C++ RandomPermute函数代码示例

/*************************************************************************
* This file randomly permutes the contents of an array.
* flag == 0, don't initialize perm
* flag == 1, set p[i] = i 
**************************************************************************/
void FastRandomPermute(int n, idxtype *p, int flag)
{
  int i, u, v;
  idxtype tmp;

  /* this is for very small arrays */
  if (n < 25) {
    RandomPermute(n, p, flag);
    return;
  }

  if (flag == 1) {
    for (i=0; i<n; i++)
      p[i] = i;
  }

  for (i=0; i<n; i+=8) {
    v = RandomInRange(n-4);
    u = RandomInRange(n-4);
    SWAP(p[v], p[u], tmp);
    SWAP(p[v+1], p[u+1], tmp);
    SWAP(p[v+2], p[u+2], tmp);
    SWAP(p[v+3], p[u+3], tmp);
  }
}

/*************************************************************************
* This function finds a matching using the HEM heuristic
**************************************************************************/
void Match_HEM(CtrlType *ctrl, GraphType *graph)
{
  int i, ii, j, k, nvtxs, cnvtxs, maxidx, dim;
  idxtype *xadj, *vwgt, *adjncy;
  idxtype *match, *cmap, *perm, *tperm;
  realtype curwgt, maxwgt;
  realtype *vvol, *vsurf, *adjwgt, *adjwgtsum;

  dim       = ctrl->dim;
  nvtxs     = graph->nvtxs;
  xadj      = graph->xadj;
  vwgt      = graph->vwgt;
  vvol      = graph->vvol;
  vsurf     = graph->vsurf;
  adjncy    = graph->adjncy;
  adjwgt    = graph->adjwgt;
  adjwgtsum = graph->adjwgtsum;

  cmap = graph->cmap = idxsmalloc(nvtxs, -1, "cmap");
  match = idxsmalloc(nvtxs, -1, "match");

  perm = idxmalloc(nvtxs, "perm");
  tperm = idxmalloc(nvtxs, "tperm");

  RandomPermute(nvtxs, tperm, 1);
  BucketSortKeysInc(nvtxs, vwgt[iamax(nvtxs, vwgt)], vwgt, tperm, perm);
  /* RandomPermute(nvtxs, perm, 1);  */

  cnvtxs = 0;

  /* Compute a heavy-edge style matching giving preferance to small vertices */
  for (ii=0; ii<nvtxs; ii++) {
     i = perm[ii];

     if (match[i] == UNMATCHED) {
       maxidx = i;
       maxwgt = 0.0;

       /* Find a heavy-edge matching, subject to maxvwgt constraints */
       for (j=xadj[i]; j<xadj[i+1]; j++) {
          k = adjncy[j];
          curwgt = 1.0/ARATIO2(dim, vsurf[i]+vsurf[k]+adjwgtsum[i]+adjwgtsum[k]-
                   2.0*adjwgt[j], vvol[i]+vvol[k]);
          if (match[k] == UNMATCHED && vwgt[i]+vwgt[k] <= ctrl->maxsize &&
              curwgt > maxwgt) {
            maxwgt = curwgt;
            maxidx = k;
          }
       }

       cmap[i] = cmap[maxidx] = cnvtxs++;
       match[i] = maxidx;
       match[maxidx] = i;
     }
  }

  CreateCoarseGraph(graph, cnvtxs, match, perm);

  IMfree((void**)&tperm, &perm, &match, LTERM);
}

int main(int argc, char **argv) {

    long *X, *Tmp, n, i;
    double *D;

    printf("Test RandomPermute: ");
    n=1000 ;

    X  = (long *) malloc(n* sizeof(long)) ;
    Tmp = (long *) malloc(n* sizeof(long)) ;
    D  = (double *) malloc(n* sizeof(double)) ;
    if ( X == NULL || Tmp  == NULL || D == NULL){
        printf("Error\n") ;
        exit(1);
    }

    for (i=0; i<n; i++){
        X[i] = i ;
        D[i] = i;
    }
#ifdef INFO2
    printf("RAND_MAX = %ld ", (long)(RAND_MAX) );
#endif
    
    /* Permute randomly */
    RandomPermute(X,NULL,D,NULL,0,n-1);

    /* Check result values and corresponding indices */
    for (i=0; i<n; i++){ 
        if (X[i] != (long)(D[i]+0.5) || X[i] < 0 || X[i] >= n){
          /* round to nearest integer */
            printf("Error\n") ;
            exit(1);
        }
    }

    /* Check whether X is a permutation of 0..n-1.
       Use Tmp as a temporary array */ 
    for (i=0; i<n; i++) 
        Tmp[i] = -1; 

    for (i=0; i<n; i++){ 
        Tmp[X[i]]= X[i];
    }

    for (i=0; i<n; i++){  
        if (Tmp[i] != i){
            printf("Error\n") ; 
            exit(1); 
        } 
    }

    printf("OK\n") ;
    exit(0);

