ometis.c

Go to the documentation of this file.

/*
 * Copyright 1997, Regents of the University of Minnesota
 *
 * ometis.c
 *
 * This file contains the top level routines for the multilevel recursive
 * bisection algorithm PMETIS.
 *
 * Started 7/24/97
 * George
 *
 * $Id: ometis.c 10513 2011-07-07 22:06:03Z karypis $
 *
 */

#include "metislib.h"


/*************************************************************************/
/*************************************************************************/
int METIS_NodeND(idx_t *nvtxs, idx_t *xadj, idx_t *adjncy, idx_t *vwgt,
          idx_t *options, idx_t *perm, idx_t *iperm) 
{
  int sigrval=0, renumber=0;
  idx_t i, ii, j, l, nnvtxs=0;
  graph_t *graph=NULL;
  ctrl_t *ctrl;
  idx_t *cptr, *cind, *piperm;
  int numflag = 0;

  /* set up malloc cleaning code and signal catchers */
  if (!gk_malloc_init()) 
    return METIS_ERROR_MEMORY;

  gk_sigtrap();

  if ((sigrval = gk_sigcatch()) != 0) 
    goto SIGTHROW;


  /* set up the run time parameters */
  ctrl = SetupCtrl(METIS_OP_OMETIS, options, 1, 3, NULL, NULL);
  if (!ctrl) {
    gk_siguntrap();
    return METIS_ERROR_INPUT;
  }

  /* if required, change the numbering to 0 */
  if (ctrl->numflag == 1) {
    Change2CNumbering(*nvtxs, xadj, adjncy);
    renumber = 1;
  }

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, InitTimers(ctrl));
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->TotalTmr));

  /* prune the dense columns */
  if (ctrl->pfactor > 0.0) { 
    piperm = imalloc(*nvtxs, "OMETIS: piperm");

    graph = PruneGraph(ctrl, *nvtxs, xadj, adjncy, vwgt, piperm, ctrl->pfactor);
    if (graph == NULL) {
      /* if there was no prunning, cleanup the pfactor */
      gk_free((void **)&piperm, LTERM);
      ctrl->pfactor = 0.0;
    }
    else {
      nnvtxs = graph->nvtxs;
      ctrl->compress = 0;  /* disable compression if prunning took place */
    }
  }

  /* compress the graph; note that compression only happens if not prunning 
     has taken place. */
  if (ctrl->compress) { 
    cptr = imalloc(*nvtxs+1, "OMETIS: cptr");
    cind = imalloc(*nvtxs, "OMETIS: cind");

    graph = CompressGraph(ctrl, *nvtxs, xadj, adjncy, vwgt, cptr, cind);
    if (graph == NULL) {
      /* if there was no compression, cleanup the compress flag */
      gk_free((void **)&cptr, &cind, LTERM);
      ctrl->compress = 0; 
    }
    else {
      nnvtxs = graph->nvtxs;
      ctrl->cfactor = 1.0*(*nvtxs)/nnvtxs;
      if (ctrl->cfactor > 1.5 && ctrl->nseps == 1)
        ctrl->nseps = 2;
      //ctrl->nseps = (idx_t)(ctrl->cfactor*ctrl->nseps);
    }
  }

  /* if no prunning and no compression, setup the graph in the normal way. */
  if (ctrl->pfactor == 0.0 && ctrl->compress == 0) 
    graph = SetupGraph(ctrl, *nvtxs, 1, xadj, adjncy, vwgt, NULL, NULL);

  ASSERT(CheckGraph(graph, ctrl->numflag, 1));

  /* allocate workspace memory */
  AllocateWorkSpace(ctrl, graph);

