrder(Relation_t *head, char *baseName);
static int ImgLinearCAPORun(char *capoExe, char *baseName, int brief);
static void ImgLinearCAPOInterfaceAux(Relation_t *head, char *baseName);
static void ImgLinearCAPOInterfaceConjunctPl(Relation_t *head, char *baseName);
static void ImgLinearCAPOInterfaceConjunctScl(Relation_t *head, char *baseName);
static void ImgLinearCAPOInterfaceConjunctNet(Relation_t *head, char *baseName);
static void ImgLinearCAPOInterfaceConjunctNodes(Relation_t *head, char *baseName);
static void ImgLinearConjunctionOrder(Relation_t *head, char *baseName, int refineFlag);
static void ImgLinearConjunctOrderMain(Relation_t *head, int bRefineConjunctOrder);
static void ImgLinearPrintDebugInfo(Relation_t *head);
static void ImgLinearPrintVariableProfile(Relation_t *head, char *baseName);
static void ImgLinearInsertClusterCandidate(Relation_t *head, int from, int to, int nDead, int nVar, double affinityLimit);
static void ImgLinearInsertPairClusterCandidate(Relation_t *head, int from, double affinityLimit, int varLimit, int rangeFlag);
static void ImgLinearBuildInitialCandidate(Relation_t *head, double affinityLimit, int varLimit, int rangeFlag, int (*compare_func)(const void *, const void *));
static bdd_t * ImgLinearClusteringPairSmooth(Relation_t *head, Cluster_t *clu, int **failureHistory, int andExistLimit, int bddLimit);
static void ImgLinearVariableArrayInit(Relation_t *head);
static void ImgLinearSetEffectiveNumberOfStateVariable(Relation_t *head, int *rangeId, int *domainId, int *existStateVariable) ;
static void ImgLinearVariableLifeQuit(VarLife_t *var);
static void ImgLinearAddNextStateCase(Relation_t *head);
static void ImgLinearAddSingletonCase(Relation_t *head);

static int ImgLinearCompareDeadAffinityLive(const void *c1, const void *c2);
static int ImgLinearCompareDeadLiveAffinity(const void *c1, const void *c2);
static int ImgLinearCompareAffinityDeadLive(const void *c1, const void *c2);
static int ImgLinearCompareLiveAffinityDead(const void *c1, const void *c2);
static int ImgLinearHeapCompareDeadAffinityLive(const void *c1, const void *c2);
static int ImgLinearHeapCompareDeadLiveAffinity(const void *c1, const void *c2);
static int ImgLinearHeapCompareAffinityDeadLive(const void *c1, const void *c2);
static int ImgLinearHeapCompareLiveAffinityDead(const void *c1, const void *c2);

static int ImgLinearCompareVarIndex(const void *c1, const void *c2);
static int ImgLinearCompareVarSize(const void *c1, const void *c2);
static int ImgLinearCompareVarEffFromSmall(const void *c1, const void *c2);
static int ImgLinearCompareVarEffFromLarge(const void *c1, const void *c2);
static int ImgLinearCompareConjunctDummy(const void *c1, const void *c2);
static int ImgLinearCompareConjunctIndex(const void *c1, const void *c2);
static int ImgLinearCompareConjunctSize(const void *c1, const void *c2);
static int ImgLinearCompareConjunctRangeMinusDomain(const void *c1, const void *c2);
static int ImgLinearCompareVarId(const void *c1, const void *c2);
static int ImgCheckRangeTestAndOverapproximate(Relation_t *head);
static void ImgCountOnsetDisjunctiveArray(Relation_t *head);
static int linearCheckRange(const void *tc);

static void ImgLinearConjunctArrayRefine(Relation_t *head);
/**AutomaticEnd***************************************************************/


/*---------------------------------------------------------------------------*/
/* Definition of exported functions                                          */
/*---------------------------------------------------------------------------*/
void ImgLinearConjunctOrderMainCC(Relation_t *head, int refineFlag);
int ImgLinearClustering(Relation_t *head, Img_OptimizeType optDir);
int ImgLinearPropagateConstant(Relation_t *head, int nextStateFlag);
int ImgLinearOptimizeStateVariables(Relation_t *head, Img_OptimizeType optDir);
void ImgLinearExtractNextStateCase(Relation_t *head);
void ImgLinearExtractSingletonCase(Relation_t *head);
/*void ImgLinearClusterRelationArray(mdd_manager *mgr, ImgFunctionData_t *functionData, array_t *relationArray, Img_DirectionType direction, array_t **clusteredRelationArrayPtr, array_t **arraySmoothVarBddArrayPtr, array_t **optClusteredRelationArrayPtr, array_t **optArraySmoothVarBddArrayPtr, ImgTrmOption_t *option);
*/
void ImgLinearConnectedComponent(Relation_t *head);
void ImgLinearBuildConjunctArrayWithQuotientCC(Relation_t *head);
void ImgLinearFindConnectedComponent(Relation_t *head, Conjunct_t *conjunct, int cc_index);
void ImgLinearAddConjunctIntoClusterArray(Conjunct_t *base, Conjunct_t *con);


/**Function********************************************************************

  Synopsis    [Cluster fine grain transition relation]

  Description [First the linear arrangement of transition relation that minimze max cut is generated and the iterative clustering is applied on it.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearClusterRelationArray(mdd_manager *mgr, 
                             ImgFunctionData_t *functionData, 
                             array_t *relationArray, 
                             Img_DirectionType direction, 
                             array_t **clusteredRelationArrayPtr, 
                             array_t **arraySmoothVarBddArrayPtr, 
                             array_t **optClusteredRelationArrayPtr, 
                             array_t **optArraySmoothVarBddArrayPtr, 
                             ImgTrmOption_t *option)
{
Img_OptimizeType optDir;
int bGroupStateVariable;
int bOrderVariable;

int includeCS;
int includeNS;
int quantifyCS;
array_t *initRelationArray;
int bOptimize;
Relation_t *head;
bdd_t **smoothCubeArr, **optSmoothCubeArr;
array_t *optRelationArr, *optSmoothVarBddArr;
array_t *relationArr, *smoothVarBddArr;

  if(option->linearComputeRange) {
    option->linearIncludeCS = 0;
    option->linearIncludeNS = 0;
    option->linearQuantifyCS = 1;
  }
  
  optRelationArr = relationArr = 0;
  optSmoothVarBddArr = smoothVarBddArr = 0;

  includeCS = option->linearIncludeCS;
  includeNS = option->linearIncludeNS;
  quantifyCS = option->linearQuantifyCS;
  if(option->linearFineGrainFlag)       includeNS = 1;
  optDir = option->linearOptimize;
  bOrderVariable = option->linearOrderVariable;
  bGroupStateVariable = option->linearGroupStateVariable;

  head = ImgLinearRelationInit(mgr, relationArray, 
          functionData->domainBddVars, functionData->rangeBddVars, 
          functionData->quantifyBddVars, option);

  if(head->verbosity >= 5) ImgLinearPrintDebugInfo(head);

  ImgLinearOptimizeAll(head, Opt_None, 0);
  ImgLinearRefineRelation(head);
  initRelationArray = ImgLinearExtractRelationArrayT(head);

  bOptimize = 0;

  ImgLinearPrintMatrix(head);

  if(bOrderVariable)
    ImgLinearVariableOrder(head, "VarOrder", !bGroupStateVariable);

  if((direction==0) || (direction==2))  {
    ImgLinearPrintMatrix(head);

    bOptimize |= ImgLinearOptimizeAll(head, optDir, 0);
    ImgLinearRefineRelation(head);
    ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);

    ImgLinearConjunctOrderMainCC(head, 0);

    ImgLinearPrintMatrix(head);

    bOptimize |= ImgLinearClustering(head, optDir);

    ImgLinearRefineRelation(head);
    ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
    ImgLinearPrintTransitionInfo(head);

    ImgLinearPrintMatrix(head);

    ImgLinearPrintMatrixFull(head, 2);

    if(bOptimize) {
      optRelationArr = ImgLinearExtractRelationArrayT(head);
      optSmoothCubeArr = ALLOC(bdd_t *, head->nSize+1);
      optSmoothVarBddArr = ImgLinearMakeSmoothVarBdd(head, optSmoothCubeArr);
    }
    else {
      optRelationArr = ImgLinearExtractRelationArrayT(head);
      optSmoothCubeArr = ALLOC(bdd_t *, head->nSize+1);
      optSmoothVarBddArr = ImgLinearMakeSmoothVarBdd(head, optSmoothCubeArr);
      relationArr = 0;
      smoothVarBddArr = 0;
    }
    ImgLinearPrintDebugInfo(head);
    ImgLinearRelationQuit(head);

    if(bOptimize) {
      fprintf(vis_stdout, "Get Schedules without optimization\n");
      head = ImgLinearRelationInit(mgr, initRelationArray, 
          functionData->domainBddVars, functionData->rangeBddVars, 
          functionData->quantifyBddVars, option);
      ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
      ImgLinearConjunctOrderMainCC(head, 0);
      if(head->verbosity >= 5)
        ImgLinearPrintMatrix(head);
      ImgLinearClustering(head, Opt_None);
       
      relationArr = ImgLinearExtractRelationArrayT(head);
      smoothCubeArr = ALLOC(bdd_t *, head->nSize+1);
      smoothVarBddArr = ImgLinearMakeSmoothVarBdd(head, smoothCubeArr);

      ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
      ImgLinearPrintDebugInfo(head);
      ImgLinearPrintTransitionInfo(head);

      ImgLinearRelationQuit(head);
    }

    if(optClusteredRelationArrayPtr)
      *optClusteredRelationArrayPtr = optRelationArr;
    else
      mdd_array_free(optRelationArr);

    if(optArraySmoothVarBddArrayPtr)
      *optArraySmoothVarBddArrayPtr = optSmoothVarBddArr;
    else if(optSmoothVarBddArr)
      ImgLinearFreeSmoothArray(optSmoothVarBddArr);

    if(clusteredRelationArrayPtr)
      *clusteredRelationArrayPtr = relationArr;
    else
      mdd_array_free(relationArr);

    if(arraySmoothVarBddArrayPtr)
      *arraySmoothVarBddArrayPtr = smoothVarBddArr;
    else if(smoothVarBddArr)
      ImgLinearFreeSmoothArray(smoothVarBddArr);
  }

  if((direction==1) || (direction==2)) {
  }
}


/**Function********************************************************************

  Synopsis    [Initialize the data structure for linear arrangement and clustering.]

  Description [Build initial data structure]

  SideEffects []

  SeeAlso     []

******************************************************************************/
Relation_t *
ImgLinearRelationInit(mdd_manager *mgr,
                        array_t *relationArray,
                        array_t *domainBddVars,
                        array_t *rangeBddVars,
                        array_t *quantifyBddVars,
                        ImgTrmOption_t *option)
{
Relation_t *head;
Conjunct_t *conjunct, **conjunctArray;
bdd_t *varBdd;
int *domain2range, *range2domain;
int *varArrayMap, *varType;
bdd_t **constantCase, *relation;
int i, j, id, tid, nSize;
int *supList, listSize;
char *flagValue;
int *quantifyVars, nQuantify, *visited;

  head = ALLOC(Relation_t, 1);
  memset(head, 0, sizeof(Relation_t));
  head->mgr = mgr;
  head->nVar = bdd_num_vars(head->mgr);
  head->bddLimit = option->clusterSize;

  head->verbosity = option->verbosity;
  flagValue = Cmd_FlagReadByName("linear_verbosity");
  if(flagValue) {
    head->verbosity += atoi(flagValue);
  }


  head->includeCS = option->linearIncludeCS;
  head->includeNS = option->linearIncludeNS;
  head->quantifyCS = option->linearQuantifyCS;
  head->computeRange = option->linearComputeRange;

  head->nInitRange = 0;
  head->nInitDomain = 0;
  head->nInitQuantify = 0;
  head->nEffRange = 0;
  head->nEffDomain = 0;
  head->nEffQuantify = 0;

  head->clusterArray = 0;
  head->nClusterArray = 0;

  head->nVarArray = 0;
  head->varArray = 0;

  head->nSingletonArray = 0;
  head->singletonArray = 0;
  head->nNextStateArray = 0;
  head->nextStateArray = 0;

  domain2range = ALLOC(int, head->nVar);
  head->domain2range = domain2range;
  memset(domain2range, -1, sizeof(int)*head->nVar);

  range2domain = ALLOC(int, head->nVar);
  head->range2domain = range2domain;
  memset(range2domain, -1, sizeof(int)*head->nVar);

  varType = ALLOC(int, head->nVar);
  head->varType = varType;
  memset(varType, 0, sizeof(int)*head->nVar);

  head->nRange = array_n(rangeBddVars);
  head->nDomain = array_n(domainBddVars);

  head->domainVars = ALLOC(int, head->nDomain);
  head->rangeVars = ALLOC(int, head->nRange);
  for(i=0; i<head->nDomain; i++) {
    varBdd = array_fetch(bdd_t *, domainBddVars, i);
    id = (int)bdd_top_var_id(varBdd);
    head->domainVars[i] = id;
    varType[id] = 1;

    varBdd = array_fetch(bdd_t *, rangeBddVars, i);
    tid = (int)bdd_top_var_id(varBdd);
    head->rangeVars[i] = tid;
    varType[tid] = 2;

    domain2range[id] = tid;
    range2domain[tid] = id;
  }

  head->quantifyVars = quantifyVars = ALLOC(int, head->nVar);
  memset(quantifyVars, 0, sizeof(int)*head->nVar);
  for(nQuantify=0, i=0; i<array_n(quantifyBddVars); i++) {
    varBdd = array_fetch(bdd_t *, quantifyBddVars, i);
    id = (int)bdd_top_var_id(varBdd);
    quantifyVars[nQuantify++] = id;
    varType[id] = 3;
  }

  varArrayMap = ALLOC(int, head->nVar);
  head->varArrayMap = varArrayMap;
  memset(varArrayMap, -1, sizeof(int)*head->nVar);

  constantCase = ALLOC(bdd_t *, head->nVar);
  head->constantCase = constantCase;
  memset(constantCase, 0, sizeof(bdd_t *)*head->nVar);


  nSize = array_n(relationArray);
  conjunctArray = ALLOC(Conjunct_t *, nSize+1);
  head->nSize = nSize;
  head->conjunctArray = conjunctArray;

  visited = ALLOC(int, head->nVar);
  memset(visited, 0, sizeof(int)*head->nVar);
  for(i=0; i<nSize; i++) {
    conjunct = ALLOC(Conjunct_t, 1);
    memset(conjunct, 0, sizeof(Conjunct_t));
    conjunct->index = i;
    relation = array_fetch(bdd_t *, relationArray, i);

    conjunct->relation = mdd_dup(relation);

    supList = ImgLinearGetSupportBddId(head->mgr, relation, &listSize);
    conjunct->supList = supList;
    conjunct->nSize = listSize;
    for(j=0; j<listSize; j++) {
      id = supList[j];
      if(varType[id] == 1)      conjunct->nDomain++;
      else if(varType[id] == 2) conjunct->nRange++;
      else if(varType[id] == 3) conjunct->nQuantify++;
      else if(visited[id] == 0) {
        quantifyVars[nQuantify++] = id;
        visited[id] = 1;
      }
    }

    conjunctArray[i] = conjunct;
  }
  conjunctArray[i] = 0;

  head->nQuantify= nQuantify;
  free(visited);

  ImgLinearVariableArrayInit(head);
  return(head);
}


/**Function********************************************************************

  Synopsis    [Find support varaibles of bdd]

  Description [Find support varaibles of bdd]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int *
ImgLinearGetSupportBddId(mdd_manager *mgr, bdd_t *f, int *nSize)
{
var_set_t *vset;
array_t *bvar_list;
int *supList, i, size;

  bvar_list = mdd_ret_bvar_list(mgr);
  vset = bdd_get_support(f);
  size = 0;
  supList = ALLOC(int, size+1);
  supList[0] = -1;
  for(i=0; i<array_n(bvar_list); i++) {
    if(var_set_get_elt(vset, i) == 1) {
      supList = REALLOC(int, supList, size+2); 
      supList[size++] = i;
      supList[size] = -1;
    }
  }
  var_set_free(vset);
  *nSize = size;
  if(size == 0) {
    free(supList);
    supList = 0;
  }
  return(supList);
}

/**Function********************************************************************

  Synopsis    [Create relation array for image computation from Relation_t data structure]

  Description [Create relation array for image computation from Relation_t data structure]

  SideEffects []

  SeeAlso     []

******************************************************************************/
bdd_t **
ImgLinearExtractRelationArray(Relation_t *head)
{
int i;
bdd_t **relationArray;
Conjunct_t *conjunct;

  relationArray = ALLOC(bdd_t *, head->nSize+1);
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    relationArray[i] = bdd_dup(conjunct->relation);
  }
  relationArray[i] = 0;
  return(relationArray);
}
/**Function********************************************************************