} /* end main */

/*************************************************************************
* This function finds a matching using the HEM heuristic
**************************************************************************/
void MCMatch_HEM(CtrlType *ctrl, GraphType *graph)
{
  int i, ii, j, k, nvtxs, cnvtxs, ncon, maxidx, maxwgt;
  idxtype *xadj, *adjncy, *adjwgt;
  idxtype *match, *cmap, *perm;
  float *nvwgt;

  IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->MatchTmr));

  nvtxs = graph->nvtxs;
  ncon = graph->ncon;
  xadj = graph->xadj;
  nvwgt = graph->nvwgt;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;

  cmap = graph->cmap;
  match = idxset(nvtxs, UNMATCHED, idxwspacemalloc(ctrl, nvtxs));

  perm = idxwspacemalloc(ctrl, nvtxs);
  RandomPermute(nvtxs, perm, 1);

  cnvtxs = 0;
  for (ii=0; ii<nvtxs; ii++) {
    i = perm[ii];

    if (match[i] == UNMATCHED) {  /* Unmatched */
      maxidx = i;
      maxwgt = 0;

      /* Find a heavy-edge matching, subject to maxvwgt constraints */
      for (j=xadj[i]; j<xadj[i+1]; j++) {
        k = adjncy[j];
        if (match[k] == UNMATCHED && maxwgt <= adjwgt[j] &&
               AreAllVwgtsBelowFast(ncon, nvwgt+i*ncon, nvwgt+k*ncon, ctrl->nmaxvwgt)) {
          maxwgt = adjwgt[j];
          maxidx = adjncy[j];
        }
      }

      cmap[i] = cmap[maxidx] = cnvtxs++;
      match[i] = maxidx;
      match[maxidx] = i;
    }
  }

  IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->MatchTmr));

  CreateCoarseGraph(ctrl, graph, cnvtxs, match, perm);

  idxwspacefree(ctrl, nvtxs);
  idxwspacefree(ctrl, nvtxs);
}

/*************************************************************************
* This function finds a matching using the HEM heuristic
**************************************************************************/
void Match_RM(CtrlType *ctrl, GraphType *graph)
{
  int i, ii, j, nvtxs, cnvtxs, maxidx;
  idxtype *xadj, *vwgt, *adjncy, *adjwgt;
  idxtype *match, *cmap, *perm;

  IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->MatchTmr));

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  vwgt = graph->vwgt;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;

  cmap = graph->cmap;
  match = idxset(nvtxs, UNMATCHED, idxwspacemalloc(ctrl, nvtxs));

  perm = idxwspacemalloc(ctrl, nvtxs);
  RandomPermute(nvtxs, perm, 1);

  cnvtxs = 0;
  for (ii=0; ii<nvtxs; ii++) {
    i = perm[ii];

    if (match[i] == UNMATCHED) {  /* Unmatched */
      maxidx = i;

      /* Find a random matching, subject to maxvwgt constraints */
      for (j=xadj[i]; j<xadj[i+1]; j++) {
        if (match[adjncy[j]] == UNMATCHED && vwgt[i]+vwgt[adjncy[j]] <= ctrl->maxvwgt) {
          maxidx = adjncy[j];
          break;
        }
      }

      cmap[i] = cmap[maxidx] = cnvtxs++;
      match[i] = maxidx;
      match[maxidx] = i;
    }
  }

  IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->MatchTmr));

  CreateCoarseGraph(ctrl, graph, cnvtxs, match, perm);

  idxwspacefree(ctrl, nvtxs);
  idxwspacefree(ctrl, nvtxs);
}

/*************************************************************************
* This function generates random initialization 
**************************************************************************/
void RandomInit(int n, int k, idxtype *label)
{
  int i, chunksize, j;
  idxtype tmp;
  idxtype *p= idxmalloc(n, "Util: RandomInit\n");

  RandomPermute(n, p, 1);
  chunksize = n / k +1;
  j=0;
  for (i=0; i<n; i++){
    label[p[i]] = j;
    if ((i+1)% chunksize ==0)
      j++;
  }
  free (p);
}

/*************************************************************************
* This function finds a matching using the HEM heuristic
**************************************************************************/
void Match_RM(CtrlType *ctrl, GraphType *graph)
{
  int i, ii, j, k, nvtxs, cnvtxs, maxidx;
  idxtype *xadj, *vwgt, *adjncy;
  idxtype *match, *cmap, *perm;

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  vwgt = graph->vwgt;
  adjncy = graph->adjncy;

  cmap = graph->cmap = idxsmalloc(nvtxs, -1, "graph->cmap");
  match = idxsmalloc(nvtxs, -1, "match");
  perm = idxmalloc(nvtxs, "perm");

  RandomPermute(nvtxs, perm, 1);

  cnvtxs = 0;
  for (ii=0; ii<nvtxs; ii++) {
     i = perm[ii];

     if (match[i] == UNMATCHED) {
       maxidx = i;