  /* do the nested dissection ordering  */
  if (ctrl->ccorder) 
    MlevelNestedDissectionCC(ctrl, graph, iperm, graph->nvtxs);
  else
    MlevelNestedDissection(ctrl, graph, iperm, graph->nvtxs);


  if (ctrl->pfactor > 0.0) { /* Order any prunned vertices */
    icopy(nnvtxs, iperm, perm);  /* Use perm as an auxiliary array */
    for (i=0; i<nnvtxs; i++)
      iperm[piperm[i]] = perm[i];
    for (i=nnvtxs; i<*nvtxs; i++)
      iperm[piperm[i]] = i;

    gk_free((void **)&piperm, LTERM);
  }
  else if (ctrl->compress) { /* Uncompress the ordering */
    /* construct perm from iperm */
    for (i=0; i<nnvtxs; i++)
      perm[iperm[i]] = i; 
    for (l=ii=0; ii<nnvtxs; ii++) {
      i = perm[ii];
      for (j=cptr[i]; j<cptr[i+1]; j++)
        iperm[cind[j]] = l++;
    }

    gk_free((void **)&cptr, &cind, LTERM);
  }

  for (i=0; i<*nvtxs; i++)
    perm[iperm[i]] = i;

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->TotalTmr));
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, PrintTimers(ctrl));

  /* clean up */
  FreeCtrl(&ctrl);

SIGTHROW:
  /* if required, change the numbering back to 1 */
  if (renumber)
    Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);

  gk_siguntrap();
  gk_malloc_cleanup(0);

  return metis_rcode(sigrval);
}


/*************************************************************************/
/*************************************************************************/
void MlevelNestedDissection(ctrl_t *ctrl, graph_t *graph, idx_t *order, 
         idx_t lastvtx)
{
  idx_t i, j, nvtxs, nbnd;
  idx_t *label, *bndind;
  graph_t *lgraph, *rgraph;

  nvtxs = graph->nvtxs;

  MlevelNodeBisectionMultiple(ctrl, graph);

  IFSET(ctrl->dbglvl, METIS_DBG_SEPINFO, 
      printf("Nvtxs: %6"PRIDX", [%6"PRIDX" %6"PRIDX" %6"PRIDX"]\n", 
        graph->nvtxs, graph->pwgts[0], graph->pwgts[1], graph->pwgts[2]));


  /* Order the nodes in the separator */
  nbnd   = graph->nbnd;
  bndind = graph->bndind;
  label  = graph->label;
  for (i=0; i<nbnd; i++) 
    order[label[bndind[i]]] = --lastvtx;

  SplitGraphOrder(ctrl, graph, &lgraph, &rgraph);

  /* Free the memory of the top level graph */
  FreeGraph(&graph);

  /* Recurse on lgraph first, as its lastvtx depends on rgraph->nvtxs, which
     will not be defined upon return from MlevelNestedDissection. */
  if (lgraph->nvtxs > MMDSWITCH && lgraph->nedges > 0) 
    MlevelNestedDissection(ctrl, lgraph, order, lastvtx-rgraph->nvtxs);
  else {
    MMDOrder(ctrl, lgraph, order, lastvtx-rgraph->nvtxs); 
    FreeGraph(&lgraph);
  }
  if (rgraph->nvtxs > MMDSWITCH && rgraph->nedges > 0) 
    MlevelNestedDissection(ctrl, rgraph, order, lastvtx);
  else {
    MMDOrder(ctrl, rgraph, order, lastvtx); 
    FreeGraph(&rgraph);
  }
}


/*************************************************************************/
/*************************************************************************/
void MlevelNestedDissectionCC(ctrl_t *ctrl, graph_t *graph, idx_t *order, 
         idx_t lastvtx)
{
  idx_t i, j, nvtxs, nbnd, ncmps, rnvtxs, snvtxs;
  idx_t *label, *bndind;
  idx_t *cptr, *cind;
  graph_t **sgraphs;

  nvtxs = graph->nvtxs;

  MlevelNodeBisectionMultiple(ctrl, graph);

  IFSET(ctrl->dbglvl, METIS_DBG_SEPINFO, 
      printf("Nvtxs: %6"PRIDX", [%6"PRIDX" %6"PRIDX" %6"PRIDX"]\n", 
        graph->nvtxs, graph->pwgts[0], graph->pwgts[1], graph->pwgts[2]));

  /* Order the nodes in the separator */
  nbnd   = graph->nbnd;
  bndind = graph->bndind;
  label  = graph->label;
  for (i=0; i<nbnd; i++) 
    order[label[bndind[i]]] = --lastvtx;