  Synopsis    [Create relation array for image computation from Relation_t data structure]

  Description [Create relation array for image computation from Relation_t data structure]

  SideEffects []

  SeeAlso     []

******************************************************************************/
array_t *
ImgLinearExtractRelationArrayT(Relation_t *head)
{
int i;
array_t *relationArray;
Conjunct_t *conjunct;

  relationArray = array_alloc(bdd_t *, head->nSize);
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    array_insert_last(bdd_t *, relationArray, bdd_dup(conjunct->relation));
  }
  return(relationArray);
}


/**Function********************************************************************

  Synopsis    [Function for optimizing state varaibles]

  Description [If the next or current state variables are eleminated after
  applying clustering and constant propagation then delete corresponding
  state variable from transition relation.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
ImgLinearOptimizeAll(Relation_t *head, Img_OptimizeType optDir, int constantNSOpt)
{
int bOptimize;

  bOptimize = 0;
  bOptimize |= ImgLinearPropagateConstant(head, constantNSOpt);
  bOptimize |= ImgLinearOptimizeStateVariables(head, optDir);
  ImgLinearOptimizeInternalVariables(head);
  return(bOptimize);
}
/**Function********************************************************************

  Synopsis    [Propagate the constant to simply the transition relation]

  Description [Propagate the constant to simply the transition relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
ImgLinearPropagateConstant(Relation_t *head, int nextStateFlag)
{
int nSize, i, j;
int *supList;
Conjunct_t **conjunctArray;
Conjunct_t *conjunct;
mdd_manager *mgr;
bdd_t **constantCase;
bdd_t *relation, *simpleRelation;
int nConstantCase;
int bOptimize;
int id, cid, index;
int *varType;
int size;

  bOptimize = 0;
  mgr = head->mgr;
  constantCase = head->constantCase;
  varType = head->varType;

  conjunctArray = head->conjunctArray;
  nSize = head->nSize;
  nConstantCase = 0;
  for(index=0, i=0; i<nSize; i++) {
    conjunct = conjunctArray[i];
    if(conjunct == 0)   continue;
    if(conjunct->relation == 0) continue;
    
    if(conjunct->nSize == 1) {
      id = conjunct->supList[0];
      if(varType[id] == 2) {
        if(nextStateFlag) {
          cid = head->range2domain[id]; 
          if(constantCase[cid] == 0) {
            constantCase[cid] = bdd_dup(conjunct->relation);
            if(head->verbosity >= 4)
              fprintf(vis_stdout, "Detect Constant Case %3d(%c)\n", cid, linearVarString[varType[cid]]);
            nConstantCase++;
          }
        }
        continue;
      }
      else {
        if(constantCase[id] == 0) {
          constantCase[id] = bdd_dup(conjunct->relation);
          if(head->verbosity >= 4)
            fprintf(vis_stdout, "Detect Constant Case %3d(%c)\n", id, linearVarString[varType[id]]);
          nConstantCase++;
        }
        continue;
      }
    }
  }

  if(nConstantCase > 0) {
    for(i=0; i<head->nSize; i++) {
      conjunct = conjunctArray[i]; 
      if(conjunct == 0) continue;
      if(conjunct->relation == 0)       continue;
      relation = conjunct->relation;
      size = conjunct->nSize;
      supList = conjunct->supList;

      for(j=0; j<size; j++) {
        id = supList[j];
        if(constantCase[id] == 0)       continue;

        simpleRelation = bdd_cofactor(relation, constantCase[id]); 
        if(bdd_equal(relation, simpleRelation)) {
          bdd_free(simpleRelation);
          continue;
        }
        if(varType[id] == 1) bOptimize++;
        bdd_free(conjunct->relation);
        conjunct->relation = simpleRelation;
        relation = conjunct->relation;
        conjunct->bModified = 1;
        head->bModified = 1;
        head->bRefineVarArray = 1;


        if(head->verbosity >= 2)
          fprintf(vis_stdout, "Constant propagation is applied %3d(%c) to %3d'th relation\n", id, linearVarString[varType[id]],  i);
      }
      ImgLinearConjunctRefine(head, conjunct);
    }
  }

  return(bOptimize);
}

/**Function********************************************************************

  Synopsis    [Remove corresponding current (next) state variables if the next (current state variables are eleminated aftetr clustering]

  Description [Remove corresponding current (next) state variables if the next (current state variables are eleminated aftetr clustering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
ImgLinearOptimizeStateVariables(Relation_t *head, Img_OptimizeType optDir)
{
int *rangeId, *domainId, *existStateVar;
int *domain2range;
int *range2domain;
bdd_t *oneBdd, *varBdd;
VarLife_t **varArray, *var;
array_t *smoothVarBddArray;
Conjunct_t *conjunct;
int i, id;
int bOptimize;
int rangeBound, domainBound;
int nRangeReduced, nDomainReduced;

  if(optDir == Opt_None)        return(0);

  id = 0;
  ImgLinearVariableArrayInit(head);

  bOptimize = 0;
  rangeId = ALLOC(int, head->nRange+1);
  memset(rangeId, 0, sizeof(int)*(head->nRange+1));
  domainId = ALLOC(int, head->nDomain+1);
  memset(domainId, 0, sizeof(int)*(head->nDomain+1));
  existStateVar = ALLOC(int, head->nVar);
  memset(existStateVar, 0, sizeof(int)*head->nVar);
  ImgLinearSetEffectiveNumberOfStateVariable(head, rangeId, domainId, existStateVar);

  rangeBound = (int)((double)head->nInitRange * BACKWARD_REDUCTION_RATE);
  domainBound = (int)((double)head->nInitDomain * FORWARD_REDUCTION_RATE);
  if(head->nEffDomain < domainBound) {
    if(optDir == Opt_Both)      optDir = Opt_NS;
    else if(optDir == Opt_CS)   optDir = Opt_None;
  }
  if(head->nEffRange < rangeBound) {
    if(optDir == Opt_Both)      optDir = Opt_CS;
    else if(optDir == Opt_NS)   optDir = Opt_None;
  }
  if(optDir == Opt_None)        return(0);

  oneBdd = bdd_one(head->mgr);
  domain2range = head->domain2range;
  range2domain = head->range2domain;
  varArray = head->varArray;

  if(optDir == Opt_Both || optDir == Opt_CS) {
    smoothVarBddArray = array_alloc(bdd_t *, 0);
    nDomainReduced = 0;
    for(i=0; i<head->nEffDomain; i++) {
      id = domainId[i];
      if(existStateVar[domain2range[id]])       continue;

      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] : 0;
      if(var) {
        if(head->nEffDomain-nDomainReduced < domainBound)       break;
        if(var->nSize-head->includeCS == 1) {
          varBdd = bdd_get_variable(head->mgr, id);
          array_insert_last(bdd_t *, smoothVarBddArray, varBdd);
          nDomainReduced++;
        }           
      } 
    }

    if(array_n(smoothVarBddArray)) {
      for(i=0; i<head->nSize; i++) {
        conjunct = head->conjunctArray[i];
        if(conjunct->nDomain == 0)      continue;
        if(ImgLinearQuantifyVariablesFromConjunct(
                      head, conjunct, smoothVarBddArray, &bOptimize)) {
          fprintf(vis_stdout, "NOTICE : CS %3d quantified from %d'th relation\n", id, i);
        }
      }
    }
    mdd_array_free(smoothVarBddArray);
  }

  if(optDir == Opt_Both || optDir == Opt_NS) {
    smoothVarBddArray = array_alloc(bdd_t *, 0);
    nRangeReduced = 0;
    for(i=0; i<head->nEffRange; i++) {
      id = rangeId[i];
      if(existStateVar[range2domain[id]])       continue;

      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] :
0;
      if(var) {
        if(head->nEffRange-nRangeReduced < rangeBound)  break;
        if(var->nSize-head->includeNS == 1) {
          varBdd = bdd_get_variable(head->mgr, id);
          array_insert_last(bdd_t *, smoothVarBddArray, varBdd);
          nRangeReduced++;
        }           
      } 
    }

    if(array_n(smoothVarBddArray)) {
      for(i=0; i<head->nSize; i++) {
        conjunct = head->conjunctArray[i];
        if(conjunct->nRange == 0)       continue;
        if(ImgLinearQuantifyVariablesFromConjunct(
                  head, conjunct, smoothVarBddArray, &bOptimize)) {
          fprintf(vis_stdout, "NOTICE : NS %3d quantified from %d'th relation\n", id, i);
        }
      }
    }
    mdd_array_free(smoothVarBddArray);
  }

  bdd_free(oneBdd);
  free(rangeId);
  free(domainId);
  free(existStateVar);

  ImgLinearVariableArrayInit(head);

  return(bOptimize);
}

/**Function********************************************************************

  Synopsis    [Remove intermediate variables after propagating constant.]

  Description [Remove intermediate variables after propagating constant.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearOptimizeInternalVariables(Relation_t *head)
{
bdd_t *oneBdd, *varBdd;
VarLife_t **varArray, *var;
Conjunct_t **conjunctArray;
array_t *smoothVarBddArray;
int *varType;
int i, bModified;

  oneBdd = bdd_one(head->mgr);
  while(1) {
    bModified = 0;
    varArray = head->varArray;
    varType = head->varType;
    conjunctArray = head->conjunctArray;
    for(i=0; i<head->nVarArray; i++) {
      var = head->varArray[i];
      if(varType[var->id] == 2)
        continue;
      if(varType[var->id] == 1 && head->quantifyCS == 0)
        continue;
      if(var->from == var->to) {
        if(conjunctArray[var->from] == 0)       continue;
        varBdd = bdd_get_variable(head->mgr, var->id);
        smoothVarBddArray = array_alloc(bdd_t *, 0);
        array_insert_last(bdd_t *, smoothVarBddArray, varBdd);
        ImgLinearQuantifyVariablesFromConjunct(
                head, head->conjunctArray[var->from], smoothVarBddArray, &bModified);
        mdd_array_free(smoothVarBddArray);
      }
    }
    if(bModified == 0)  break;
    ImgLinearVariableArrayInit(head);
  }
  bdd_free(oneBdd);
  return;
}




/**Function********************************************************************

  Synopsis    [Refine transition relation.]

  Description [Clean up the Relation_t data structure after applying linear arrangement of transition relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearRefineRelation(Relation_t *head)
{
  ImgLinearConjunctArrayRefine(head);
  ImgLinearVariableArrayInit(head);
}

/**Function********************************************************************

  Synopsis    [Order the fine grain transition relation.]

  Description [First find the connected component and apply ordering procedure for each component.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearConjunctOrderMainCC(Relation_t *head, int refineFlag)
{
Conjunct_t **connectedArray;
int i, index;
char baseName[1024];

  ImgLinearPrintMatrix(head);
  ImgLinearExtractNextStateCase(head);
  ImgLinearClusterSameSupportSet(head);
  ImgLinearRefineRelation(head);

  ImgLinearExtractSingletonCase(head);
  ImgLinearRefineRelation(head);

  ImgLinearConnectedComponent(head);

  for(i=0; i<head->nConnectedComponent; i++) {
    connectedArray = head->connectedComponent[i];
    for(index=0; (long)(connectedArray[index])>0; index++);
    head->conjunctArray = connectedArray;
    head->nSize = index;
    head->bModified = 1;
    head->bRefineVarArray = 1;
    qsort(head->conjunctArray, head->nSize, sizeof(Conjunct_t *), 
          ImgLinearCompareConjunctSize);
    ImgLinearVariableArrayInit(head);

    ImgLinearConjunctOrderMain(head, 0);
    fprintf(stdout, "NOTICE : %d'th connected component\n", i);
    head->connectedComponent[i] = head->conjunctArray;
    head->conjunctArray = 0;
  }

  ImgLinearBuildConjunctArrayWithQuotientCC(head);
  
  ImgLinearAddSingletonCase(head);
  ImgLinearAddNextStateCase(head);
  ImgLinearExpandSameSupportSet(head);
  ImgLinearRefineRelation(head);

  ImgLinearRefineRelation(head);
  ImgLinearPrintMatrix(head);

  sprintf(baseName, "profile");
  ImgLinearPrintVariableProfile(head, baseName);
  ImgLinearPrintMatrixFull(head, 2);
}
/**Function********************************************************************

  Synopsis    [Order the each connected component]

  Description [The new Relation_t is created for each connected component]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearBuildConjunctArrayWithQuotientCC(Relation_t *head)
{
Conjunct_t *conjunct, *tConjunct;
Conjunct_t **connectedArray;
Conjunct_t **conjunctArray;
Conjunct_t **newConjunctArray;
st_table *table;
int i, j, k, l;
int index, id, size;
int *varType, *supList;
st_generator *gen;
char baseName[1024];

  if(head->nConnectedComponent == 1) {
    size = 0;
    newConjunctArray = ALLOC(Conjunct_t *, size+1);
    connectedArray = head->connectedComponent[0];
    for(j=0; (long)(connectedArray[j])>0; j++) {
      tConjunct = connectedArray[j];
      newConjunctArray[size++] = tConjunct;
      newConjunctArray = REALLOC(Conjunct_t *, newConjunctArray, size+1);
    }
    free(head->conjunctArray);
    head->nSize = size;
    head->conjunctArray = newConjunctArray;
    head->bModified = 1;
    head->bRefineVarArray = 1;
    ImgLinearRefineRelation(head);
    return;
  }

  head->includeCS = 1;
  head->includeNS = 1;
  varType = head->varType;
  conjunctArray = ALLOC(Conjunct_t *, head->nConnectedComponent);
  for(i=0; i<head->nConnectedComponent; i++) {
    connectedArray = head->connectedComponent[i];

    table = st_init_table(st_ptrcmp, st_ptrhash);
    for(j=0; (long)(connectedArray[j])>0; j++) {
      conjunct = connectedArray[j];
      size = conjunct->nSize;
      supList = conjunct->supList;
      for(k=0; k<size; k++) {
        id = supList[k];
        st_insert(table, (char *)(long)id, (char *)(long)id);
      }
      for(l=0; l<conjunct->nCluster; l++) {
        tConjunct = conjunct->clusterArray[l];
        size = tConjunct->nSize;
        supList = tConjunct->supList;
        for(k=0; k<size; k++) {
          id = supList[k];
          st_insert(table, (char *)(long)id, (char *)(long)id);
        }
      }
    }

    conjunct = ALLOC(Conjunct_t, 1);
    memset(conjunct, 0, sizeof(Conjunct_t));
    conjunct->index = i;
    conjunct->dummy = (long)connectedArray;
    supList = ALLOC(int, table->num_entries);
    index = 0;
    st_foreach_item(table, gen, &id, &id) {
      if(varType[id] == 1)      conjunct->nDomain++;
      else if(varType[id] == 2) conjunct->nRange++;
      else if(varType[id] == 3) conjunct->nQuantify++;
      supList[index++] = id;
    }
    conjunct->supList = supList;
    conjunct->nSize = index;

    conjunctArray[i] = conjunct;
    conjunct->index = i;
    conjunct->relation = bdd_zero(head->mgr);
  }

  head->nSize = head->nConnectedComponent;
  head->conjunctArray = conjunctArray;
  head->bRefineVarArray = 1;
  ImgLinearVariableArrayInit(head);

  sprintf(baseName, "TopCon");
  ImgLinearCAPOInterfaceConjunctNodes(head, baseName);
  ImgLinearCAPOInterfaceConjunctNet(head, baseName);
  ImgLinearCAPOInterfaceConjunctScl(head, baseName);
  ImgLinearCAPOInterfaceConjunctPl(head, baseName);
  ImgLinearCAPOInterfaceAux(head, baseName);
  ImgLinearCAPORun("MetaPlacer", baseName, 0);
  ImgLinearCAPOReadConjunctOrder(head, baseName);

  size = 0;
  newConjunctArray = ALLOC(Conjunct_t *, size+1);
  conjunctArray = head->conjunctArray;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    connectedArray = (Conjunct_t **)conjunct->dummy;
    for(j=0; (long)(connectedArray[j])>0; j++) {
      tConjunct = connectedArray[j];
      newConjunctArray[size++] = tConjunct;
      newConjunctArray = REALLOC(Conjunct_t *, newConjunctArray, size+1);
    }
    ImgLinearConjunctQuit(conjunct);
  }
  free(conjunctArray);
  head->conjunctArray = newConjunctArray;
  head->nSize = size;
  head->bModified = 1;
  head->bRefineVarArray = 1;
  ImgLinearRefineRelation(head);

}


/**Function********************************************************************

  Synopsis    [Find the connected component from fine grain transition relation]

  Description [Find the connected component from fine grain transition relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearConnectedComponent(Relation_t *head)
{
Conjunct_t *conjunct;
Conjunct_t **connectedArray;
int i, j, index, cc_index;
int pre_index, pre_cc_index;

  ImgLinearVariableArrayInit(head);