       /* Find a random matching, subject to maxvwgt constraints */
       for (j=xadj[i]; j<xadj[i+1]; j++) {
          k = adjncy[j];
          if (match[k] == UNMATCHED && vwgt[i]+vwgt[k] <= ctrl->maxsize) {
            maxidx = k;
            break;
          }
       }

       cmap[i] = cmap[maxidx] = cnvtxs++;
       match[i] = maxidx;
       match[maxidx] = i;
     }
  }

  CreateCoarseGraph(graph, cnvtxs, match, perm);

  IMfree((void**)&match, &perm, LTERM);
}

/*************************************************************************
* This function finds a matching using the HEM heuristic
**************************************************************************/
void EstimateCFraction(int nvtxs, idxtype *xadj, idxtype *adjncy, floattype *vfraction, floattype *efraction)
{
  int i, ii, j, cnvtxs, cnedges, maxidx;
  idxtype *match, *cmap, *perm;

  cmap = idxmalloc(nvtxs, "cmap");
  match = idxsmalloc(nvtxs, UNMATCHED, "match");
  perm = idxmalloc(nvtxs, "perm");
  RandomPermute(nvtxs, perm, 1);

  cnvtxs = 0;
  for (ii=0; ii<nvtxs; ii++) {
    i = perm[ii];

    if (match[i] == UNMATCHED) {  /* Unmatched */
      maxidx = i;

      /* Find a random matching, subject to maxvwgt constraints */
      for (j=xadj[i]; j<xadj[i+1]; j++) {
        if (match[adjncy[j]] == UNMATCHED) {
          maxidx = adjncy[j];
          break;
        }
      }

      cmap[i] = cmap[maxidx] = cnvtxs++;
      match[i] = maxidx;
      match[maxidx] = i;
    }
  }

  cnedges = ComputeCoarseGraphSize(nvtxs, xadj, adjncy, cnvtxs, cmap, match, perm);

  *vfraction = (1.0*cnvtxs)/(1.0*nvtxs);
  *efraction = (1.0*cnedges)/(1.0*xadj[nvtxs]);

  GKfree(&cmap, &match, &perm, LTERM);
}

/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void MCRandom_KWayEdgeRefineHorizontal(CtrlType *ctrl, GraphType *graph, int nparts, 
       float *orgubvec, int npasses)
{
  int i, ii, iii, j, /*jj,*/ k, /*l,*/ pass, nvtxs, ncon, nmoves, nbnd, myndegrees, same; 
  int from, me, to, oldcut, gain;
  idxtype *xadj, *adjncy, *adjwgt;
  idxtype *where, *perm, *bndptr, *bndind;
  EDegreeType *myedegrees;
  RInfoType *myrinfo;
  float *npwgts, *nvwgt, *minwgt, *maxwgt, maxlb, minlb, ubvec[MAXNCON], tvec[MAXNCON];

  nvtxs = graph->nvtxs;
  ncon = graph->ncon;
  xadj = graph->xadj;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;

  bndptr = graph->bndptr;
  bndind = graph->bndind;

  where = graph->where;
  npwgts = graph->npwgts;
  
  /* Setup the weight intervals of the various subdomains */
  minwgt =  fwspacemalloc(ctrl, nparts*ncon);
  maxwgt = fwspacemalloc(ctrl, nparts*ncon);

  /* See if the orgubvec consists of identical constraints */
  maxlb = minlb = orgubvec[0];
  for (i=1; i<ncon; i++) {
    minlb = (orgubvec[i] < minlb ? orgubvec[i] : minlb);
    maxlb = (orgubvec[i] > maxlb ? orgubvec[i] : maxlb);
  }
  same = (fabs(maxlb-minlb) < .01 ? 1 : 0);


  /* Let's not get very optimistic. Let Balancing do the work */
  ComputeHKWayLoadImbalance(ncon, nparts, npwgts, ubvec);
  for (i=0; i<ncon; i++)
    ubvec[i] = amax(ubvec[i], orgubvec[i]);

  if (!same) {
    for (i=0; i<nparts; i++) {
      for (j=0; j<ncon; j++) {
        maxwgt[i*ncon+j] = ubvec[j]/nparts;
        minwgt[i*ncon+j] = 1.0/(ubvec[j]*nparts);
      }
    }
  }
  else {
    maxlb = ubvec[0];
    for (i=1; i<ncon; i++) 
      maxlb = (ubvec[i] > maxlb ? ubvec[i] : maxlb);

    for (i=0; i<nparts; i++) {
      for (j=0; j<ncon; j++) {
        maxwgt[i*ncon+j] = maxlb/nparts;
        minwgt[i*ncon+j] = 1.0/(maxlb*nparts);
      }
    }
  }


  perm = idxwspacemalloc(ctrl, nvtxs);

  if (ctrl->dbglvl&DBG_REFINE) {
    printf("Partitions: [%5.4f %5.4f], Nv-Nb[%6d %6d]. Cut: %6d, LB: ",
            npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], 
            graph->nvtxs, graph->nbnd, graph->mincut);
    ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec);
    for (i=0; i<ncon; i++)
      printf("%.3f ", tvec[i]);
    printf("\n");
  }

  for (pass=0; pass<npasses; pass++) {
    ASSERT(ComputeCut(graph, where) == graph->mincut);

    oldcut = graph->mincut;
    nbnd = graph->nbnd;