  WCOREPUSH;
  cptr  = iwspacemalloc(ctrl, nvtxs+1);
  cind  = iwspacemalloc(ctrl, nvtxs);
  ncmps = FindSepInducedComponents(ctrl, graph, cptr, cind);

  if (ctrl->dbglvl&METIS_DBG_INFO) {
    if (ncmps > 2)
      printf("  Bisection resulted in %"PRIDX" connected components\n", ncmps);
  }
  
  sgraphs = SplitGraphOrderCC(ctrl, graph, ncmps, cptr, cind);

  WCOREPOP;

  /* Free the memory of the top level graph */
  FreeGraph(&graph);

  /* Go and process the subgraphs */
  for (rnvtxs=i=0; i<ncmps; i++) {
    /* Save the number of vertices in sgraphs[i] because sgraphs[i] is freed 
       inside MlevelNestedDissectionCC, and as such it will be undefined. */
    snvtxs = sgraphs[i]->nvtxs;

    if (sgraphs[i]->nvtxs > MMDSWITCH && sgraphs[i]->nedges > 0) {
      MlevelNestedDissectionCC(ctrl, sgraphs[i], order, lastvtx-rnvtxs);
    }
    else {
      MMDOrder(ctrl, sgraphs[i], order, lastvtx-rnvtxs);
      FreeGraph(&sgraphs[i]);
    }
    rnvtxs += snvtxs;
  }

  gk_free((void **)&sgraphs, LTERM);
}


/*************************************************************************/
/*************************************************************************/
void MlevelNodeBisectionMultiple(ctrl_t *ctrl, graph_t *graph)
{
  idx_t i, mincut;
  idx_t *bestwhere;

  /* if the graph is small, just find a single vertex separator */
  if (ctrl->nseps == 1 || graph->nvtxs < (ctrl->compress ? 1000 : 2000)) {
    MlevelNodeBisectionL2(ctrl, graph, LARGENIPARTS);
    return;
  }

  WCOREPUSH;

  bestwhere = iwspacemalloc(ctrl, graph->nvtxs);

  mincut = graph->tvwgt[0];
  for (i=0; i<ctrl->nseps; i++) {
    MlevelNodeBisectionL2(ctrl, graph, LARGENIPARTS);

    if (i == 0 || graph->mincut < mincut) {
      mincut = graph->mincut;
      if (i < ctrl->nseps-1)
        icopy(graph->nvtxs, graph->where, bestwhere);
    }

    if (mincut == 0)
      break;

    if (i < ctrl->nseps-1) 
      FreeRData(graph);
  }

  if (mincut != graph->mincut) {
    icopy(graph->nvtxs, bestwhere, graph->where);
    Compute2WayNodePartitionParams(ctrl, graph);
  }

  WCOREPOP;
}


/*************************************************************************/
/*************************************************************************/
void MlevelNodeBisectionL2(ctrl_t *ctrl, graph_t *graph, idx_t niparts)
{
  idx_t i, mincut, nruns=5;
  graph_t *cgraph; 
  idx_t *bestwhere;

  /* if the graph is small, just find a single vertex separator */
  if (graph->nvtxs < 5000) {
    MlevelNodeBisectionL1(ctrl, graph, niparts);
    return;
  }

  WCOREPUSH;

  ctrl->CoarsenTo = gk_max(100, graph->nvtxs/30);

  cgraph = CoarsenGraphNlevels(ctrl, graph, 4);

  bestwhere = iwspacemalloc(ctrl, cgraph->nvtxs);

  mincut = graph->tvwgt[0];
  for (i=0; i<nruns; i++) {
    MlevelNodeBisectionL1(ctrl, cgraph, 0.7*niparts);

    if (i == 0 || cgraph->mincut < mincut) {
      mincut = cgraph->mincut;
      if (i < nruns-1)
        icopy(cgraph->nvtxs, cgraph->where, bestwhere);
    }

    if (mincut == 0)
      break;

    if (i < nruns-1) 
      FreeRData(cgraph);
  }

  if (mincut != cgraph->mincut) 
    icopy(cgraph->nvtxs, bestwhere, cgraph->where);

  WCOREPOP;

  Refine2WayNode(ctrl, graph, cgraph);