  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    conjunct->dummy = 0;
  }

  cc_index = 0;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct->dummy) continue;
    cc_index++;
    ImgLinearFindConnectedComponent(head, conjunct, cc_index);
  }
  qsort(head->conjunctArray, head->nSize, sizeof(Conjunct_t *), 
                     ImgLinearCompareConjunctDummy);

  head->nConnectedComponent = 0;
  pre_index = 0;
  pre_cc_index = 1;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct->dummy != pre_cc_index) {
      if((i-pre_index) == 1) { /** singleton case **/
        head->singletonArray = ImgLinearAddConjunctIntoArray(
                head->singletonArray, &(head->nSingletonArray), 
                head->conjunctArray[i-1]);
      }
      else { /** connected component case **/
        if(head->nConnectedComponent)
          head->connectedComponent = REALLOC(Conjunct_t **, head->connectedComponent, head->nConnectedComponent+1);
        else
          head->connectedComponent = ALLOC(Conjunct_t **, head->nConnectedComponent+1);

        connectedArray = ALLOC(Conjunct_t *, (i-pre_index+2));
        head->connectedComponent[head->nConnectedComponent++] = connectedArray;
        for(index=0, j=pre_index; j<i; j++)
          connectedArray[index++] = head->conjunctArray[j];
        connectedArray[index] = 0;
      }

      pre_cc_index = conjunct->dummy;
      pre_index = i;
    }
  }

  if((i-pre_index) == 1) { /** singleton case **/
    head->singletonArray = ImgLinearAddConjunctIntoArray(
                head->singletonArray, &(head->nSingletonArray), 
                head->conjunctArray[i-1]);
  }
  else { /** connected component case **/
    if(head->nConnectedComponent)
      head->connectedComponent = REALLOC(Conjunct_t **,
head->connectedComponent, head->nConnectedComponent+1);

    else
      head->connectedComponent = ALLOC(Conjunct_t **,
head->nConnectedComponent+1);

    connectedArray = ALLOC(Conjunct_t *, (i-pre_index+2));
    head->connectedComponent[head->nConnectedComponent++] = connectedArray;
    for(index=0, j=pre_index; j<i; j++)
      connectedArray[index++] = head->conjunctArray[j];
    connectedArray[index] = 0;
  }
  free(head->conjunctArray);
}

/**Function********************************************************************

  Synopsis    [Find the connected component from fine grain transition relation]

  Description [Find the connected component from fine grain transition relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearFindConnectedComponent(Relation_t *head, 
                                 Conjunct_t *conjunct, 
                                 int cc_index)
{
VarLife_t *var;
int *supList;
int id, size;
int index, i, j;
int *relArr;
Conjunct_t *tConjunct;
  
  if(conjunct->dummy)   return;
  supList = conjunct->supList;
  size = conjunct->nSize;
  conjunct->dummy = cc_index;
  for(i=0; i<size; i++) {
    id = supList[i];
    var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] : 0;
   if(!var)     continue;
    relArr = var->relArr;
    for(j=0; j<var->nSize; j++) {
      index = relArr[j];
      if(index == MAXINT)       continue;
      if(index == MAXINT-1)     continue;
      tConjunct = head->conjunctArray[index];
      if(tConjunct->dummy)      continue;
      ImgLinearFindConnectedComponent(head, tConjunct, cc_index);
    }
  }
}


/**Function********************************************************************

  Synopsis    [Extract the relation contains only one next state varaible]

  Description [Extract the relation contains only one next state varaible]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearExtractSingletonCase(Relation_t *head) 
{
int i, j, k, id, index;
VarLife_t **varArray, *var;
int nSingleton;
int *supList, *varType;
Conjunct_t *conjunct, **newSingletonArray;
int *singletonArray;

  varType = head->varType;
  varArray = head->varArray;
  nSingleton = 0;
  singletonArray = ALLOC(int , nSingleton+1);
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->stateVar == 2)      continue;
    if(var->stateVar == 1) {
      if(var->nSize - head->includeCS > 1)      continue;
    }
    else {
      if(var->nSize > 1)        continue;
    }

    for(j=0; j<var->nSize; j++) {
      if(var->relArr[j] == MAXINT)      continue;
      if(var->relArr[j] == MAXINT-1)    continue;
      singletonArray[nSingleton++] = var->relArr[j];
      singletonArray = REALLOC(int , singletonArray, nSingleton+1);
    }
  }

  for(i=0; i<nSingleton; i++) {
    conjunct = head->conjunctArray[singletonArray[i]];
    conjunct->bSingleton = 1;
  }

  for(i=0; i<nSingleton; i++) {
    conjunct = head->conjunctArray[singletonArray[i]];
    if(conjunct->nRange == conjunct->nSize-conjunct->nRange &&
       conjunct->nSize-conjunct->nRange != 1) {
      conjunct->bSingleton = 0;
      continue;
    }

    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      if(varType[id] == 2)  continue;
      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] : 0;
      if(!var)  continue;

      if(var->stateVar == 1) {
        if(var->nSize - head->includeCS == 1) continue;
      }
      else {
        if(var->nSize == 1)     continue;
      }
      for(k=0; k<var->nSize; k++) {
        index = var->relArr[k];
        if(index == MAXINT)     continue;
        if(index == MAXINT-1)   continue;
        (head->conjunctArray[index])->bSingleton = 0;
      }
    }
  }
  
  newSingletonArray = ALLOC(Conjunct_t *, nSingleton);
  for(index=0, i=0; i<nSingleton; i++) {
    conjunct = head->conjunctArray[singletonArray[i]];
    if(conjunct == 0)   continue;
    if(conjunct->bSingleton) {
      newSingletonArray[index++] = conjunct;
      head->conjunctArray[singletonArray[i]] = 0;
    }
  }
  head->nSingletonArray = index;
  free(singletonArray);
  qsort(newSingletonArray, head->nSingletonArray, 
          sizeof(Conjunct_t *), ImgLinearCompareConjunctRangeMinusDomain);
  head->singletonArray = newSingletonArray;

  if(head->nSingletonArray)     {
    head->bModified = 1;
    head->bRefineVarArray = 1;
  }
}

/**Function********************************************************************

  Synopsis    [Add Conjunct into Cluster Array]

  Description [Add Conjunct into Cluster Array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearAddConjunctIntoClusterArray(Conjunct_t *base, Conjunct_t *con)
{
  if(base->clusterArray == 0) {
    base->clusterArray = ALLOC(Conjunct_t *, base->nCluster+1);
    base->clusterArray[base->nCluster++] = con;
  }
  else {
    base->clusterArray = REALLOC(Conjunct_t *, base->clusterArray, base->nCluster+1);
    base->clusterArray[base->nCluster++] = con;
  }
  base->bClustered = 1;
}



/**Function********************************************************************

  Synopsis    [Extract the relation that contains next state varaibles only]

  Description [Extract the relation that contains next state varaibles only]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearExtractNextStateCase(Relation_t *head) 
{
int i, index, flag;
Conjunct_t *conjunct;
Conjunct_t **nextStateArray;

  index = 0;
  flag = 1;
  nextStateArray = ALLOC(Conjunct_t *, index+1);
  for(index=0, i=head->nSize-1; i>=0; i--) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)   continue;
    if(conjunct->nSize == conjunct->nRange && flag == 0) {
      nextStateArray[index++] = conjunct;
      nextStateArray = REALLOC(Conjunct_t *, nextStateArray, index+1);
      head->conjunctArray[i] = 0;
      head->bModified = 1;
    }
    if(conjunct->nSize != conjunct->nRange) flag = 0;
  }
  head->nextStateArray = nextStateArray;
  head->nNextStateArray = index;

  ImgLinearRefineRelation(head);
}

/**Function********************************************************************

  Synopsis    [Free Relation_t data structure]

  Description [Free Relation_t data structure]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearRelationQuit(Relation_t *head)
{
int i;
Conjunct_t *conjunct;

  if(head->varArray)            ImgLinearVariableArrayQuit(head);
  if(head->rangeVars)           free(head->rangeVars);
  if(head->domainVars)          free(head->domainVars);
  if(head->quantifyVars)        free(head->quantifyVars);
  if(head->varType)             free(head->varType);
  if(head->varArrayMap)         free(head->varArrayMap);

  if(head->singletonArray)      free(head->singletonArray);
  if(head->nextStateArray)      free(head->nextStateArray);

  if(head->constantCase) {
    for(i=0; i<head->nVar; i++)
      if(head->constantCase[i]) bdd_free(head->constantCase[i]);
  }

  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    ImgLinearConjunctQuit(conjunct);
  }
  free(head);
}


/**Function********************************************************************

  Synopsis    [Apply clustering iteratively]

  Description [Apply clustering iteratively]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
ImgLinearClusteringIteratively(Relation_t *head,
                                double affinityLimit,
                                int andExistLimit,
                                int varLimit,
                                int includeZeroGain,
                                int useFailureHistory,
                                Img_OptimizeType optDir,
                                int (*compare_func)(const void *, const void *))
{
int bddLimit, gainLimit;
int clusterLimit;
int bOptimize;

  if(head->nSize < 2)   return(0);

  bOptimize = 0;
  bddLimit = head->bddLimit;
  gainLimit = 50;

  while(1) {
    if(head->nSize < 50)clusterLimit = head->nSize/2;
    else                clusterLimit = head->nSize/3+1;
    if(clusterLimit > 50)       clusterLimit = 50;
    /**
    clusterLimit = head->nSize/5;
    if(clusterLimit < 1)        clusterLimit = 3;
    **/

    ImgLinearClusteringByConstraints(head, includeZeroGain, varLimit, clusterLimit, 
                                      gainLimit, affinityLimit, andExistLimit,
                                      bddLimit,  useFailureHistory, compare_func);
    if(head->bModified) {
      ImgLinearRefineRelation(head);
      bOptimize |= ImgLinearOptimizeAll(head, optDir, 0);
    }
    else break;
  }
  return(bOptimize);
}
/**Function********************************************************************

  Synopsis    [Apply clustering with given priority function]

  Description [Apply clustering with given priority function]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearClusteringByConstraints(Relation_t *head, 
                                   int includeZeroGain,
                                   int varLimit,
                                   int clusterLimit,
                                   int gainLimit,
                                   double affinityLimit,
                                   int andExistLimit,
                                   int bddLimit, 
                                   int useFailureHistory,
                                   int (*compare_func)(const void *, const void *))
{
int size, begin, end;
int **nDead, **nVar, **nFailure;
int *dirtyBit;
int i, j, k, l, index;
int start, preGain;
int nClusterArray;
VarLife_t **varArray, *var;
Cluster_t **clusterArray, *clu;
Conjunct_t *conjunct;
bdd_t *clusteredRelation;
int fail_flag;
int from, to, splitable;

  varArray = head->varArray;
  size = head->nSize;

  nDead = ALLOC(int *, size);
  nVar = ALLOC(int *, size);
  nFailure = 0;
  if(useFailureHistory)
    nFailure = ALLOC(int *, size);
  for(i=0; i<size; i++) {
    nDead[i] = ALLOC(int, size);
    nVar[i] = ALLOC(int, size);
    if(useFailureHistory)
      nFailure[i] = ALLOC(int, size);
    memset(nDead[i], 0, sizeof(int)*size);
    memset(nVar[i], 0, sizeof(int)*size);
    if(useFailureHistory)
      memset(nFailure[i], 0, sizeof(int)*size);
  }

  index = 0;
  for(l=0; l<head->nVarArray; l++) {
    var = varArray[l];
    begin = var->from;
    end = var->to;
    if(var->stateVar == 1)      begin = -1;
    else if(var->stateVar == 2) end = size;

    for(i=0; i<=begin; i++)
      for(j=end; j<size; j++)
        nDead[i][j]++;

    for(i=0; i<=var->effTo; i++) {
      if(i > var->effFrom) {
        for(k=0; k<var->nSize; k++) {
          index = var->relArr[k];
          if(index == MAXINT)   continue;
          if(index == MAXINT-1) continue;
          if(index >= i)        break;
        }
        if(index < i)   start = var->effTo;
        else            start = index;
      }
      else {
        start = var->effFrom;
      }

      for(j=start; j<size; j++)
        nVar[i][j]++;
    }
  }

  for(i=0; i<size; i++) {
    end = (size-1) < i+clusterLimit ? size-1 : i+clusterLimit;
    if(i==end)  continue;
    if(nDead[i][end] == 0 && !includeZeroGain)  continue;

    preGain = -1;
    for(j=end; j>=i; j--) {
      if(varLimit < nVar[i][j]-nDead[i][j])     continue;
      if(gainLimit < nDead[i][j])               continue; 


      if(preGain != -1) {
        if(nDead[i][j] < preGain && nDead[i][j] >= 0) {
          to = j+1;
          for(from=i; from < to; from++) {
            if(nDead[from+1][to] != nDead[from][to])    break;
          }
          if(from != i) continue;

          splitable = 0;
          for(k=from; k<to; k++) {
            if(nDead[from][to] == (nDead[from][k] + nDead[k+1][to])) {
              splitable = 1;
              break;
            }
          }
          if(!splitable)
            ImgLinearInsertClusterCandidate(head, from, to, 
                             nDead[from][to], nVar[from][to], affinityLimit);
        }
      }

      if(nDead[i][j] == 0)      {
        if(includeZeroGain)
          ImgLinearInsertClusterCandidate(head, i, i+1, 
                             nDead[i][i+1], nVar[i][i+1], affinityLimit);
        break;
      }

      preGain = nDead[i][j];

    }
  }
  
  if(head->nClusterArray == 0)  return;
  qsort(head->clusterArray, head->nClusterArray, sizeof(Cluster_t *),
compare_func);

  dirtyBit = ALLOC(int, size);
  memset(dirtyBit, 0, sizeof(int)*size);

  clusterArray = head->clusterArray;
  nClusterArray = head->nClusterArray;
  for(i=0; i<nClusterArray; i++) {
    clu = clusterArray[i];
    if(useFailureHistory) {
      if(nFailure[clu->from][clu->to] == 1)     continue;
    }
    fail_flag = 0;
    for(j=clu->from; j<=clu->to; j++) {
      if(dirtyBit[j] == 1)      {
          fail_flag = 1;
        continue;
      }
    }
    if(fail_flag)       continue;

    clusteredRelation = ImgLinearClusteringSmooth(head, clu, 
                           nFailure, andExistLimit, bddLimit);

    conjunct = 0;
    if(clusteredRelation) {
      for(j=clu->from; j<=clu->to; j++) {
        conjunct = head->conjunctArray[j];
        if(conjunct->relation)  bdd_free(conjunct->relation);
        conjunct->relation = 0;
      }
      conjunct->relation = clusteredRelation;
      conjunct->bModified = 1;
      head->bModified = 1;
      for(j=clu->from; j<=clu->to; j++) dirtyBit[j] = 1;

      if(head->verbosity >= 5)
        fprintf(stdout, "\tClustering Success : %4d -%4d G(%3d) V(%3d) A(%3d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity);
    }
    fflush(stdout);
  }

  for(i=0; i<nClusterArray; i++)
    free(clusterArray[i]);
  free(clusterArray);
  head->clusterArray = 0;
  head->nClusterArray = 0;

  for(i=0; i<head->nSize; i++) {
    free(nDead[i]);
    free(nVar[i]);
    if(useFailureHistory)
      free(nFailure[i]);
  }
  free(nDead);
  free(nVar);
  if(useFailureHistory)
    free(nFailure);

  return;
}
/**Function********************************************************************

  Synopsis    [Add candidates for clustering]

  Description [Add candidates for clustering, each condidate has pair of relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearInsertClusterCandidate(Relation_t *head, 
                                 int from, int to, 
                                 int nDead, int nVar,
                                 double affinityLimit)
{
Conjunct_t *conjunct;
Cluster_t *clu;
int *varType, *supList;
int i, j, id, size;
st_table *table;
double affinity, tAffinity;
int preSize, postSize, curSize, overlap;

  varType = head->varType;

  conjunct = head->conjunctArray[from];
  if(conjunct->relation == 0)   {
    return;
  }

  supList = conjunct->supList;
  size = conjunct->nSize;
  table = st_init_table(st_numcmp, st_numhash);
  for(i=0; i<size; i++) {
    id = supList[i];
    if(varType[id] == 2)        continue;
    st_insert(table, (char *)(long)id, (char *)(long)id);
  }

  tAffinity = 0.0;
  for(i=from+1; i<=to; i++) {
    preSize = table->num_entries;

    conjunct = head->conjunctArray[i];
    if(conjunct->relation == 0) continue;
    supList = conjunct->supList;
    size = conjunct->nSize;
    curSize = 0;
    for(j=0; j<size; j++) {
      id = supList[j];

      if(varType[id] == 2)      continue;
      curSize++;
      st_insert(table, (char *)(long)id, (char *)(long)id);
    }

    postSize = table->num_entries;

    overlap = curSize - (postSize-preSize);

    if(curSize > preSize)       affinity = (double)overlap/(double)preSize;
    else                        affinity = (double)overlap/(double)curSize;