    RandomPermute(nbnd, perm, 1);
    for (nmoves=iii=0; iii<graph->nbnd; iii++) {
      ii = perm[iii];
      if (ii >= nbnd)
        continue;
      i = bndind[ii];

      myrinfo = graph->rinfo+i;

      if (myrinfo->ed >= myrinfo->id) { /* Total ED is too high */
        from = where[i];
        nvwgt = graph->nvwgt+i*ncon;

        if (myrinfo->id > 0 && AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, -1.0, nvwgt, minwgt+from*ncon)) 
          continue;   /* This cannot be moved! */

//.........这里部分代码省略.........

/*************************************************************************
* This function performs an edge-based FM refinement
**************************************************************************/
void MocGeneral2WayBalance2(CtrlType *ctrl, GraphType *graph, float *tpwgts, float *ubvec)
{
  int i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, limit, tmp, cnum;
  idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind;
  idxtype *moved, *swaps, *perm, *qnum;
  float *nvwgt, *npwgts, origbal[MAXNCON], minbal[MAXNCON], newbal[MAXNCON];
  PQueueType parts[MAXNCON][2];
  int higain, oldgain, mincut, newcut, mincutorder;
  float *maxwgt, *minwgt, tvec[MAXNCON];


  nvtxs = graph->nvtxs;
  ncon = graph->ncon;
  xadj = graph->xadj;
  nvwgt = graph->nvwgt;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;
  where = graph->where;
  id = graph->id;
  ed = graph->ed;
  npwgts = graph->npwgts;
  bndptr = graph->bndptr;
  bndind = graph->bndind;

  moved = idxwspacemalloc(ctrl, nvtxs);
  swaps = idxwspacemalloc(ctrl, nvtxs);
  perm = idxwspacemalloc(ctrl, nvtxs);
  qnum = idxwspacemalloc(ctrl, nvtxs);

  limit = amin(amax(0.01*nvtxs, 15), 100);

  /* Setup the weight intervals of the two subdomains */
  minwgt = fwspacemalloc(ctrl, 2*ncon);
  maxwgt = fwspacemalloc(ctrl, 2*ncon);

  for (i=0; i<2; i++) {
    for (j=0; j<ncon; j++) {
      maxwgt[i*ncon+j] = tpwgts[i]*ubvec[j];
      minwgt[i*ncon+j] = tpwgts[i]*(1.0/ubvec[j]);
    }
  }


  /* Initialize the queues */
  for (i=0; i<ncon; i++) {
    PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1);
    PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1);
  }
  for (i=0; i<nvtxs; i++)
    qnum[i] = samax(ncon, nvwgt+i*ncon);

  Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, origbal);
  for (i=0; i<ncon; i++) 
    minbal[i] = origbal[i];

  newcut = mincut = graph->mincut;
  mincutorder = -1;

  if (ctrl->dbglvl&DBG_REFINE) {
    printf("Parts: [");
    for (l=0; l<ncon; l++)
      printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
    printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: ", tpwgts[0], tpwgts[1], 
            graph->nvtxs, graph->nbnd, graph->mincut);
    for (i=0; i<ncon; i++)
      printf("%.3f ", origbal[i]);
    printf("[B]\n");
  }

  idxset(nvtxs, -1, moved);

  ASSERT(ComputeCut(graph, where) == graph->mincut);
  ASSERT(CheckBnd(graph));

  /* Insert all nodes in the priority queues */
  nbnd = graph->nbnd;
  RandomPermute(nvtxs, perm, 1);
  for (ii=0; ii<nvtxs; ii++) {
    i = perm[ii];
    PQueueInsert(&parts[qnum[i]][where[i]], i, ed[i]-id[i]);
  }


  for (nswaps=0; nswaps<nvtxs; nswaps++) {
    if (AreAllBelow(ncon, minbal, ubvec))
      break;

    SelectQueue3(ncon, npwgts, tpwgts, &from, &cnum, parts, maxwgt);
    to = (from+1)%2;

    if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1)
      break;

    saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
    saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1);
    newcut -= (ed[higain]-id[higain]);
    Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, newbal);
//.........这里部分代码省略.........