}


/*************************************************************************/
/*************************************************************************/
void MlevelNodeBisectionL1(ctrl_t *ctrl, graph_t *graph, idx_t niparts)
{
  graph_t *cgraph;

  ctrl->CoarsenTo = graph->nvtxs/8;
  if (ctrl->CoarsenTo > 100)
    ctrl->CoarsenTo = 100;
  else if (ctrl->CoarsenTo < 40)
    ctrl->CoarsenTo = 40;

  cgraph = CoarsenGraph(ctrl, graph);

  niparts = gk_max(1, (cgraph->nvtxs <= ctrl->CoarsenTo ? niparts/2: niparts));
  /*niparts = (cgraph->nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);*/
  InitSeparator(ctrl, cgraph, niparts);

  Refine2WayNode(ctrl, graph, cgraph);
}


/*************************************************************************/
/*************************************************************************/
void SplitGraphOrder(ctrl_t *ctrl, graph_t *graph, graph_t **r_lgraph, 
         graph_t **r_rgraph)
{
  idx_t i, ii, j, k, l, istart, iend, mypart, nvtxs, snvtxs[3], snedges[3];
  idx_t *xadj, *vwgt, *adjncy, *adjwgt, *label, *where, *bndptr, *bndind;
  idx_t *sxadj[2], *svwgt[2], *sadjncy[2], *sadjwgt[2], *slabel[2];
  idx_t *rename;
  idx_t *auxadjncy;
  graph_t *lgraph, *rgraph;

  WCOREPUSH;

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->SplitTmr));

  nvtxs   = graph->nvtxs;
  xadj    = graph->xadj;
  vwgt    = graph->vwgt;
  adjncy  = graph->adjncy;
  adjwgt  = graph->adjwgt;
  label   = graph->label;
  where   = graph->where;
  bndptr  = graph->bndptr;
  bndind  = graph->bndind;
  ASSERT(bndptr != NULL);

  rename = iwspacemalloc(ctrl, nvtxs);
  
  snvtxs[0] = snvtxs[1] = snvtxs[2] = snedges[0] = snedges[1] = snedges[2] = 0;
  for (i=0; i<nvtxs; i++) {
    k = where[i];
    rename[i] = snvtxs[k]++;
    snedges[k] += xadj[i+1]-xadj[i];
  }

  lgraph      = SetupSplitGraph(graph, snvtxs[0], snedges[0]);
  sxadj[0]    = lgraph->xadj;
  svwgt[0]    = lgraph->vwgt;
  sadjncy[0]  = lgraph->adjncy; 
  sadjwgt[0]  = lgraph->adjwgt; 
  slabel[0]   = lgraph->label;

  rgraph      = SetupSplitGraph(graph, snvtxs[1], snedges[1]);
  sxadj[1]    = rgraph->xadj;
  svwgt[1]    = rgraph->vwgt;
  sadjncy[1]  = rgraph->adjncy; 
  sadjwgt[1]  = rgraph->adjwgt; 
  slabel[1]   = rgraph->label;

  /* Go and use bndptr to also mark the boundary nodes in the two partitions */
  for (ii=0; ii<graph->nbnd; ii++) {
    i = bndind[ii];
    for (j=xadj[i]; j<xadj[i+1]; j++)
      bndptr[adjncy[j]] = 1;
  }

  snvtxs[0] = snvtxs[1] = snedges[0] = snedges[1] = 0;
  sxadj[0][0] = sxadj[1][0] = 0;
  for (i=0; i<nvtxs; i++) {
    if ((mypart = where[i]) == 2)
      continue;

    istart = xadj[i];
    iend   = xadj[i+1];
    if (bndptr[i] == -1) { /* This is an interior vertex */
      auxadjncy = sadjncy[mypart] + snedges[mypart] - istart;
      for(j=istart; j<iend; j++) 
        auxadjncy[j] = adjncy[j];
      snedges[mypart] += iend-istart;
    }
    else {
      auxadjncy = sadjncy[mypart];
      l = snedges[mypart];
      for (j=istart; j<iend; j++) {
        k = adjncy[j];
        if (where[k] == mypart) 
          auxadjncy[l++] = k;
      }
      snedges[mypart] = l;
    }

    svwgt[mypart][snvtxs[mypart]]    = vwgt[i];
    slabel[mypart][snvtxs[mypart]]   = label[i];
    sxadj[mypart][++snvtxs[mypart]]  = snedges[mypart];
  }

  for (mypart=0; mypart<2; mypart++) {
    iend = snedges[mypart];
    iset(iend, 1, sadjwgt[mypart]);

    auxadjncy = sadjncy[mypart];
    for (i=0; i<iend; i++) 
      auxadjncy[i] = rename[auxadjncy[i]];
  }

  lgraph->nvtxs  = snvtxs[0];
  lgraph->nedges = snedges[0];
  rgraph->nvtxs  = snvtxs[1];
  rgraph->nedges = snedges[1];