    /**
    if(affinity < affinityLimit)        {
      st_free_table(table);
      return;
    }
    **/
    tAffinity += affinity;
  }
  st_free_table(table);

  tAffinity /= (double)(to-from);
  clu = ALLOC(Cluster_t, 1);
  clu->from = from;
  clu->to = to;
  clu->nVar = nVar;
  clu->nDead = nDead;
  clu->nAffinity = (int)(tAffinity * 100.0);

  head->clusterArray = REALLOC(Cluster_t *, head->clusterArray, head->nClusterArray+1);
  head->clusterArray[head->nClusterArray++] = clu;
  if(head->verbosity >= 5) {
    fprintf(stdout, "Candidate Cluster : %4d-%4d G(%3d) V(%3d) A(%3d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity);
    fflush(stdout);
  }

}

/**Function********************************************************************

  Synopsis    [Apply clustering while quantifying the variables that are isolated]

  Description [Apply clustering while quantifying the variables that are isolated]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static bdd_t *
ImgLinearClusteringSmooth(Relation_t *head, 
                           Cluster_t *clu, 
                           int **failureHistory, 
                           int andExistLimit,
                           int bddLimit)
{
int *varType, *supList;
array_t *smoothVarBddArray, *smoothArray;
Conjunct_t *conjunct;
bdd_t *relation, *totalRelation;
bdd_t *varBdd, *tempRelation;
int i, j, k, tempSize, failFlag;
int id, tid;
st_table *deadTable;
VarLife_t *var;

  varType = head->varType;

  smoothVarBddArray = array_alloc(array_t *, 0);
  for(i=clu->from; i<=clu->to; i++) {
    smoothArray = array_alloc(bdd_t *, 0);
    array_insert_last(array_t *, smoothVarBddArray, smoothArray);
  }

  deadTable = st_init_table(st_numcmp, st_numhash);
  for(i=clu->from; i<=clu->to; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)           continue;
    if(conjunct->relation == 0) continue;
    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      if(varType[id] == 1 || varType[id] == 2)  continue;

      if(st_lookup(deadTable, (char *)(long)id, &tid))  continue;

      var = head->varArray[head->varArrayMap[id]];

      if(clu->from <= var->from && var->to <= clu->to) {
        st_insert(deadTable, (char *)(long)id, (char *)(long)id);
        smoothArray = array_fetch(array_t *, smoothVarBddArray,
var->to-clu->from);
        varBdd = bdd_get_variable(head->mgr, var->id);
        array_insert_last(bdd_t *, smoothArray, varBdd);
      }
    }
  }
  st_free_table(deadTable);


  totalRelation = bdd_one(head->mgr);
  failFlag = 0;
  for(i=clu->from; i<=clu->to; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)           continue;
    if(conjunct->relation == 0) continue;
    relation = conjunct->relation;
    smoothArray = array_fetch(array_t *, smoothVarBddArray, i-clu->from);

    tempRelation = bdd_and_smooth_with_limit(totalRelation, relation, 
                                        smoothArray, andExistLimit);
    if(tempRelation)    tempSize = bdd_size(tempRelation);
    else                tempSize = MAXINT;

    if(tempSize > bddLimit) {
      bdd_free(totalRelation);
      if(tempRelation)  bdd_free(tempRelation);
      totalRelation = 0;
      
      if(failureHistory) {
        for(j=0; j<=clu->from; j++) 
          for(k=i; k<head->nSize; k++)
            failureHistory[j][k] = 1;
      }

      if(head->verbosity >= 3)
        fprintf(stdout, "Clustering Failure : %4d-%4d G(%3d) V(%3d) A(%3d) At %3d S(%d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity, i, tempSize);
      break;
    }

    bdd_free(totalRelation);
    totalRelation = tempRelation;
  }
  ImgLinearFreeSmoothArray(smoothVarBddArray);

  if(failFlag)  return(0);
  else          return(totalRelation);
}


/**Function********************************************************************

  Synopsis    [ Apply clustering with priority queue]

  Description [ Apply clustering with priority queue]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearClusterUsingHeap(Relation_t *head,
                           double affinityLimit,
                           int andExistLimit,
                           int varLimit,
                           Img_OptimizeType optDir,
                           int rangeFlag,
                           int (*compare_func)(const void *, const void *))
{
Cluster_t *clu;
int j;
Conjunct_t *conjunct;
bdd_t *clusteredRelation;
Heap_t *heap;
int bOptimize;
long dummy;

  bOptimize = 0;
  ImgLinearBuildInitialCandidate(head, affinityLimit, varLimit, rangeFlag, compare_func);
  /** need to consider statevariable optimization **/
  heap = head->clusterHeap;
  while(Heap_HeapExtractMin(heap, &clu, &dummy)) {
    if(clu->flag) {
      free(clu);
      continue;
    }
    if(clu->to >= head->nSize) {
      free(clu);
      continue;
    }

    clusteredRelation = ImgLinearClusteringPairSmooth(head, clu, 
                           0, andExistLimit, head->bddLimit);
    if(clusteredRelation) {
      if(head->verbosity >= 5)
        fprintf(stdout, "\tClustering Success : %4d -%4d G(%3d) V(%3d) A(%3d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity);
      fflush(stdout);

      for(j=clu->from+1; j<=clu->to; j++) {
        conjunct = head->conjunctArray[j];
        if(conjunct == 0)       continue;
        if(conjunct->relation == 0)     continue;
        bdd_free(conjunct->relation);
        conjunct->relation = 0;
      }
      conjunct = head->conjunctArray[clu->from];
      if(conjunct->relation)
        bdd_free(conjunct->relation);
      conjunct->relation = clusteredRelation;
      conjunct->bModified = 1;
      ImgLinearConjunctRefine(head, conjunct);
      head->bModified = 1;
      head->bRefineVarArray = 1;

      Heap_HeapApplyForEachElement(heap, linearCheckRange);
      /**
      for(i=0; i<heap->nitems; i++) {
        tclu = (Cluster_t *)(heap->slots[i].item);
        if(tclu->from <= clu->from && clu->from <= tclu->to)
          tclu->flag = 1;
        if(tclu->from <= clu->to && clu->to <= tclu->to)
          tclu->flag = 1;
      }
      **/

      ImgLinearInsertPairClusterCandidate(head, clu->from, affinityLimit, varLimit, rangeFlag);
      ImgLinearInsertPairClusterCandidate(head, clu->from-1, affinityLimit, varLimit, rangeFlag);
    }
    if(clu->nDead && clusteredRelation) {
      ImgLinearVariableArrayInit(head);
      bOptimize |= ImgLinearOptimizeAll(head, optDir, 0);
    }
    free(clu);
  }
  Heap_HeapFree(heap);
  head->clusterHeap = 0;

  if(head->bModified) {
    if(head->verbosity >= 5)
      ImgLinearPrintMatrix(head);

    bOptimize |= ImgLinearOptimizeAll(head, optDir, 0);
    ImgLinearRefineRelation(head);

    if(head->verbosity >= 5)
      ImgLinearPrintMatrix(head);
  }
  return(bOptimize);
}

/**Function********************************************************************

  Synopsis    [compare function for checking range of cluster]

  Description [compare function for checking range of cluster]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
linearCheckRange(const void *tc)
{
Cluster_t *tclu;

  tclu = (Cluster_t *)tc;
  if(tclu->from <= __clu->from && __clu->from <= tclu->to)
    tclu->flag = 1;
  if(tclu->from <= __clu->to && __clu->to <= tclu->to)
    tclu->flag = 1;

  return(1);
}

/**Function********************************************************************

  Synopsis    [Clustering pair of transition relation]

  Description [Clustering pair of transition relation]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static bdd_t *
ImgLinearClusteringPairSmooth(Relation_t *head, 
                           Cluster_t *clu, 
                           int **failureHistory, 
                           int andExistLimit,
                           int bddLimit)
{
int *varType, *supList;
array_t *smoothArray;
Conjunct_t *conjunct;
bdd_t *totalRelation;
bdd_t *fromRelation, *toRelation;
bdd_t *varBdd;
int i, j, k, tempSize;
int id, tid, effTo;
st_table *deadTable;
VarLife_t *var;

  varType = head->varType;

  smoothArray = array_alloc(bdd_t *, 0);

  for(effTo = clu->to+1; effTo<head->nSize; effTo++) {
    conjunct = head->conjunctArray[effTo];
    if(conjunct && conjunct->relation)  break;
  }
  effTo--;

  deadTable = st_init_table(st_numcmp, st_numhash);
  for(i=clu->from; i<=clu->to; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)           continue;
    if(conjunct->relation == 0) continue;
    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      if(varType[id] == 1 || varType[id] == 2)  continue;

      if(st_lookup(deadTable, (char *)(long)id, &tid))  continue;

      var = head->varArray[head->varArrayMap[id]];

      if(clu->from <= var->from && var->to <= effTo) {
        st_insert(deadTable, (char *)(long)id, (char *)(long)id);
        varBdd = bdd_get_variable(head->mgr, var->id);
        array_insert_last(bdd_t *, smoothArray, varBdd);
      }
    }
  }
  st_free_table(deadTable);

  conjunct = head->conjunctArray[clu->from];
  fromRelation = conjunct->relation;
  toRelation = 0;
  for(i=clu->from+1; i<=clu->to; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)           continue;
    if(conjunct->relation == 0) continue;
    toRelation = conjunct->relation;
    break;
  }
  if(toRelation == 0) {
    mdd_array_free(smoothArray);
    return(0);
  }
  if(fromRelation == 0 && toRelation == 0)      return(0);
  if(fromRelation == 0) {
    totalRelation = bdd_dup(toRelation);
  }
  else if(toRelation == 0) {
    totalRelation = bdd_dup(fromRelation);
  }
  else {
    totalRelation = bdd_and_smooth_with_limit(fromRelation, toRelation, 
                                                smoothArray, andExistLimit);
  }
  if(totalRelation)     tempSize = bdd_size(totalRelation);
  else                  tempSize = MAXINT;

  if(tempSize > bddLimit) {
    if(totalRelation)   bdd_free(totalRelation);
    totalRelation = 0;
    if(failureHistory) {
      for(j=0; j<=clu->from; j++) 
        for(k=i; k<head->nSize; k++)
          failureHistory[j][k] = 1;
    }
    if(head->verbosity >= 3)
      fprintf(stdout, "Clustering Failure : %4d-%4d G(%3d) V(%3d) A(%3d) At %3d S(%d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity, i, tempSize);
  }
  mdd_array_free(smoothArray);

  return(totalRelation);
}



/**Function********************************************************************

  Synopsis    [Build data structure for clustering]

  Description [Build data structure for clustering]

  SideEffects []

  SeeAlso     []

******************************************************************************/

static void 
ImgLinearBuildInitialCandidate(Relation_t *head, 
                                double affinityLimit,
                                int varLimit, 
                                int rangeFlag,
                                int (*compare_func)(const void *, const void *))
{
int size, i;

  head->clusterHeap = Heap_HeapInitCompare(head->nSize, compare_func);
  size = head->nSize;
  for(i=0; i<size; i++) {
    ImgLinearInsertPairClusterCandidate(head, i, affinityLimit, varLimit, rangeFlag);
  }
  
  return;
}
/**Function********************************************************************

  Synopsis    [Insert initial candidate set]

  Description [Insert initial candidate set]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearInsertPairClusterCandidate(Relation_t *head, 
                                     int from, 
                                     double affinityLimit,
                                     int varLimit,
                                     int rangeFlag)
{
Conjunct_t *conjunct, *fromC, *toC;
Cluster_t *clu;
int *varType, *supList;
st_table *table;
double affinity;
int preSize, postSize, curSize, overlap;
int i, j, id, tid, size, nDead;
int to, effTo;
VarLife_t *var;

  if(from < 0)  return;
  if(from == head->nSize-1)     return;
 
  conjunct = head->conjunctArray[from];
  if(conjunct == 0 || conjunct->relation == 0) {
    for(; from>=0; from--) {
      conjunct = head->conjunctArray[from];
      if(conjunct == 0) continue;
      if(conjunct->relation == 0)       continue;
      break;
    }
  }
  if(from < 0)  return;

  to = -1;
  for(i=from+1; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    if(!conjunct)       continue;
    if(conjunct->relation == 0) continue;
    to = i;
    break;
  }
  if(to == -1)  return;
  for(effTo = to+1; effTo<head->nSize; effTo++) {
    conjunct = head->conjunctArray[effTo];
    if(conjunct && conjunct->relation)  break;
  }
  effTo--;


  varType = head->varType;

  fromC = head->conjunctArray[from];
  toC = head->conjunctArray[to];

  if(rangeFlag && 
     (fromC->nSize == fromC->nRange || toC->nSize == toC->nRange))
      return;

  if(fromC->nSize == fromC->nRange && toC->nSize != toC->nRange)
    return;
  if(fromC->nSize != fromC->nRange && toC->nSize == toC->nRange)
    return;

  nDead = 0;
  supList = fromC->supList;
  size = fromC->nSize;
  table = st_init_table(st_numcmp, st_numhash);
  for(i=0; i<size; i++) {
    id = supList[i];
    if(varType[id] == 2)        continue;
    preSize++;
    st_insert(table, (char *)(long)id, (char *)(long)id);
    var = head->varArray[head->varArrayMap[id]];
    if(from <= var->from && var->to <= effTo)   nDead++;
  }

  preSize = table->num_entries;
  supList = toC->supList;
  size = toC->nSize;
  curSize = 0;
  for(j=0; j<size; j++) {
    id = supList[j];
    if(varType[id] == 2)        continue;
    curSize++;
    if(st_lookup(table, (char *)(long)id, &tid))        continue;
    st_insert(table, (char *)(long)id, (char *)(long)id);
    var = head->varArray[head->varArrayMap[id]];
    if(from <= var->from && var->to <= effTo)   nDead++;
  }

  postSize = table->num_entries;
  overlap = curSize - (postSize-preSize);
  if(overlap == 0)      affinity = 0.0;
  else {
    if(curSize > preSize)affinity = (double)overlap/(double)preSize;
    else                 affinity = (double)overlap/(double)curSize;
  }
  st_free_table(table);

  if(affinity < affinityLimit)  return;

  if(affinity == 0.0 && postSize > 10 && 
          (fromC->bSingleton || toC->bSingleton))       return;
  if(postSize-nDead > varLimit) return;

  clu = ALLOC(Cluster_t, 1);
  memset(clu, 0, sizeof(Cluster_t));
  clu->from = from;
  clu->to = to;
  clu->nVar = postSize;
  clu->nDead = nDead;
  clu->nAffinity = (int)(affinity * 100.0);

  Heap_HeapInsertCompare(head->clusterHeap, (void *)clu, (long)clu);
  if(head->verbosity >= 5) {
    fprintf(stdout, "Candidate Cluster : %4d -%4d G(%3d) V(%3d) A(%3d)\n",
              clu->from, clu->to, clu->nDead, clu->nVar, clu->nAffinity);
    fflush(stdout);
  }
}

/**Function********************************************************************

  Synopsis    [Print information of debug information]

  Description [Print information of debug information]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearPrintDebugInfo(Relation_t *head)
{
int i, j, id;
Conjunct_t *conjunct;
int *supList;
array_t *smoothVarBddArray;
array_t *smoothArray;
bdd_t *varBdd;
int idPerLine;

  idPerLine = 12;

  fprintf(vis_stdout, "-----------------------------------------------------\n");
  fprintf(vis_stdout, "     Debug Information for Transition Relations\n");
  fprintf(vis_stdout, "-----------------------------------------------------\n");
  fprintf(vis_stdout, "List of Quantify Variables---------------------------\n");
  for(i=0; i<head->nQuantify; i++) {
    if(i!=0 && i%idPerLine == 0) fprintf(vis_stdout, "\n");
    fprintf(vis_stdout, "%3d ", head->quantifyVars[i]);
  }
  fprintf(vis_stdout, "\n");

  fprintf(vis_stdout, "List of Domain Variables-----------------------------\n");
  for(i=0; i<head->nDomain; i++) {
    if(i!=0 && i%idPerLine == 0) fprintf(vis_stdout, "\n");
    fprintf(vis_stdout, "%3d ", head->domainVars[i]);
  }
  fprintf(vis_stdout, "\n");

  fprintf(vis_stdout, "List of Range Variables------------------------------\n");
  for(i=0; i<head->nRange; i++) {
    if(i!=0 && i%idPerLine == 0) fprintf(vis_stdout, "\n");
    fprintf(vis_stdout, "%3d ", head->rangeVars[i]);
  }
  fprintf(vis_stdout, "\n");

  fprintf(vis_stdout, "Varibles in Each Transition Relation-----------------\n");
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    supList = conjunct->supList;
    fprintf(vis_stdout, "%3d'th : ", i);
    for(j=0; j<conjunct->nSize; j++) {
      if(j!=0 && j%idPerLine == 0) fprintf(vis_stdout, "\n         ");
      fprintf(vis_stdout, "%3d ", supList[j]);
    }
    fprintf(vis_stdout, "\n");
  }

  smoothVarBddArray = ImgLinearMakeSmoothVarBdd(head, 0);
  fprintf(vis_stdout, "Quantified Schedule----------------------------------\n");
  for(i=0; i<=head->nSize; i++) {
    fprintf(vis_stdout, "%3d'th : ", i);
    smoothArray = array_fetch(array_t *, smoothVarBddArray, i);
    for(j=0; j<array_n(smoothArray); j++) {
      varBdd = array_fetch(bdd_t *, smoothArray, j);
      id = bdd_top_var_id(varBdd);
      if(j!=0 && j%idPerLine == 0) fprintf(vis_stdout, "\n         ");
      fprintf(vis_stdout, "%3d ", id);
    }
    fprintf(vis_stdout, "\n");
  }
  ImgLinearFreeSmoothArray(smoothVarBddArray);
}