/*************************************************************************
* This function performs a node-based FM refinement 
**************************************************************************/
void FM_2WayNodeBalance(CtrlType *ctrl, GraphType *graph, float ubfactor)
{
  idxtype i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps;
  idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr;
  idxtype *perm, *moved;
  PQueueType parts; 
  NRInfoType *rinfo;
  idxtype higain, oldgain;	
  idxtype pass, to, other;

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  adjncy = graph->adjncy;
  vwgt = graph->vwgt;

  bndind = graph->bndind;
  bndptr = graph->bndptr;
  where = graph->where;
  pwgts = graph->pwgts;
  rinfo = graph->nrinfo;

  if (idxtype_abs(pwgts[0]-pwgts[1]) < (int)((ubfactor-1.0)*(pwgts[0]+pwgts[1])))
    return;
  if (idxtype_abs(pwgts[0]-pwgts[1]) < 3*idxsum(nvtxs, vwgt, 1)/nvtxs)
    return;

  to = (pwgts[0] < pwgts[1] ? 0 : 1); 
  other = (to+1)%2;

  PQueueInit(ctrl, &parts, nvtxs, ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt));

  perm = idxwspacemalloc(ctrl, nvtxs);
  moved = idxset(nvtxs, -1, idxwspacemalloc(ctrl, nvtxs));

  IFSET(ctrl->dbglvl, DBG_REFINE,
    mprintf("Partitions: [%6D %6D] Nv-Nb[%6D %6D]. ISep: %6D [B]\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));

  nbnd = graph->nbnd;
  RandomPermute(nbnd, perm, 1);
  for (ii=0; ii<nbnd; ii++) {
    i = bndind[perm[ii]];
    ASSERT(where[i] == 2);
    PQueueInsert(&parts, i, vwgt[i]-rinfo[i].edegrees[other]);
  }

  ASSERT(CheckNodeBnd(graph, nbnd));
  ASSERT(CheckNodePartitionParams(graph));

  /******************************************************
  * Get into the FM loop
  *******************************************************/
  for (nswaps=0; nswaps<nvtxs; nswaps++) {
    if ((higain = PQueueGetMax(&parts)) == -1)
      break;

    moved[higain] = 1;

    if (pwgts[other] - rinfo[higain].edegrees[other] < (pwgts[0]+pwgts[1])/2) 
      continue;
#ifdef XXX
    if (pwgts[other] - rinfo[higain].edegrees[other] < pwgts[to]+vwgt[higain]) 
      break;
#endif

    ASSERT(bndptr[higain] != -1);

    pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[other]);

    BNDDelete(nbnd, bndind, bndptr, higain);
    pwgts[to] += vwgt[higain];
    where[higain] = to;

    IFSET(ctrl->dbglvl, DBG_MOVEINFO,
          mprintf("Moved %6D to %3D, Gain: %3D, \t[%5D %5D %5D]\n", higain, to, vwgt[higain]-rinfo[higain].edegrees[other], pwgts[0], pwgts[1], pwgts[2]));


    /**********************************************************
    * Update the degrees of the affected nodes
    ***********************************************************/
    for (j=xadj[higain]; j<xadj[higain+1]; j++) {
      k = adjncy[j];
      if (where[k] == 2) { /* For the in-separator vertices modify their edegree[to] */
        rinfo[k].edegrees[to] += vwgt[higain];
      }
      else if (where[k] == other) { /* This vertex is pulled into the separator */
        ASSERTP(bndptr[k] == -1, ("%d %d %d\n", k, bndptr[k], where[k]));
        BNDInsert(nbnd, bndind, bndptr, k);

        where[k] = 2;
        pwgts[other] -= vwgt[k];

        edegrees = rinfo[k].edegrees;
        edegrees[0] = edegrees[1] = 0;
        for (jj=xadj[k]; jj<xadj[k+1]; jj++) {
          kk = adjncy[jj];
          if (where[kk] != 2) 
            edegrees[where[kk]] += vwgt[kk];
//.........这里部分代码省略.........

/*************************************************************************
* This function performs a node-based FM refinement 
**************************************************************************/
void FM_2WayNodeRefineEqWgt(CtrlType *ctrl, GraphType *graph, idxtype npasses)
{
  idxtype i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps, nmind;
  idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr;
  idxtype *mptr, *mind, *moved, *swaps, *perm;
  PQueueType parts[2]; 
  NRInfoType *rinfo;
  idxtype higain, oldgain, mincut, initcut, mincutorder;	
  idxtype pass, to, other, limit;
  idxtype mindiff, newdiff;
  idxtype u[2], g[2];

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  adjncy = graph->adjncy;
  vwgt = graph->vwgt;

  bndind = graph->bndind;
  bndptr = graph->bndptr;
  where = graph->where;
  pwgts = graph->pwgts;
  rinfo = graph->nrinfo;


  i = ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt);
  PQueueInit(ctrl, &parts[0], nvtxs, i);
  PQueueInit(ctrl, &parts[1], nvtxs, i);

  moved = idxwspacemalloc(ctrl, nvtxs);
  swaps = idxwspacemalloc(ctrl, nvtxs);
  mptr  = idxwspacemalloc(ctrl, nvtxs+1);
  mind  = idxwspacemalloc(ctrl, nvtxs);
  perm  = idxwspacemalloc(ctrl, nvtxs);