/**Function********************************************************************

  Synopsis    [ Main function of linear arrangement]

  Description [ Main function of linear arrangement]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearConjunctOrderMain(Relation_t *head, int bRefineConjunctOrder)
{
double aal, atl;

/**
  head->includeCS = 0;
  ImgLinearConjunctionOrder(head, "FirstCon", bRefineConjunctOrder);
  ImgLinearComputeLifeTime(head, &aal, &atl);
  ImgLinearPrintMatrixFull(head, 0);
  head->includeCS = 1;
  tempConjunctArray = ALLOC(Conjunct_t *, head->nSize+1);
  for(i=0; i<head->nSize; i++) 
    tempConjunctArray[i] = head->conjunctArray[i];
  tempAal = aal;
  tempAtl = atl;
  fprintf(stdout, "NOTICE : aal %.3f atl %.3f\n", aal, atl);
  ImgLinearPrintMatrix(head);
  **/


  ImgLinearConjunctionOrder(head, "SecondCon", bRefineConjunctOrder);
  ImgLinearComputeLifeTime(head, &aal, &atl);
  ImgLinearPrintMatrixFull(head, 1);
  fprintf(stdout, "NOTICE : aal %.3f atl %.3f\n", aal, atl);
  ImgLinearPrintMatrix(head);

  /**
  if(tempAal < aal) {
    if( (aal-tempAal) > (tempAtl-atl)*2.0 ) {
      free(head->conjunctArray);
      head->conjunctArray = tempConjunctArray;
      head->bModified = 1;
      head->bRefineVarArray = 1;
      ImgLinearRefineRelation(head);
      fprintf(stdout, "includeCS = 0 is taken\n");
    }
    else {
      fprintf(stdout, "includeCS = 1 is taken\n");
    }
  }
  else {
    fprintf(stdout, "includeCS = 1 is taken\n");
  }
  **/
}

/**Function********************************************************************

  Synopsis    [Generate linear arrangement with CAPO]

  Description [Generate linear arrangement with CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearConjunctionOrder(Relation_t *head, char *baseName, int refineFlag)
{
Conjunct_t *conjunct;
int i, j;


  if(head->nSize < 2)   return;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    conjunct->dummy = 0;
    for(j=0; j<conjunct->nSize; j++)
      conjunct->dummy += conjunct->supList[j];
  }
  qsort(head->conjunctArray, head->nSize, sizeof(Conjunct_t *), 
          ImgLinearCompareConjunctSize);
  head->bRefineVarArray = 1;
  ImgLinearRefineRelation(head);

  ImgLinearCAPOInterfaceConjunctNodes(head, baseName);
  ImgLinearCAPOInterfaceConjunctNet(head, baseName);
  ImgLinearCAPOInterfaceConjunctScl(head, baseName);
  ImgLinearCAPOInterfaceConjunctPl(head, baseName);
  ImgLinearCAPOInterfaceAux(head, baseName);
  ImgLinearCAPORun("MetaPlacer", baseName, 0);
  ImgLinearCAPOReadConjunctOrder(head, baseName);
}


/**Function********************************************************************

  Synopsis    [Make interface files for CAPO]

  Description [Make interface files for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceConjunctNodes(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;
int i;

  sprintf(filename, "%s.nodes", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA nodes 1.0\n");
  if(head->includeNS) {
    if(head->includeCS) {
      fprintf(fout, "NumNodes : %d\n", head->nSize+2);
      fprintf(fout, "NumTerminals : 2\n");
    }
    else {
      fprintf(fout, "NumNodes : %d\n", head->nSize+1);
      fprintf(fout, "NumTerminals : 1\n");
    }
  }
  else if(head->includeCS) {
    fprintf(fout, "NumNodes : %d\n", head->nSize+1);
    fprintf(fout, "NumTerminals : 1\n");
  }
  else {
    fprintf(fout, "NumNodes : %d\n", head->nSize);
    fprintf(fout, "NumTerminals : 0\n");
  }
  
  for(i=0; i<head->nSize; i++)
    fprintf(fout, "C%d 1 1\n", i);

  if(head->includeCS) 
    fprintf(fout, "C%d 1 1 terminal\n", MAXINT-1);

  if(head->includeNS)
    fprintf(fout, "C%d 1 1 terminal\n", MAXINT);

  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Make interface files for CAPO]

  Description [Make interface files for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceConjunctNet(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;
VarLife_t **varArray, *var;
int i, j, nPin;

  varArray = head->varArray;
  sprintf(filename, "%s.nets", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA nets 1.0\n");
  fprintf(fout, "#NumNets : %d\n", head->nVarArray);

  qsort(head->varArray, head->nVarArray, sizeof(VarLife_t *), ImgLinearCompareVarId);
  nPin = 0;
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->nSize == 1) nPin += 2;
    else                nPin += var->nSize;
  }
  fprintf(fout, "NumPins : %d\n", nPin);

  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->nSize == 1)
      fprintf(fout, "NetDegree : %d S%d\n", var->nSize+1, var->id);
    else
      fprintf(fout, "NetDegree : %d S%d\n", var->nSize, var->id);

    for(j=0; j<var->nSize; j++)
      fprintf(fout, "C%d B\n", var->relArr[j]);

    if(var->nSize == 1) 
      fprintf(fout, "C%d B\n", var->relArr[0]);
  }
  fclose(fout);
}


/**Function********************************************************************

  Synopsis    [Make interface files for CAPO]

  Description [Make interface files for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceConjunctScl(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;

  sprintf(filename, "%s.scl", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA scl 1.0\n");
  fprintf(fout, "Numrows : 1\n");
  fprintf(fout, "CoreRow Horizontal\n");
  fprintf(fout, " Coordinate   : 1\n");
  fprintf(fout, " Height       : 1\n");
  fprintf(fout, " Sitewidth    : 1\n");
  fprintf(fout, " Sitespacing  : 1\n");
  fprintf(fout, " Siteorient   : N\n");
  fprintf(fout, " Sitesymmetry : Y\n");
  fprintf(fout, " SubrowOrigin : 0\n");
  fprintf(fout, " Numsites     : %d\n", head->nSize*2+2);
  fprintf(fout, "End\n");
  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Make interface files for CAPO]

  Description [Make interface files for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceConjunctPl(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;
int i;

  sprintf(filename, "%s.pl", baseName);
  fout = fopen(filename, "w");

  fprintf(fout, "UCLA pl 1.0\n");
  for(i=0; i<head->nSize; i++)
    fprintf(fout, "C%d %d 1\n", i, (i+2)*2+1);

  if(head->includeCS)
    fprintf(fout, "C%d 0 1 / N / FIXED\n", MAXINT-1);

  if(head->includeNS)
    fprintf(fout, "C%d %d 1 / N / FIXED\n", MAXINT, (head->nSize+2)*2+1);

  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Make interface files for CAPO]

  Description [Make interface files for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceAux(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;

  sprintf(filename, "%s.aux", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "RowBasedPlacement : ");
  fprintf(fout, "%s.nodes %s.nets %s.pl %s.scl\n", 
                baseName, baseName, baseName, baseName);
  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Run batch job of CAPO]

  Description [Run batch job of CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCAPORun(char *capoExe, char *baseName, int brief)
{
char logFile[1024];
char capoOption[1024];
char command[1024];
char cpCommand[1024];
FILE *fout;
int cmdStatus;

  fout = fopen("seeds.in", "w");
  fprintf(fout, "0\n");
  fprintf(fout, "460427264\n");
  fclose(fout);


  if(brief)     
    sprintf(capoOption, "-replaceSmallBlocks Never -noRowIroning -save -saveXorder");
  else          
    sprintf(capoOption, "-save -saveXorder -clust CutOpt");

  sprintf(logFile, "%s.log", baseName);
  sprintf(command, "%s -f %s.aux %s > %s", 
            capoExe, baseName, capoOption, logFile);
  cmdStatus = system(command);
  sprintf(cpCommand, "cp left2right.ord %s.ord", baseName);
  cmdStatus |= system(cpCommand);

  unlink("seeds.out");
  unlink("left2right.ord");
  return (cmdStatus == 0);
}


/**Function********************************************************************

  Synopsis    [Read result of CAPO]

  Description [Read result of CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOReadConjunctOrder(Relation_t *head, char *baseName)
{
char ordFile[1024];
char line[1024];
int index, id;
char *next;
FILE *fin;
Conjunct_t *conjunct;

  sprintf(ordFile, "%s.ord", baseName);
  if(!(fin = fopen(ordFile, "r"))) {
    fprintf(stdout, "Can't open order file %s\n", ordFile);
    exit(0);
  }
  index = 0;
  while(fgets(line, 1024, fin)){
    next = strchr(line, 'C');
    next++;
    sscanf(next, "%d", &id);
    if(id == MAXINT) continue;
    if(id == MAXINT-1) continue;
    conjunct = head->conjunctArray[id];
    conjunct->index = index;
    index++;
  }
  fclose(fin);

  qsort(head->conjunctArray, head->nSize, sizeof(Conjunct_t *), ImgLinearCompareConjunctIndex);

  head->bModified = 1;
  head->bRefineVarArray = 1;
  ImgLinearRefineRelation(head);
}

/**Function********************************************************************

  Synopsis    [Make interface for variable ordering]

  Description [Make interface for variable ordering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearVariableOrder(Relation_t *head, char *baseName, int includeNS)
{
  ImgLinearCAPOInterfaceVariableNodes(head, baseName, includeNS);
  ImgLinearCAPOInterfaceVariableNet(head, baseName, includeNS);
  ImgLinearCAPOInterfaceVariableScl(head, baseName);
  ImgLinearCAPOInterfaceVariablePl(head, baseName, includeNS);
  ImgLinearCAPOInterfaceAux(head, baseName);
  ImgLinearCAPORun("MetaPlacer", baseName, 0);
  ImgLinearCAPOReadVariableOrder(head, baseName, includeNS);
}

/**Function********************************************************************

  Synopsis    [Make interface for CAPO]

  Description [Make interface for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearCAPOInterfaceVariableNodes(Relation_t *head, char *baseName, int includeNS)
{
int i, size;
VarLife_t **varArray, *var;
int *varType;
char filename[1024];
FILE *fout;
int numUnused;

  varArray = head->varArray;
  varType = head->varType;
  sprintf(filename, "%s.nodes", baseName);
  fout = fopen(filename, "w");

  fprintf(fout, "UCLA nodes 1.0\n");

  size = 0;
  if(includeNS) size = head->nVarArray;
  else {
    for(i=0; i<head->nVarArray; i++) {
      if(varType[varArray[i]->id] == 2) continue;
      size++;
    }
  }

  numUnused = 0;
  for(i=0; i<head->nVar; i++) {
    if(varType[i] != 1) continue; /* if it is not domain variable **/
    var = head->varArrayMap[i] >=0 ? head->varArray[head->varArrayMap[i]] : 0;
    if(var)     continue;
    numUnused++;
  }
  if(includeNS) {
    for(i=0; i<head->nVar; i++) {
      if(varType[i] != 2)       continue; /* if it is not range variable **/
      var = head->varArrayMap[i] >=0 ? head->varArray[head->varArrayMap[i]] : 0;
     if(var)    continue;
      numUnused++;
    }
  }
  
  fprintf(fout, "NumNodes : %d\n", size+numUnused);
  fprintf(fout, "NumTerminals : 0\n");
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(includeNS == 0 && varType[var->id] == 2) continue;
    fprintf(fout, "C%d 1 1\n", var->id);
  }

  for(i=0; i<head->nVar; i++) {
    if(varType[i] != 1) continue; /* if it is not domain variable **/
    var = head->varArrayMap[i] >=0 ? head->varArray[head->varArrayMap[i]] : 0;
    if(var)     continue;
    fprintf(fout, "C%d 1 1\n", i);
  }
  if(includeNS) {
    for(i=0; i<head->nVar; i++) {
      if(varType[i] != 2)       continue; /* if it is not range variable **/
      var = head->varArrayMap[i] >=0 ? head->varArray[head->varArrayMap[i]] : 0;
     if(var)    continue;
      fprintf(fout, "C%d 1 1\n", i);
    }
  }
  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Make interface for CAPO]

  Description [Make interface for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceVariableNet(Relation_t *head, 
                                  char *baseName, 
                                  int includeNS)
{
int nPin, i, j;
int id, size;
Conjunct_t *conjunct;
bdd_t *relation;
int *supList, *varType;
char filename[1024];
FILE *fout;

  nPin = 0;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    relation = conjunct->relation;
    if(relation == (mdd_t *)(MAXINT-1)) continue;
    supList = conjunct->supList;
    if(includeNS) {
      if(conjunct->nSize == 1)  nPin += 2; 
      else                      nPin += conjunct->nSize-conjunct->nRange;
    }
    else {
      if(conjunct->nSize-conjunct->nRange == 1) nPin += 2;
      else                                      nPin += conjunct->nSize-conjunct->nRange;
    }
  }
  nPin += head->nDomain;
  if(includeNS)
    nPin += head->nRange;

  varType = head->varType;
  sprintf(filename, "%s.nets", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA nets 1.0\n");
  fprintf(fout, "#NumNets : %d\n", head->nSize);
  fprintf(fout, "NumPins : %d\n", nPin);
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    relation = conjunct->relation;
    if(relation == (mdd_t *)(MAXINT-1)) continue;

    supList = conjunct->supList;
    if(includeNS)       size = conjunct->nSize;
    else                size = conjunct->nSize - conjunct->nRange;

    if(size == 1)       fprintf(fout, "NetDegree : %d \n", 2);
    else                fprintf(fout, "NetDegree : %d \n", size);

    id = 0;
    if(includeNS) {
      for(j=0; j<conjunct->nSize; j++) {
        id = supList[j];
        fprintf(fout, "C%d B\n", id);
      }
    }
    else {
      for(j=0; j<conjunct->nSize; j++) {
        id = supList[j];
        if(varType[id] == 2)    continue;
        fprintf(fout, "C%d B\n", id);
      }
    }
    if(size == 1)
      fprintf(fout, "C%d B\n", id);
  }
  fprintf(fout, "NetDegree : %d \n", head->nDomain);
  for(i=0; i<head->nVar; i++) {
    if(varType[i] == 1) 
      fprintf(fout, "C%d B\n", i);
  }
  if(includeNS) {
    fprintf(fout, "NetDegree : %d \n", head->nRange);
    for(i=0; i<head->nVar; i++) {
      if(varType[i] == 2) 
        fprintf(fout, "C%d B\n", i);
    }
  }
  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Make interface for CAPO]

  Description [Make interface for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceVariableScl(Relation_t *head, char *baseName)
{
char filename[1024];
FILE *fout;

  sprintf(filename, "%s.scl", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA scl 1.0\n");
  fprintf(fout, "Numrows : 1\n");
  fprintf(fout, "CoreRow Horizontal\n");
  fprintf(fout, " Coordinate   : 1\n");
  fprintf(fout, " Height       : 1\n");
  fprintf(fout, " Sitewidth    : 1\n");
  fprintf(fout, " Sitespacing  : 1\n");
  fprintf(fout, " Siteorient   : N\n");
  fprintf(fout, " Sitesymmetry : Y\n");
  fprintf(fout, " SubrowOrigin : 0\n");
  fprintf(fout, " Numsites     : %d\n", head->nVarArray*2+2);
  fprintf(fout, "End\n");
  fclose(fout);
}


/**Function********************************************************************

  Synopsis    [Make interface for CAPO]

  Description [Make interface for CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOInterfaceVariablePl(Relation_t *head, char *baseName, int includeNS)
{
char filename[1024];
FILE *fout;
VarLife_t *var, **varArray;
int i, index, *varType;

  varType = head->varType;
  sprintf(filename, "%s.pl", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "UCLA pl 1.0\n");
  varArray = head->varArray;
  for(index=0, i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(includeNS == 0 && varType[var->id] == 2) continue;
    fprintf(fout, "C%d %d 1\n", var->id, (index+1)*2+1);
    index++;
  }
  fclose(fout);
}



/**Function********************************************************************

  Synopsis    [Read result of  CAPO]

  Description [Read result of CAPO]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearCAPOReadVariableOrder(Relation_t *head, char *baseName, int includeNS)
{
char ordFile[1024], line[1024];
FILE *fin;
char *next;
int i, id, index, *permutation, *exist;

  sprintf(ordFile, "%s.ord", baseName);
  if(!(fin = fopen(ordFile, "r"))) {
    fprintf(stdout, "Can't open order file %s\n", ordFile);
    exit(0);
  }

  permutation = ALLOC(int, head->nVar);
  exist = ALLOC(int, head->nVar);
  memset(exist, 0, sizeof(int)*head->nVar);

  index = 0;
  while(fgets(line, 1024, fin)){
    next = strchr(line, 'C');
    next++;
    sscanf(next, "%d", &id);
    permutation[index++] = id;
    exist[id] = 1;
    if(includeNS == 0 && head->varType[id] == 1) {
      permutation[index++] = head->domain2range[id];
      exist[head->domain2range[id]] = 1;
    }
  }
  fclose(fin);

  for(i=0; i<head->nVar; i++)
    if(exist[i] == 0)
      permutation[index++] = i;

  free(exist);

  bdd_shuffle_heap(head->mgr, permutation);

  free(permutation);
}

/**Function********************************************************************

  Synopsis    [Print profile of variables]

  Description [Print profile of variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearPrintVariableProfile(Relation_t *head, char *baseName)
{
double aal, atl;
char filename[1024];
FILE *fout;
st_table *cutSet;
int i, j, nDead, id;
int *varType;
int *supList;
Conjunct_t *conjunct;
VarLife_t *var;
st_generator *gen;

  ImgLinearVariableArrayInit(head);
  varType = head->varType;

  sprintf(filename, "%s.data", baseName);
  fout = fopen(filename, "w");

  cutSet = st_init_table(st_numcmp, st_numhash);
  for(i=0; i<head->nVar; i++) {
    if(varType[i] == 1) 
      st_insert(cutSet, (char *)(long)i, (char *)(long)i);
  }

  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++)
      st_insert(cutSet, (char *)(long)supList[j], (char *)(long)supList[j]);

    nDead = 0;
    st_foreach_item(cutSet, gen, &id, &id) {
      if(varType[id] == 2) continue;

      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] :
0;
      if(!var) continue;
      
      if(var->to <= i)  {
        nDead++;
        st_delete(cutSet, (&id), NULL);
      }
    }
    fprintf(fout, "%d %d %d\n", i, cutSet->num_entries, cutSet->num_entries+nDead);
  }
  fclose(fout);

  ImgLinearComputeLifeTime(head, &aal, &atl);

  sprintf(filename, "%s.gnu", baseName);
  fout = fopen(filename, "w");
  fprintf(fout, "set terminal postscript \n");
  fprintf(fout, "set output \"%s.ps\"\n", baseName);
  fprintf(fout, "set title \"profile of live variable aal %.3f atl %.3f\"\n",
          aal, atl);
  fprintf(fout, "plot \"%s.data\" using 1:2 title \"%s\" with lines, \\\n", baseName, "cut");
  fprintf(fout, "     \"%s.data\" using 1:3 title \"%s\" with lines\n", baseName, "cut+dead");
  fclose(fout);
}

/**Function********************************************************************

  Synopsis    [Print matrix]

  Description [Print matrix. Its x axis is varaible and its y axis is relation]

  SideEffects [Print matrix. Its x axis is varaible and its y axis is relation]

  SeeAlso     []

******************************************************************************/
void
ImgLinearPrintMatrix(Relation_t *head)
{
int i, j, id, index;
int *mapArray;
VarLife_t **varArray, *var;
VarLife_t **auxArr, **sortArr;
int nAuxArr, nSortArr;
array_t *smoothVarBddArr, *smoothArray;
bdd_t *varBdd;
Conjunct_t *conjunct;
bdd_t *relation;
int *supList, *varType;
char *buffer;
int maxIndex;

  if(head->verbosity < 5)       return;

  ImgLinearVariableArrayInit(head);

  mapArray = ALLOC(int, head->nVar);
  memset(mapArray, -1, sizeof(int)*head->nVar);

  varArray = head->varArray;

  smoothVarBddArr = ImgLinearMakeSmoothVarBdd(head, 0);
  for(index=0, i=0; i<array_n(smoothVarBddArr); i++) {
    smoothArray = array_fetch(array_t *, smoothVarBddArr, i);
    nAuxArr = 0;
    auxArr = ALLOC(VarLife_t *, nAuxArr+1);
    for(j=0; j<array_n(smoothArray); j++) {
      varBdd = array_fetch(bdd_t *, smoothArray, j);
      id = (int)bdd_top_var_id(varBdd);

      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] :
0;
      if(var) {
        auxArr[nAuxArr++] = var;
        auxArr = REALLOC(VarLife_t *, auxArr, nAuxArr+1);
      }
    }
    qsort(auxArr, nAuxArr, sizeof(VarLife_t *), ImgLinearCompareVarIndex);
    for(j=0; j<nAuxArr; j++)
      mapArray[auxArr[j]->id] = index++;
    free(auxArr);
  }

  varArray = head->varArray;
  nSortArr = 0;
  sortArr = ALLOC(VarLife_t *, nSortArr+1);
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->stateVar == 2)      continue;
    if(mapArray[var->id] >= 0) {
      var->index = mapArray[var->id];
      sortArr[nSortArr++] = var;
      sortArr = REALLOC(VarLife_t *, sortArr, nSortArr+1);
    }
    else {
      var->index = (double)MAXINT;
    }
  }
  qsort(sortArr, nSortArr, sizeof(VarLife_t *), ImgLinearCompareVarIndex);

  fprintf(stdout, "     ");
  for(i=0; i<nSortArr; i++) fprintf(stdout, "%d", (i/10)%10);
  fprintf(stdout, "\n");

  fprintf(stdout, "     ");
  for(i=0; i<nSortArr; i++) fprintf(stdout, "%d", i%10);
  fprintf(stdout, "\n");

  buffer = ALLOC(char , nSortArr+1);
  for(i=0; i<nSortArr; i++) {
    var = sortArr[i];
    var->index = (double)i;
    if(var->stateVar == 1)      buffer[i] = 'C';
    else                        buffer[i] = 'T';
  }
  buffer[i] = '\0';
  free(sortArr);
  fprintf(stdout, "     %s\n", buffer);

  maxIndex = i;
  for(i=0; i<maxIndex; i++)     buffer[i] = '.';
  buffer[i] = '\0';

  varType = head->varType;
  for(index=0,i=head->nSize-1;i>=0; i--) {
    conjunct = head->conjunctArray[i];
    if(conjunct == 0)   continue;
    if(conjunct->relation == 0) continue;
    relation = conjunct->relation;
    if(relation == (mdd_t *)(MAXINT-1)) continue;
    if(relation == 0)                   continue;
    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      if(varType[id] == 2)              continue;
      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] :
0;
      if(!var)  continue;
      if((int)var->index == MAXINT)     continue;
      buffer[(int)var->index] = '1';
    }
    index++;
    fprintf(stdout, "%4d %s %d %d\n", i, buffer, conjunct->nRange, bdd_size(relation));
    fflush(stdout);
    for(j=0; j<maxIndex; j++)   buffer[j] = '.';
    buffer[j] = '\0';
  }
  free(buffer);
}
/**Function********************************************************************

  Synopsis    [Print matrix]

  Description [Print matrix]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearPrintMatrixFull(Relation_t *head, int matrixIndex)
{
int i, j, id, index;
int *mapArray;
VarLife_t **varArray, *var;
VarLife_t **auxArr, **sortArr;
int nAuxArr, nSortArr;
array_t *smoothVarBddArr, *smoothArray;
FILE *fout;
int min, max;
bdd_t *varBdd;
char filename[1024];
Conjunct_t *conjunct;
bdd_t *relation;
int *supList;

  ImgLinearVariableArrayInit(head);

  mapArray = ALLOC(int, head->nVar);
  memset(mapArray, -1, sizeof(int)*head->nVar);
  varArray = head->varArray;

  smoothVarBddArr = ImgLinearMakeSmoothVarBdd(head, 0);
  for(index=0, i=0; i<array_n(smoothVarBddArr); i++) {
    smoothArray = array_fetch(array_t *, smoothVarBddArr, i);
    nAuxArr = 0;
    auxArr = ALLOC(VarLife_t *, nAuxArr+1);
    for(j=0; j<array_n(smoothArray); j++) {
      varBdd = array_fetch(bdd_t *, smoothArray, j);
      id = (int)bdd_top_var_id(varBdd);

      var = head->varArrayMap[id] >=0 ? varArray[head->varArrayMap[id]] : 0;
      if(var) {
        auxArr[nAuxArr++] = var;
        auxArr = REALLOC(VarLife_t *, auxArr, nAuxArr+1);
      }
    }
    qsort(auxArr, nAuxArr, sizeof(VarLife_t *), ImgLinearCompareVarIndex);
    for(j=0; j<nAuxArr; j++)
      mapArray[auxArr[j]->id] = index++;
    free(auxArr);
  }

  nSortArr = 0;
  sortArr = ALLOC(VarLife_t *, nSortArr+1);
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->stateVar == 2)      continue;
    if(mapArray[var->id] >= 0) {
      var->index = mapArray[var->id];
      sortArr[nSortArr++] = var;
      sortArr = REALLOC(VarLife_t *, sortArr, nSortArr+1);
    }
    else {
      var->index = (double)MAXINT;
    }
  }

  qsort(sortArr, nSortArr, sizeof(VarLife_t *), ImgLinearCompareVarIndex);
  free(mapArray);

  sprintf(filename, "fullmatrix%d.data", matrixIndex);
  fout = fopen(filename, "w");
  min = 0;
  max = head->nSize+1;
  for(i=0; i<nSortArr; i++) {
    var = sortArr[i];
    if(var->stateVar == 1)
      fprintf(fout, "%d %d\n", (int)var->index, min);
  }
  free(sortArr);

  for(index=0, i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    relation = conjunct->relation;
    if(relation == (mdd_t *)(MAXINT-1)) continue;
    if(relation == 0)                   continue;
    supList = conjunct->supList;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] : 0;
      if(!var)  continue; 
      if(var->stateVar == 2)
      if((int)var->index == MAXINT) continue;
      fprintf(fout, "%d %d\n", (int)var->index, index+1);
    }
    index++;
  }
  fclose(fout);

  sprintf(filename, "fullmatrix%d.gnu", matrixIndex);
  fout = fopen(filename, "w");
  fprintf(fout, "set terminal postscript \n");
  fprintf(fout, "set output \"fullmatrix%d.ps\"\n", matrixIndex);
  fprintf(fout, "set title \"profile of live variable\"\n");
  fprintf(fout, "set yrange [-1:%d]\n", head->nSize+2);
  fprintf(fout, "plot \"fullmatrix%d.data\" using 1:2 title \"%d\" with point\n",
                  matrixIndex, matrixIndex);
  fclose(fout);

  ImgLinearFreeSmoothArray(smoothVarBddArr);
}

/**Function********************************************************************

  Synopsis    [Free smooth variable array]

  Description [Free smooth variable array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearFreeSmoothArray(array_t *smoothVarBddArray)
{
int i;
array_t *smoothArray;

  for(i=0; i<array_n(smoothVarBddArray); i++) {
    smoothArray = array_fetch(array_t *, smoothVarBddArray, i);
    mdd_array_free(smoothArray);
  }
  array_free(smoothVarBddArray);
}

/**Function********************************************************************

  Synopsis    [Compute life time of variables]

  Description [Compute life time of variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
void
ImgLinearComputeLifeTime(Relation_t *head, double *paal, double *patl)
{
double aal, atl;
int i;
VarLife_t **varArray, *var;

  aal = atl = 0.0;
  varArray = head->varArray;
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    aal += var->effTo - var->effFrom;
    if(var->stateVar == 1)      atl += var->to+1;
    else if(var->stateVar == 2) atl += head->nSize+1 - var->from;
    else                        atl += var->to - var->from;
  }
  atl = atl / (double)(head->nVarArray * head->nSize);
  aal = aal / (double)(head->nVarArray * head->nSize);

  *paal = aal;
  *patl = atl;
}

/**Function********************************************************************

  Synopsis    [Print transition relation info]

  Description [Print transition relation info]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearPrintTransitionInfo(Relation_t *head)
{
double aal, atl;

  fprintf(stdout, "SUMMARY : domain   variables %d -> %d -> %d\n", 
          head->nDomain, head->nInitDomain, head->nEffDomain);
  fprintf(stdout, "SUMMARY : range    variables %d -> %d -> %d\n", 
          head->nRange, head->nInitRange, head->nEffRange);
  fprintf(stdout, "SUMMARY : quantify variables %d -> %d -> %d\n", 
          head->nQuantify, head->nInitQuantify, head->nEffQuantify);
  fprintf(stdout, "SUMMARY : number of transition relation %d\n", 
          head->nSize);
  ImgLinearComputeLifeTime(head, &aal, &atl);
  fprintf(stdout, "Active  Life Time : %g\n", aal);
  fprintf(stdout, "Average Life Time : %g\n", atl);
}



/**Function********************************************************************

  Synopsis    [Make the array of smooth variables]

  Description [Make the array of smooth variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
array_t *
ImgLinearMakeSmoothVarBdd(Relation_t *head, bdd_t **smoothCubeArr)
{
array_t *smoothVarBddArray;
array_t *smoothArray;
VarLife_t **varArray;
int i, j, id;
VarLife_t *var;
bdd_t *varBdd, *cube, *newCube;

  smoothVarBddArray = array_alloc(array_t *, 0);
  for(i=0; i<=head->nSize; i++) {
    smoothArray = array_alloc(bdd_t *, 0);
    array_insert_last(array_t *, smoothVarBddArray, smoothArray);
  } 

  varArray = head->varArray;
  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(var->stateVar == 2)      continue;
    smoothArray = array_fetch(array_t *, smoothVarBddArray, var->to+1);
    varBdd = bdd_get_variable(head->mgr, var->id);
    array_insert_last(bdd_t *, smoothArray, varBdd);
  }

  smoothArray = array_fetch(array_t *, smoothVarBddArray, 0);
  for(i=0; i<head->nDomain; i++) {
    id = head->domainVars[i];
    var = head->varArrayMap[id] >=0 ? head->varArray[head->varArrayMap[id]] : 0;
   if(var)      continue;
    varBdd = bdd_get_variable(head->mgr, id);
    array_insert_last(bdd_t *, smoothArray, varBdd);
  }

  if(smoothCubeArr) {
    for(i=0; i<=head->nSize; i++) {
      smoothArray = array_fetch(array_t *, smoothVarBddArray, i);
      cube = bdd_one(head->mgr);
      for(j=0; j<array_n(smoothArray); j++) {
        varBdd = array_fetch(bdd_t *, smoothArray, j);
        newCube = bdd_and(varBdd, cube, 1, 1);
        bdd_free(cube);
        cube = newCube;
      }
      smoothCubeArr[i] = cube;
    }
  }

  return(smoothVarBddArray);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarEffFromSmall(const void *c1, const void *c2)
{
VarLife_t *con1, *con2;

  con1 = *(VarLife_t **)c1;
  con2 = *(VarLife_t **)c2;
  return(con1->effFrom > con2->effFrom);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarDummyLarge(const void *c1, const void *c2)
{
VarLife_t *con1, *con2;

  con1 = *(VarLife_t **)c1;
  con2 = *(VarLife_t **)c2;
  return(con1->dummy < con2->dummy);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarEffFromLarge(const void *c1, const void *c2)
{
VarLife_t *con1, *con2;

  con1 = *(VarLife_t **)c1;
  con2 = *(VarLife_t **)c2;
  return(con1->effFrom < con2->effFrom);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarId(const void *c1, const void *c2)
{
VarLife_t *con1, *con2;

  con1 = *(VarLife_t **)c1;
  con2 = *(VarLife_t **)c2;
  return(con1->id < con2->id);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarSize(const void *c1, const void *c2)
{
VarLife_t *con1, *con2;

  con1 = *(VarLife_t **)c1;
  con2 = *(VarLife_t **)c2;
  return(con1->nSize > con2->nSize);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareConjunctRangeMinusDomain(const void *c1, const void *c2)
{
Conjunct_t *con1, *con2;

  con1 = *(Conjunct_t **)c1;
  con2 = *(Conjunct_t **)c2;
  return(con1->nRange-con1->nDomain > con2->nRange-con2->nDomain);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareConjunctDummy(const void *c1, const void *c2)
{
Conjunct_t *con1, *con2;