  IFSET(ctrl->dbglvl, DBG_REFINE,
    mprintf("Partitions: [%6D %6D] Nv-Nb[%6D %6D]. ISep: %6D\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));

  for (pass=0; pass<npasses; pass++) {
    idxset(nvtxs, -1, moved);
    PQueueReset(&parts[0]);
    PQueueReset(&parts[1]);

    mincutorder = -1;
    initcut = mincut = graph->mincut;
    nbnd = graph->nbnd;

    RandomPermute(nbnd, perm, 1);
    for (ii=0; ii<nbnd; ii++) {
      i = bndind[perm[ii]];
      ASSERT(where[i] == 2);
      PQueueInsert(&parts[0], i, vwgt[i]-rinfo[i].edegrees[1]);
      PQueueInsert(&parts[1], i, vwgt[i]-rinfo[i].edegrees[0]);
    }

    ASSERT(CheckNodeBnd(graph, nbnd));
    ASSERT(CheckNodePartitionParams(graph));

    limit = (ctrl->oflags&OFLAG_COMPRESS ? amin(5*nbnd, 400) : amin(2*nbnd, 300));

    /******************************************************
    * Get into the FM loop
    *******************************************************/
    mptr[0] = nmind = 0;
    mindiff = idxtype_abs(pwgts[0]-pwgts[1]);
    to = (pwgts[0] < pwgts[1] ? 0 : 1);
    for (nswaps=0; nswaps<nvtxs; nswaps++) {
      to = (pwgts[0] < pwgts[1] ? 0 : 1);

      if (pwgts[0] == pwgts[1]) {
        u[0] = PQueueSeeMax(&parts[0]);  
        u[1] = PQueueSeeMax(&parts[1]);
        if (u[0] != -1 && u[1] != -1) {
          g[0] = vwgt[u[0]]-rinfo[u[0]].edegrees[1];
          g[1] = vwgt[u[1]]-rinfo[u[1]].edegrees[0];

          to = (g[0] > g[1] ? 0 : (g[0] < g[1] ? 1 : pass%2)); 
        }
      }
      other = (to+1)%2;

      if ((higain = PQueueGetMax(&parts[to])) == -1)
        break;

      if (moved[higain] == -1) /* Delete if it was in the separator originally */
        PQueueDelete(&parts[other], higain, vwgt[higain]-rinfo[higain].edegrees[to]);

      ASSERT(bndptr[higain] != -1);

      pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[other]);

      newdiff = idxtype_abs(pwgts[to]+vwgt[higain] - (pwgts[other]-rinfo[higain].edegrees[other]));
      if (pwgts[2] < mincut || (pwgts[2] == mincut && newdiff < mindiff)) {
        mincut = pwgts[2];
        mincutorder = nswaps;
        mindiff = newdiff;
      }
      else {
//.........这里部分代码省略.........

/*************************************************************************
* This function performs a node-based FM refinement. This is the 
* one-way version 
**************************************************************************/
void FM_2WayNodeRefine_OneSided(CtrlType *ctrl, GraphType *graph, float ubfactor, idxtype npasses)
{
  idxtype i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps, nmind;
  idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr;
  idxtype *mptr, *mind, *swaps, *perm;
  PQueueType parts; 
  NRInfoType *rinfo;
  idxtype higain, oldgain, mincut, initcut, mincutorder;	
  idxtype pass, to, other, limit;
  idxtype badmaxpwgt, mindiff, newdiff;

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  adjncy = graph->adjncy;
  vwgt = graph->vwgt;

  bndind = graph->bndind;
  bndptr = graph->bndptr;
  where = graph->where;
  pwgts = graph->pwgts;
  rinfo = graph->nrinfo;

  PQueueInit(ctrl, &parts, nvtxs, ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt));

  perm  = idxwspacemalloc(ctrl, nvtxs);
  swaps = idxwspacemalloc(ctrl, nvtxs);
  mptr  = idxwspacemalloc(ctrl, nvtxs+1);
  mind  = idxwspacemalloc(ctrl, nvtxs);

  IFSET(ctrl->dbglvl, DBG_REFINE,
    mprintf("Partitions-N1: [%6D %6D] Nv-Nb[%6D %6D]. ISep: %6D\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));

  badmaxpwgt = (int)(ubfactor*(pwgts[0]+pwgts[1]+pwgts[2])/2);

  to = (pwgts[0] < pwgts[1] ? 1 : 0);
  for (pass=0; pass<npasses; pass++) {
    other = to; 
    to = (to+1)%2;

    PQueueReset(&parts);

    mincutorder = -1;
    initcut = mincut = graph->mincut;
    nbnd = graph->nbnd;