  con1 = *(Conjunct_t **)c1;
  con2 = *(Conjunct_t **)c2;
  return(con1->dummy > con2->dummy); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareConjunctIndex(const void *c1, const void *c2)
{
Conjunct_t *con1, *con2;

  con1 = *(Conjunct_t **)c1;
  con2 = *(Conjunct_t **)c2;

  return(con1->index > con2->index); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareConjunctSize(const void *c1, const void *c2)
{
Conjunct_t *con1, *con2;

  con1 = *(Conjunct_t **)c1;
  con2 = *(Conjunct_t **)c2;

  if(con1->nSize == con2->nSize)
    return(con1->dummy < con2->dummy);
  return(con1->nSize < con2->nSize); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareVarIndex(const void *c1, const void *c2)
{
VarLife_t *v1, *v2;

  v1 = *(VarLife_t **)c1;
  v2 = *(VarLife_t **)c2;

  return(v1->index < v2->index); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareDeadAffinityLive(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = *(Cluster_t **)c1;
  clu2 = *(Cluster_t **)c2;
  if(clu1->nDead == clu2->nDead) {
    if(clu1->nAffinity == clu2->nAffinity) {
      return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead); 
    }
    return(clu1->nAffinity < clu2->nAffinity); 
  }
  return(clu1->nDead < clu2->nDead); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareDeadLiveAffinity(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = *(Cluster_t **)c1;
  clu2 = *(Cluster_t **)c2;
  if(clu1->nDead == clu2->nDead) {
    if(clu1->nVar-clu1->nDead == clu2->nVar-clu2->nDead) {
      return(clu1->nAffinity < clu2->nAffinity); 
    }
    return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead); 
  }
  return(clu1->nDead < clu2->nDead); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareAffinityDeadLive(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = *(Cluster_t **)c1;
  clu2 = *(Cluster_t **)c2;
  if(clu1->nAffinity == clu2->nAffinity) {
    if(clu1->nDead == clu2->nDead) {
      return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead); 
    }
    return(clu1->nDead < clu2->nDead); 
  }
  return(clu1->nAffinity < clu2->nAffinity); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearCompareLiveAffinityDead(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = *(Cluster_t **)c1;
  clu2 = *(Cluster_t **)c2;
  if(clu1->nVar-clu1->nDead == clu2->nVar-clu2->nDead) {
    if(clu1->nAffinity == clu2->nAffinity) {
      return(clu1->nDead < clu2->nDead);
    }
    return(clu1->nAffinity < clu2->nAffinity);
  }
  return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead);
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearHeapCompareDeadAffinityLive(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = (Cluster_t *)c1;
  clu2 = (Cluster_t *)c2;
  if(clu1->nDead == clu2->nDead) {
    if(clu1->nAffinity == clu2->nAffinity) {
      return((clu1->nVar-clu1->nDead) > (clu2->nVar-clu2->nDead)); 
    }
    return(clu1->nAffinity < clu2->nAffinity); 
  }
  return(clu1->nDead < clu2->nDead); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearHeapCompareDeadLiveAffinity(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = (Cluster_t *)c1;
  clu2 = (Cluster_t *)c2;
  if(clu1->nDead == clu2->nDead) {
    if((clu1->nVar-clu1->nDead) == (clu2->nVar-clu2->nDead)) {
      return(clu1->nAffinity < clu2->nAffinity); 
    }
    return((clu1->nVar-clu1->nDead) > (clu2->nVar-clu2->nDead)); 
  }
  return(clu1->nDead < clu2->nDead); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearHeapCompareAffinityDeadLive(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = (Cluster_t *)c1;
  clu2 = (Cluster_t *)c2;
  if(clu1->nAffinity == clu2->nAffinity) {
    if(clu1->nDead == clu2->nDead) {
      return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead); 
    }
    return(clu1->nDead < clu2->nDead); 
  }
  return(clu1->nAffinity < clu2->nAffinity); 
}

/**Function********************************************************************

  Synopsis    [Priority function for clutering]

  Description [Priority function for clutering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearHeapCompareLiveAffinityDead(const void *c1, const void *c2)
{
Cluster_t *clu1, *clu2;

  clu1 = (Cluster_t *)c1;
  clu2 = (Cluster_t *)c2;
  if(clu1->nVar-clu1->nDead == clu2->nVar-clu2->nDead) {
    if(clu1->nAffinity == clu2->nAffinity) {
      return(clu1->nDead < clu2->nDead);
    }
    return(clu1->nAffinity < clu2->nAffinity);
  }
  return(clu1->nVar-clu1->nDead > clu2->nVar-clu2->nDead);
}

/**Function********************************************************************

  Synopsis    [Initialize variable array]

  Description [Initialize variable array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearVariableArrayInit(Relation_t *head)
{
mdd_manager *mgr;
Conjunct_t **conjunctArray, *conjunct;
Conjunct_t *tConjunct;
bdd_t *relation, *bddOne;
VarLife_t **varArray;
int *supList, listSize;
int *varType, *varArrayMap;
int i, j, k, id, nVarArray;
int nSize, newNum;


  if(head->bRefineVarArray) {
    ImgLinearVariableArrayQuit(head);
  }

  if(head->varArray)    return;

  mgr = head->mgr;

  if(head->nVar != (int)(bdd_num_vars(mgr))) {
    newNum = bdd_num_vars(head->mgr);
    head->domain2range = REALLOC(int, head->domain2range, newNum);
    head->range2domain = REALLOC(int, head->range2domain, newNum);
    head->varType = REALLOC(int, head->varType, newNum);
    head->varArrayMap = REALLOC(int, head->varArrayMap, newNum);
    head->constantCase = REALLOC(bdd_t *, head->constantCase, newNum);
    head->quantifyVars = REALLOC(int, head->quantifyVars, newNum);

    for(i=head->nVar; i<newNum; i++) {
      head->domain2range[i] = -1;
      head->range2domain[i] = -1;
      head->varType[i] = 0;
      head->varArrayMap[i] = -1;
      head->constantCase[i] = 0;
      head->quantifyVars[i] = 0;
    }
    head->nVar = bdd_num_vars(head->mgr);
  }

  nSize = head->nSize;
  conjunctArray = head->conjunctArray;
  varArrayMap = head->varArrayMap;

  id = 0;
  nVarArray = 0;
  varArray = ALLOC(VarLife_t *, nVarArray+1);
  head->varArray = varArray;
  head->nVarArray = nVarArray;
  bddOne = bdd_one(head->mgr);

  varType = head->varType;
  for(i=0; i<nSize; i++) {
    conjunct = conjunctArray[i];
    if(conjunct == 0)   continue;
    relation = conjunct->relation;
    if(relation == 0)   continue;
    if(bdd_equal(bddOne, relation))     continue;
    supList = conjunct->supList;
    listSize = conjunct->nSize;
    for(j=0; j<listSize; j++) {
      id = supList[j]; 
      ImgLinearUpdateVariableArrayWithId(head, i, id);
    }

    for(k=0; k<conjunct->nCluster; k++) {
      tConjunct = conjunct->clusterArray[k];
      supList = tConjunct->supList;
      listSize = tConjunct->nSize;
      for(j=0; j<listSize; j++) {
        ImgLinearUpdateVariableArrayWithId(head, i, id);
      }
    }
  }
  bdd_free(bddOne);
  head->bRefineVarArray = 0;
}

/**Function********************************************************************

  Synopsis    [Update variable array with id of variable id]

  Description [Update variable array with id of variable id]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearUpdateVariableArrayWithId(Relation_t *head, 
                                   int cindex, 
                                   int id)
{
VarLife_t *var;
int *varType;
int *varArrayMap;
int nVarArray;
VarLife_t **varArray;

  varType = head->varType;
  varArrayMap = head->varArrayMap;
  varArray = head->varArray;
  nVarArray = head->nVarArray;

  if(varArrayMap[id] == -1) {
    var = ALLOC(VarLife_t, 1);
    var->id = id;
    var->from = cindex;
    var->to = cindex;
    var->effFrom = cindex;
    var->effTo = cindex;
    var->stateVar = 0;
    var->relArr = ALLOC(int, 1);
    var->nSize = 0;
    var->index = 0.0;
    varArrayMap[id] = nVarArray;
    varArray[nVarArray++] = var;
    varArray = REALLOC(VarLife_t *, varArray, nVarArray+1);

    if(varType[id] == 1) {
      var->stateVar = 1;
      if(head->includeCS && !head->quantifyCS) { 
        var->relArr = REALLOC(int, var->relArr, var->nSize+1);
        var->relArr[var->nSize++] = MAXINT-1;
        var->from = -1;
      }
    }
    else if(varType[id] == 2) {
      var->stateVar = 2;
      if(head->includeNS) { 
        var->relArr = REALLOC(int, var->relArr, var->nSize+1);
        var->relArr[var->nSize++] = MAXINT;
        var->to = head->nSize;
      }
    }
  }
  else {
    var = varArray[varArrayMap[id]];
  }
  
  if(var->to < cindex)          var->to = cindex;
  if(var->from > cindex)        var->from = cindex;

  if(var->effTo < cindex)       var->effTo = cindex;
  if(var->effFrom > cindex)     var->effFrom = cindex;

  var->relArr = REALLOC(int, var->relArr, var->nSize+1);
  var->relArr[var->nSize++] = cindex;
  head->varArray = varArray;
  head->nVarArray = nVarArray;
}
/**Function********************************************************************

  Synopsis    [Apply quantification with candidate variables]

  Description [Apply quantification with candidate variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearQuantifyVariablesFromConjunct(Relation_t *head,
                                       Conjunct_t *conjunct, 
                                       array_t *smoothVarBddArray,
                                       int *bModified)
{
bdd_t *relation, *simpleRelation;

  if(conjunct == 0)     return 1;
  relation = conjunct->relation;
  if(relation == 0)     return 1;

  simpleRelation = bdd_smooth(relation, smoothVarBddArray);
  if(bdd_equal(relation, simpleRelation)) {
    bdd_free(simpleRelation);
    return 0;
  }
  bdd_free(relation);

  (*bModified)++;
  conjunct->relation = simpleRelation;
  conjunct->bModified = 1;
  head->bModified = 1;
  head->bRefineVarArray = 1;
  ImgLinearConjunctRefine(head, conjunct);
  return 1;
}

/**Function********************************************************************

  Synopsis    [Refine conjunction array to fill the empty slot.]

  Description [Refine conjunction array to fill the empty slot.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearConjunctRefine(Relation_t *head, Conjunct_t *conjunct)
{
int i, id, listSize, *supList;
int *varType;

  if(conjunct->relation == 0)   {
    if(conjunct->supList)       free(conjunct->supList);
    conjunct->supList = 0;
    return;
  }
  if(!conjunct->bModified)      return; 

  if(conjunct->supList) {
    free(conjunct->supList);
    conjunct->supList = 0;
  }

  supList = ImgLinearGetSupportBddId(head->mgr, conjunct->relation, &listSize);
  if(listSize == 0) {
    conjunct->relation = 0;
    if(conjunct->supList) {
      free(conjunct->supList);
      conjunct->supList = 0;
    }
    return;
  }
  else {
    varType = head->varType;
    conjunct->supList = supList;
    conjunct->nSize = listSize;
    conjunct->bModified = 0;
    conjunct->nDomain = 0;
    conjunct->nRange = 0;
    conjunct->nQuantify = 0;
    conjunct->from = 0;
    conjunct->to = 0;
    conjunct->dummy = 0;
    for(i=0; i<listSize; i++) {
      id = supList[i];
      if(varType[id] == 1)      conjunct->nDomain++;
      else if(varType[id] == 2) conjunct->nRange++;
      else if(varType[id] == 3) conjunct->nQuantify++;
    }
    head->bModified = 1;
  }
  return;
}
/**Function********************************************************************

  Synopsis    [Refine conjunction array to fill the empty slot.]

  Description [Refine conjunction array to fill the empty slot.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearConjunctArrayRefine(Relation_t *head)
{
int nSize, i;
int index;
Conjunct_t **conjunctArray, **newConjunctArray;
Conjunct_t *conjunct;

  if(head->bModified == 0)      return;

  conjunctArray = head->conjunctArray;
  newConjunctArray = ALLOC(Conjunct_t *, head->nSize+1);
  nSize = head->nSize;
  for(index=0, i=0; i<nSize; i++) {
    conjunct = conjunctArray[i];
    if(conjunct == 0)   {
      head->bRefineVarArray = 1;
      continue;
    }
    if(conjunct->relation == 0) {
      ImgLinearConjunctQuit(conjunct);
      head->bRefineVarArray = 1;
      continue;
    }

    if(conjunct->bModified) {
      ImgLinearConjunctRefine(head, conjunct);
      head->bRefineVarArray = 1;
    }

    if(conjunct == 0)   continue;
    if(conjunct->relation == 0) {
      ImgLinearConjunctQuit(conjunct);
      continue;
    }

    newConjunctArray[index] = conjunct;
    conjunct->index = index++;
  }
  newConjunctArray[index] = 0;
  free(conjunctArray);
  head->conjunctArray = newConjunctArray;
  head->nSize = index;
  head->bModified = 0;
  return; 
}

/**Function********************************************************************

  Synopsis    [Get the number of state variables after applying optimization]

  Description [Get the number of state variables after applying optimization]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearSetEffectiveNumberOfStateVariable(Relation_t *head, 
                                            int *rangeId, 
                                            int *domainId,
                                            int *existStateVariable) 
{
VarLife_t **varArray, *var;
int *varType;
int nRange, nDomain, nQuantify;
int i;

  varArray = head->varArray;
  varType = head->varType;
  nRange = nDomain = nQuantify = 0;

  for(i=0; i<head->nVarArray; i++) {
    var = varArray[i];
    if(varType[var->id] == 1)   {
      if(domainId) domainId[nDomain] = var->id;
      nDomain++;
      if(existStateVariable) existStateVariable[var->id] = 1;
    }
    else if(varType[var->id] == 2)      {
      if(rangeId) rangeId[nRange] = var->id;
      nRange++;
      if(existStateVariable) existStateVariable[var->id] = 1;
    }
    else if(varType[var->id] == 3)      {
      nQuantify++;
    }
    else
      nQuantify++;

  } 
  if(domainId)  domainId[nDomain] = -1;
  if(rangeId)   rangeId[nRange] = -1;

  head->nEffRange = nRange;
  head->nEffDomain = nDomain;
  head->nEffQuantify = nQuantify;

  if(head->nInitRange == 0 && head->nInitDomain == 0 && head->nInitQuantify == 0) {
    head->nInitRange = nRange;
    head->nInitDomain = nDomain;
    head->nInitQuantify = nQuantify;
  }
}

/**Function********************************************************************

  Synopsis    [Find the case that the relation contains only one next state varaible]

  Description [Find the case that the relation contains only one next state varaible]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearAddSingletonCase(Relation_t *head)
{
Conjunct_t **newConjunctArray;
Conjunct_t **singletonArray;
Conjunct_t *conjunct;
int i, j, index;
int nSingletonArray;
int putFlag;

  nSingletonArray = head->nSingletonArray;
  singletonArray = head->singletonArray;

  if(nSingletonArray == 0)      return;
  fprintf(stdout, "NOTICE : %d singleton case will be added\n", nSingletonArray);

  qsort(singletonArray, nSingletonArray, sizeof(Conjunct_t *), ImgLinearCompareConjunctRangeMinusDomain);

  index = 0;
  newConjunctArray = ALLOC(Conjunct_t *, head->nSize + nSingletonArray);
  putFlag = 0;
  for(i=0; i<nSingletonArray; i++) {
    conjunct = singletonArray[i];
    if(putFlag == 0 && conjunct->nRange > conjunct->nSize-conjunct->nRange) {
      putFlag = 1;
      for(j=0; j<head->nSize; j++) 
        newConjunctArray[index++] = head->conjunctArray[j];
    }
    newConjunctArray[index++] = singletonArray[i];
  }
  if(putFlag == 0) {
    for(j=0; j<head->nSize; j++) 
      newConjunctArray[index++] = head->conjunctArray[j];
  }

  head->nSize = index;
  head->bModified = 1;
  head->bRefineVarArray = 1;
  free(head->conjunctArray);
  head->conjunctArray = newConjunctArray;
  free(singletonArray);
  head->singletonArray = 0;
  head->nSingletonArray = 0;
}


/**Function********************************************************************

  Synopsis    [Find transtion relations that have smae support set]

  Description [Find transtion relations that have smae support set and use this information when finding linear arragement]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearExpandSameSupportSet(Relation_t *head)
{
int index, i, j;
Conjunct_t **newConjunctArray;
Conjunct_t *conjunct;

  newConjunctArray = ALLOC(Conjunct_t *, head->nSize);
  for(index=0, i=0; i<head->nSize; i++) {
    if(index >= head->nSize)
      newConjunctArray = REALLOC(Conjunct_t *, newConjunctArray, index+1);
    conjunct = head->conjunctArray[i];
    newConjunctArray[index++] = conjunct;
    if(conjunct->nCluster) {
      for(j=0; j<conjunct->nCluster; j++) {
        if(index >= head->nSize)
          newConjunctArray = REALLOC(Conjunct_t *, newConjunctArray, index+1);
        newConjunctArray[index++] = conjunct->clusterArray[j];
      }
      head->bModified = 1;
      head->bRefineVarArray = 1;
      conjunct->nCluster = 0;
      if(conjunct->clusterArray) {
        free(conjunct->clusterArray);
        conjunct->clusterArray = 0;
      }
    }
  }
  free(head->conjunctArray);
  head->conjunctArray = newConjunctArray;
  head->nSize = index;
}


/**Function********************************************************************

  Synopsis    [Cluster the relation that has same support set]

  Description [Cluster the relation that has same support set]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearClusterSameSupportSet(Relation_t *head) 
{
int i, j, index, id;
int *supList;
Conjunct_t *conjunct, *base;
int *varType;
Conjunct_t **conjunctArray, **newConjunctArray;

  head->nTotalCluster = 0;
  varType = head->varType;
  conjunctArray = head->conjunctArray; 

  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    supList = conjunct->supList;
    conjunct->dummy = 0;
    for(j=0; j<conjunct->nSize; j++) {
      id = supList[j];
      if(varType[id] == 2)      continue;
      conjunct->dummy += id;
    }
    conjunct->dummy *= (conjunct->nSize-conjunct->nRange);
    conjunct->dummy -= conjunct->nDomain;
  }
  qsort(conjunctArray, head->nSize, sizeof(Conjunct_t *), 
                        ImgLinearCompareConjunctDummy);

  for(i=0; i<head->nSize; i++) {
    base = head->conjunctArray[i];
    for(j=i+1; j<head->nSize; j++) {
      conjunct = head->conjunctArray[j];
      if(base->dummy != conjunct->dummy) {
        if(j == i+1)    break;
        ImgLinearFindSameSupportConjuncts(head, i, j-1);
        i = j-1;
        break;
      }
    }
  }

  if(head->bModified)   {
    conjunctArray = head->conjunctArray;
    newConjunctArray = ALLOC(Conjunct_t *, head->nSize);
    for(index=0, i=0; i<head->nSize; i++) {
      conjunct = conjunctArray[i];
      if(conjunct == 0) continue;
      newConjunctArray[index++] = conjunct;
    }
    free(conjunctArray);
    head->conjunctArray = newConjunctArray;
    head->nSize = index;
    head->bModified = 1;
    head->bRefineVarArray = 1;
  }

  conjunctArray = head->conjunctArray;
  qsort(conjunctArray, head->nSize, sizeof(Conjunct_t *), ImgLinearCompareConjunctIndex);
  if(head->bModified)   {
    conjunctArray = head->conjunctArray;
    for(i=0; i<head->nSize; i++) {
      conjunct = conjunctArray[i];
      if(conjunct == 0) continue;
      conjunct->index = i;
    }
  }
  fprintf(stdout, "NOTICE : %d conjunct clustered\n", head->nTotalCluster);
  head->nTotalCluster = 0;

}
/**Function********************************************************************

  Synopsis    [Find the conjuncts that have same support variables.]

  Description [Find the conjuncts that have same support variables.]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearFindSameSupportConjuncts(Relation_t *head, int from, int to)
{
Conjunct_t *con1, *con2;
int i, j;

  for(i=from; i<=to; i++) {
    con1 = head->conjunctArray[i];
    if(con1 == 0)       continue;

    for(j=from; j<=to; j++) {
      if(i == j)        continue;
      con2 = head->conjunctArray[j];
      if(con2 == 0)     continue;
      if(ImgLinearIsSameConjunct(head, con1, con2)) {
        ImgLinearAddConjunctIntoClusterArray(con1, con2);
        head->conjunctArray[j] = 0;

        head->bModified = 1;
        head->bRefineVarArray = 1;
        head->nTotalCluster++;
      }
    }
  }
}

/**Function********************************************************************

  Synopsis    [Check if given conjuncts have same support variables]

  Description [Check if given conjuncts have same support variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgLinearIsSameConjunct(Relation_t *head, Conjunct_t *con1, Conjunct_t *con2)
{
int i, j;
int *sup1, *sup2;
int id1, id2;
int *varType;

  if(con1->nDomain != con2->nDomain)    return(0);
  if(con1->nSize-con1->nRange != con2->nSize-con2->nRange)      return(0);
  sup1 = con1->supList;
  sup2 = con2->supList;

  varType = head->varType;

  for(j=0, i=0; i<con1->nSize; i++) {
    id1 = sup1[i];
    if(varType[id1] == 2)continue;
    while(1) {
      id2 = sup2[j];
      if(varType[id2] == 2) {
        j++;
        continue;
      }
      if(id1 != id2)    return(0);
      j++;
      break;
    }
  }
  return(1);
}

/**Function********************************************************************

  Synopsis    [Add conjunct into array]

  Description [Add conjunct into array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static Conjunct_t **
ImgLinearAddConjunctIntoArray(Conjunct_t **array, int *nArray, Conjunct_t *con)
{
  if(array)
    array = REALLOC(Conjunct_t *, array, (*nArray)+1);
  else 
    array = ALLOC(Conjunct_t *, (*nArray)+1);
  array[(*nArray)++] = con;
  return(array);

}

/**Function********************************************************************

  Synopsis    [Free conjunct_t data structure]

  Description [Free conjunct_t data structure]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearConjunctQuit(Conjunct_t *conjunct)
{
  if(conjunct->supList) {
    free(conjunct->supList);
    conjunct->supList = 0;
  }
  if(conjunct->relation) {
    bdd_free(conjunct->relation);
    conjunct->relation = 0;
  }
  free(conjunct);
}


/**Function********************************************************************

  Synopsis    [Free variable array]

  Description [Free variable array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearVariableArrayQuit(Relation_t *head)
{
int i;
VarLife_t **varArray;


  varArray = head->varArray;
  for(i=0; i<head->nVarArray; i++)
    ImgLinearVariableLifeQuit(varArray[i]);

  free(varArray);
  head->varArray = 0;
  head->nVarArray = 0;
  memset(head->varArrayMap, -1, sizeof(int)*head->nVar);
}


/**Function********************************************************************

  Synopsis    [Free variable life array]

  Description [Free variable  lifearray]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearVariableLifeQuit(VarLife_t *var) 
{
   if(var->relArr)      free(var->relArr);
   free(var);
}

/**Function********************************************************************

  Synopsis    [Main function of clustering]

  Description [Main function of clustering]

  SideEffects []

  SeeAlso     []

******************************************************************************/
int
ImgLinearClustering(Relation_t *head, Img_OptimizeType optDir)
{
int andExistLimit;
int useFailureHistory;
int includeZeroGain;
double affinityLimit;
int bOptimize;
int varLimit;

  bOptimize = 0;

  affinityLimit = 0.99;
  andExistLimit = 10;
  varLimit = 200;
  fprintf(stdout, "Heap DAL affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
  bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                varLimit, optDir, 0,
                                ImgLinearHeapCompareDeadAffinityLive);
  ImgLinearRefineRelation(head);
  if(head->verbosity >= 5)
    ImgLinearPrintMatrix(head);
  ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
  ImgLinearPrintTransitionInfo(head);

  includeZeroGain = 0;
  affinityLimit = 0.3;
  andExistLimit = 5000;
  varLimit = 50;
  useFailureHistory = 0;
  if(head->computeRange) {
    varLimit = 50;
    affinityLimit = 0.8;
    andExistLimit = 5000;
    fprintf(stdout, "Heap DAL affinity %3f, andExist %d\n", 
            affinityLimit, andExistLimit);
    bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                  varLimit, optDir, 0,
                                ImgLinearHeapCompareDeadAffinityLive);

    ImgLinearRefineRelation(head);
    ImgLinearExtractNextStateCase(head);
    ImgLinearExtractSingletonCase(head);
    ImgLinearRefineRelation(head);
    ImgLinearAddSingletonCase(head);
    ImgLinearRefineRelation(head);
    ImgLinearAddNextStateCase(head);
    ImgLinearRefineRelation(head);
  }
  else 
  {
    fprintf(stdout, "Gain DAL affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
    bOptimize |= ImgLinearClusteringIteratively(head, affinityLimit,
                                andExistLimit, varLimit, 
                                includeZeroGain, useFailureHistory, optDir,
                                ImgLinearCompareDeadAffinityLive);
    ImgLinearRefineRelation(head);
    ImgLinearExtractNextStateCase(head);
    ImgLinearExtractSingletonCase(head);
    ImgLinearRefineRelation(head);
    ImgLinearAddSingletonCase(head);
    ImgLinearRefineRelation(head);
    ImgLinearAddNextStateCase(head);
    ImgLinearRefineRelation(head);
  }

  includeZeroGain = 1;
  varLimit = 200;
  affinityLimit = 0.7;
  andExistLimit = 5000;
  fprintf(stdout, "Heap DAL affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
  bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                varLimit, optDir, 0,
                                ImgLinearHeapCompareDeadAffinityLive);

  ImgLinearRefineRelation(head);
  ImgLinearExtractNextStateCase(head);
  ImgLinearExtractSingletonCase(head);
  ImgLinearRefineRelation(head);
  ImgLinearAddSingletonCase(head);
  ImgLinearRefineRelation(head);
  ImgLinearAddNextStateCase(head);
  ImgLinearRefineRelation(head);

  if(head->verbosity >= 5)
    ImgLinearPrintMatrix(head);
  ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
  ImgLinearPrintTransitionInfo(head);

  includeZeroGain = 1;
  affinityLimit = 0.4;
  andExistLimit = 5000;
  fprintf(stdout, "Heap DAL affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
  bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                varLimit, optDir, 0,
                                ImgLinearHeapCompareDeadAffinityLive);
  ImgLinearRefineRelation(head);
  ImgLinearExtractNextStateCase(head);
  ImgLinearExtractSingletonCase(head);
  ImgLinearRefineRelation(head);
  ImgLinearAddSingletonCase(head);
  ImgLinearRefineRelation(head);
  ImgLinearAddNextStateCase(head);
  ImgLinearRefineRelation(head);

  if(head->verbosity >= 5)
    ImgLinearPrintMatrix(head);
  ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
  ImgLinearPrintTransitionInfo(head);

  affinityLimit = 0.0;
  andExistLimit = 5000;
  fprintf(stdout, "Heap DLA affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
  bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                varLimit, optDir, 0,
                                ImgLinearHeapCompareDeadLiveAffinity);
  ImgLinearRefineRelation(head);
  ImgLinearExtractNextStateCase(head);
  ImgLinearRefineRelation(head);
  ImgLinearAddNextStateCase(head);
  ImgLinearRefineRelation(head);
  if(head->verbosity >= 5)
    ImgLinearPrintMatrix(head);
  ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
  ImgLinearPrintTransitionInfo(head);

  if(head->computeRange) {
    includeZeroGain = 0;
    affinityLimit = 0.0;
    andExistLimit = andExistLimit;
    varLimit = MAXINT;
    head->bddLimit = head->bddLimit * 2;
    fprintf(stdout, "Heap DLA affinity %3f, andExist %d\n", 
          affinityLimit, andExistLimit);
    while(1) {
      bOptimize |= ImgLinearClusterUsingHeap(head, affinityLimit, andExistLimit,
                                varLimit, optDir, 1,
                                ImgLinearHeapCompareDeadLiveAffinity);
      ImgLinearRefineRelation(head);

      if(ImgCheckRangeTestAndOverapproximate(head))     break;
    }

    ImgCountOnsetDisjunctiveArray(head);
    ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
    ImgLinearPrintTransitionInfo(head);

  }

  return(bOptimize);
}

/**Function********************************************************************

  Synopsis    [Count onset of relation array]

  Description [Count onset of relation array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void 
ImgCountOnsetDisjunctiveArray(Relation_t *head)
{
EpDouble tepd;
char strValue[1024];
bdd_t *varBdd;
mdd_manager *mgr;
array_t *bddVarArray;
Conjunct_t *conjunct;
int count, i, j, id;
double onSet;

  mgr = head->mgr;
  count = 0;
  EpdConvert((double)1.0, &tepd);
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    bddVarArray = array_alloc(bdd_t *, 0);
    for(j=0; j<conjunct->nSize; j++) {
      id = conjunct->supList[j];
      varBdd = bdd_get_variable(mgr, id);
      array_insert_last(bdd_t *, bddVarArray, varBdd);
    }
    /**
    bdd_epd_count_onset(conjunct->relation, bddVarArray, &epd);
    EpdMultiply2(&tepd, &epd);
    **/
    onSet = bdd_count_onset(conjunct->relation, bddVarArray);
    EpdMultiply(&tepd, onSet);
    count += conjunct->nSize;
    mdd_array_free(bddVarArray);
  }

  if(count < head->nRange) {
    EpdMultiply(&tepd, pow(2, (double)(head->nRange-count)));
  }
  EpdGetString(&tepd, strValue);
  (void) fprintf(vis_stdout, "%-20s%10s\n", "range =", strValue);

}

/**Function********************************************************************

  Synopsis    [Check range of variables]

  Description [Check range of variables]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static int
ImgCheckRangeTestAndOverapproximate(Relation_t *head)
{
Conjunct_t *conjunct;
VarLife_t **varArray, *var;
int nVarArray, i, k, count;
int index;
int *varType;
int allRangeFlag;
bdd_t *relation, *simpleRelation, *varBdd;


  allRangeFlag = 1;
  for(i=0; i<head->nSize; i++) {
    conjunct = head->conjunctArray[i];
    if(conjunct->nRange != conjunct->nSize) {
      allRangeFlag = 0;
      break;
    }
  }

  if(allRangeFlag == 1) return(1);

  varArray = head->varArray;
  varType = head->varType;
  nVarArray = head->nVarArray;
  /**
  maxIndex = -1;
  maxSize = 0;
  for(i=0; i<nVarArray; i++) {
    var = varArray[i];
    if(varType[var->id] == 2)   continue;
    if(var->nSize > maxSize) {
      maxIndex = i;
      maxSize = var->nSize;
    }
  }

  if(maxIndex == -1)    return(1);
  **/
  count = head->nEffDomain + head->nEffQuantify;
  if(count == 0)        return(1);

  varArray = ALLOC(VarLife_t *, head->nVarArray);
  memcpy(varArray, head->varArray, sizeof(VarLife_t *)*head->nVarArray);
  qsort(varArray, head->nVarArray, sizeof(VarLife_t *), ImgLinearCompareVarSize);

  if(count != 0) {
    count = (count / 10);
    if(count == 0) count = 1;
  }
  k=0;
  index = 0;
  while(1) {
    if(index >= count)  break;
    var = varArray[k++];
    if(var->stateVar == 2)      continue;
    index++;
    varBdd = bdd_get_variable(head->mgr, var->id);
    for(i=0; i<var->nSize; i++) {
      conjunct = head->conjunctArray[var->relArr[i]];
      relation = conjunct->relation;
      simpleRelation = bdd_smooth_with_cube(relation, varBdd);
      if(bdd_equal(relation, simpleRelation)) {
        bdd_free(simpleRelation);
        continue;
      }
      bdd_free(relation);
  
      conjunct->relation = simpleRelation;
      conjunct->bModified = 1;
      head->bModified = 1;
      head->bRefineVarArray = 1;
      ImgLinearConjunctRefine(head, conjunct);
    }
  }
  free(varArray);

  ImgLinearRefineRelation(head);
  ImgLinearConjunctOrderMainCC(head, 0);
  ImgLinearRefineRelation(head);

  ImgLinearSetEffectiveNumberOfStateVariable(head, 0, 0, 0);
  ImgLinearPrintTransitionInfo(head);
  
  return(0);
}

/**Function********************************************************************

  Synopsis    [Add singleton next state variable case into array]

  Description [Add singleton next state variable case into array]

  SideEffects []

  SeeAlso     []

******************************************************************************/
static void
ImgLinearAddNextStateCase(Relation_t *head)
{
Conjunct_t **newConjunctArray;
int i, j, index;

  index = 0;
  if(head->nNextStateArray) {
    newConjunctArray = ALLOC(Conjunct_t *, head->nSize + head->nNextStateArray);
   for(j=0; j<head->nSize; j++) 
      newConjunctArray[index++] = head->conjunctArray[j];

    for(i=0; i<head->nNextStateArray; i++) 
      newConjunctArray[index++] = head->nextStateArray[i];

    head->nSize = index;
    head->bModified = 1;
    head->bRefineVarArray = 1;
    free(head->conjunctArray);
    head->conjunctArray = newConjunctArray;

    if(head->nextStateArray)    free(head->nextStateArray);
    head->nextStateArray = 0;
  }
}