    RandomPermute(nbnd, perm, 1);
    for (ii=0; ii<nbnd; ii++) {
      i = bndind[perm[ii]];
      ASSERT(where[i] == 2);
      PQueueInsert(&parts, i, vwgt[i]-rinfo[i].edegrees[other]);
    }

    ASSERT(CheckNodeBnd(graph, nbnd));
    ASSERT(CheckNodePartitionParams(graph));

    limit = (ctrl->oflags&OFLAG_COMPRESS ? amin(5*nbnd, 400) : amin(2*nbnd, 300));

    /******************************************************
    * Get into the FM loop
    *******************************************************/
    mptr[0] = nmind = 0;
    mindiff = idxtype_abs(pwgts[0]-pwgts[1]);
    for (nswaps=0; nswaps<nvtxs; nswaps++) {

      if ((higain = PQueueGetMax(&parts)) == -1)
        break;

      ASSERT(bndptr[higain] != -1);

      if (pwgts[to]+vwgt[higain] > badmaxpwgt)
        break;  /* No point going any further. Balance will be bad */

      pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[other]);

      newdiff = idxtype_abs(pwgts[to]+vwgt[higain] - (pwgts[other]-rinfo[higain].edegrees[other]));
      if (pwgts[2] < mincut || (pwgts[2] == mincut && newdiff < mindiff)) {
        mincut = pwgts[2];
        mincutorder = nswaps;
        mindiff = newdiff;
      }
      else {
        if (nswaps - mincutorder > limit) {
          pwgts[2] += (vwgt[higain]-rinfo[higain].edegrees[other]);
          break; /* No further improvement, break out */
        }
      }

      BNDDelete(nbnd, bndind, bndptr, higain);
      pwgts[to] += vwgt[higain];
      where[higain] = to;
      swaps[nswaps] = higain;  


      /**********************************************************
      * Update the degrees of the affected nodes
      ***********************************************************/
//.........这里部分代码省略.........

/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void MCGreedy_KWayEdgeBalanceHorizontal(CtrlType *ctrl, GraphType *graph, int nparts, 
       float *ubvec, int npasses)
{
  int i, ii, /*iii,*/ j, /*jj,*/ k, /*l,*/ pass, nvtxs, ncon, nbnd, myndegrees, oldgain, gain, nmoves; 
  int from, me, to, oldcut;
  idxtype *xadj, *adjncy, *adjwgt;
  idxtype *where, *perm, *bndptr, *bndind, *moved;
  EDegreeType *myedegrees;
  RInfoType *myrinfo;
  PQueueType queue;
  float *npwgts, *nvwgt, *minwgt, *maxwgt, tvec[MAXNCON];

  nvtxs = graph->nvtxs;
  ncon = graph->ncon;
  xadj = graph->xadj;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;

  bndind = graph->bndind;
  bndptr = graph->bndptr;

  where = graph->where;
  npwgts = graph->npwgts;
  
  /* Setup the weight intervals of the various subdomains */
  minwgt =  fwspacemalloc(ctrl, ncon*nparts);
  maxwgt = fwspacemalloc(ctrl, ncon*nparts);

  for (i=0; i<nparts; i++) {
    for (j=0; j<ncon; j++) {
      maxwgt[i*ncon+j] = ubvec[j]/nparts;
      minwgt[i*ncon+j] = 1.0/(ubvec[j]*nparts);
    }
  }

  perm = idxwspacemalloc(ctrl, nvtxs);
  moved = idxwspacemalloc(ctrl, nvtxs);

  PQueueInit(ctrl, &queue, nvtxs, graph->adjwgtsum[idxamax(nvtxs, graph->adjwgtsum)]);

  if (ctrl->dbglvl&DBG_REFINE) {
    printf("Partitions: [%5.4f %5.4f], Nv-Nb[%6d %6d]. Cut: %6d, LB: ",
            npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], 
            graph->nvtxs, graph->nbnd, graph->mincut);
    ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec);
    for (i=0; i<ncon; i++)
      printf("%.3f ", tvec[i]);
    printf("[B]\n");
  }


  for (pass=0; pass<npasses; pass++) {
    ASSERT(ComputeCut(graph, where) == graph->mincut);

    /* Check to see if things are out of balance, given the tolerance */
    if (MocIsHBalanced(ncon, nparts, npwgts, ubvec))
      break;

    PQueueReset(&queue);
    idxset(nvtxs, -1, moved);

    oldcut = graph->mincut;
    nbnd = graph->nbnd;

    RandomPermute(nbnd, perm, 1);
    for (ii=0; ii<nbnd; ii++) {
      i = bndind[perm[ii]];
      PQueueInsert(&queue, i, graph->rinfo[i].ed - graph->rinfo[i].id);
      moved[i] = 2;
    }

    nmoves = 0;
    for (;;) {
      if ((i = PQueueGetMax(&queue)) == -1) 
        break;
      moved[i] = 1;

      myrinfo = graph->rinfo+i;
      from = where[i];
      nvwgt = graph->nvwgt+i*ncon;

      if (AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, -1.0, nvwgt, minwgt+from*ncon))
        continue;   /* This cannot be moved! */

      myedegrees = myrinfo->edegrees;
      myndegrees = myrinfo->ndegrees;

      for (k=0; k<myndegrees; k++) {
        to = myedegrees[k].pid;
        if (IsHBalanceBetterFT(ncon, nparts, npwgts+from*ncon, npwgts+to*ncon, nvwgt, ubvec))
          break;
      }
      if (k == myndegrees) 
        continue;  /* break out if you did not find a candidate */

      for (j=k+1; j<myndegrees; j++) {
        to = myedegrees[j].pid;
//.........这里部分代码省略.........

/*************************************************************************
* This function balances two partitions by moving boundary nodes
* from the domain that is overweight to the one that is underweight.
**************************************************************************/
void Bnd2WayBalance(CtrlType *ctrl, GraphType *graph, int *tpwgts)
{
  int i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, tmp;
  idxtype *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
  idxtype *moved, *perm;
  PQueueType parts;
  int higain, oldgain, mincut, mindiff;

  nvtxs = graph->nvtxs;
  xadj = graph->xadj;
  vwgt = graph->vwgt;
  adjncy = graph->adjncy;
  adjwgt = graph->adjwgt;
  where = graph->where;
  id = graph->id;
  ed = graph->ed;
  pwgts = graph->pwgts;
  bndptr = graph->bndptr;
  bndind = graph->bndind;

  moved = idxwspacemalloc(ctrl, nvtxs);
  perm = idxwspacemalloc(ctrl, nvtxs);

  /* Determine from which domain you will be moving data */
  mindiff = abs(tpwgts[0]-pwgts[0]);
  from = (pwgts[0] < tpwgts[0] ? 1 : 0);
  to = (from+1)%2;

  IFSET(ctrl->dbglvl, DBG_REFINE, 
     printf("Partitions: [%6d %6d] T[%6d %6d], Nv-Nb[%6d %6d]. ICut: %6d [B]\n",
             pwgts[0], pwgts[1], tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));

  tmp = graph->adjwgtsum[idxamax(nvtxs, graph->adjwgtsum)];
  PQueueInit(ctrl, &parts, nvtxs, tmp);

  idxset(nvtxs, -1, moved);

  ASSERT(ComputeCut(graph, where) == graph->mincut);
  ASSERT(CheckBnd(graph));

  /* Insert the boundary nodes of the proper partition whose size is OK in the priority queue */
  nbnd = graph->nbnd;
  RandomPermute(nbnd, perm, 1);
  for (ii=0; ii<nbnd; ii++) {
    i = perm[ii];
    ASSERT(ed[bndind[i]] > 0 || id[bndind[i]] == 0);
    ASSERT(bndptr[bndind[i]] != -1);
    if (where[bndind[i]] == from && vwgt[bndind[i]] <= mindiff)
      PQueueInsert(&parts, bndind[i], ed[bndind[i]]-id[bndind[i]]);
  }

  mincut = graph->mincut;
  for (nswaps=0; nswaps<nvtxs; nswaps++) {
    if ((higain = PQueueGetMax(&parts)) == -1)
      break;
    ASSERT(bndptr[higain] != -1);

    if (pwgts[to]+vwgt[higain] > tpwgts[to])
      break;

    mincut -= (ed[higain]-id[higain]);
    INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);

    where[higain] = to;
    moved[higain] = nswaps;

    IFSET(ctrl->dbglvl, DBG_MOVEINFO, 
      printf("Moved %6d from %d. [%3d %3d] %5d [%4d %4d]\n", higain, from, ed[higain]-id[higain], vwgt[higain], mincut, pwgts[0], pwgts[1]));

    /**************************************************************
    * Update the id[i]/ed[i] values of the affected nodes
    ***************************************************************/
    SWAP(id[higain], ed[higain], tmp);
    if (ed[higain] == 0 && xadj[higain] < xadj[higain+1]) 
      BNDDelete(nbnd, bndind,  bndptr, higain);

    for (j=xadj[higain]; j<xadj[higain+1]; j++) {
      k = adjncy[j];
      oldgain = ed[k]-id[k];

      kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
      INC_DEC(id[k], ed[k], kwgt);

      /* Update its boundary information and queue position */
      if (bndptr[k] != -1) { /* If k was a boundary vertex */
        if (ed[k] == 0) { /* Not a boundary vertex any more */
          BNDDelete(nbnd, bndind, bndptr, k);
          if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)  /* Remove it if in the queues */
            PQueueDelete(&parts, k, oldgain);
        }
        else { /* If it has not been moved, update its position in the queue */
          if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
            PQueueUpdate(&parts, k, oldgain, ed[k]-id[k]);
        }
      }
      else {
//.........这里部分代码省略.........