  SetupGraph_tvwgt(lgraph);
  SetupGraph_tvwgt(rgraph);

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->SplitTmr));

  *r_lgraph = lgraph;
  *r_rgraph = rgraph;

  WCOREPOP;
}


/*************************************************************************/
/*************************************************************************/
graph_t **SplitGraphOrderCC(ctrl_t *ctrl, graph_t *graph, idx_t ncmps, 
              idx_t *cptr, idx_t *cind)
{
  idx_t i, ii, iii, j, k, l, istart, iend, mypart, nvtxs, snvtxs, snedges;
  idx_t *xadj, *vwgt, *adjncy, *adjwgt, *label, *where, *bndptr, *bndind;
  idx_t *sxadj, *svwgt, *sadjncy, *sadjwgt, *slabel;
  idx_t *rename;
  idx_t *auxadjncy;
  graph_t **sgraphs;

  WCOREPUSH;

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->SplitTmr));

  nvtxs   = graph->nvtxs;
  xadj    = graph->xadj;
  vwgt    = graph->vwgt;
  adjncy  = graph->adjncy;
  adjwgt  = graph->adjwgt;
  label   = graph->label;
  where   = graph->where;
  bndptr  = graph->bndptr;
  bndind  = graph->bndind;
  ASSERT(bndptr != NULL);

  /* Go and use bndptr to also mark the boundary nodes in the two partitions */
  for (ii=0; ii<graph->nbnd; ii++) {
    i = bndind[ii];
    for (j=xadj[i]; j<xadj[i+1]; j++)
      bndptr[adjncy[j]] = 1;
  }

  rename = iwspacemalloc(ctrl, nvtxs);
  
  sgraphs = (graph_t **)gk_malloc(sizeof(graph_t *)*ncmps, "SplitGraphOrderCC: sgraphs");

  /* Go and split the graph a component at a time */
  for (iii=0; iii<ncmps; iii++) {
    irandArrayPermute(cptr[iii+1]-cptr[iii], cind+cptr[iii], cptr[iii+1]-cptr[iii], 0);
    snvtxs = snedges = 0;
    for (j=cptr[iii]; j<cptr[iii+1]; j++) {
      i = cind[j];
      rename[i] = snvtxs++;
      snedges += xadj[i+1]-xadj[i];
    }

    sgraphs[iii] = SetupSplitGraph(graph, snvtxs, snedges);

    sxadj    = sgraphs[iii]->xadj;
    svwgt    = sgraphs[iii]->vwgt;
    sadjncy  = sgraphs[iii]->adjncy;
    sadjwgt  = sgraphs[iii]->adjwgt;
    slabel   = sgraphs[iii]->label;

    snvtxs = snedges = sxadj[0] = 0;
    for (ii=cptr[iii]; ii<cptr[iii+1]; ii++) {
      i = cind[ii];

      istart = xadj[i];
      iend   = xadj[i+1];
      if (bndptr[i] == -1) { /* This is an interior vertex */
        auxadjncy = sadjncy + snedges - istart;
        for(j=istart; j<iend; j++) 
          auxadjncy[j] = adjncy[j];
        snedges += iend-istart;
      }
      else {
        l = snedges;
        for (j=istart; j<iend; j++) {
          k = adjncy[j];
          if (where[k] != 2) 
            sadjncy[l++] = k;
        }
        snedges = l;
      }

      svwgt[snvtxs]    = vwgt[i];
      slabel[snvtxs]   = label[i];
      sxadj[++snvtxs]  = snedges;
    }

    iset(snedges, 1, sadjwgt);
    for (i=0; i<snedges; i++) 
      sadjncy[i] = rename[sadjncy[i]];

    sgraphs[iii]->nvtxs  = snvtxs;
    sgraphs[iii]->nedges = snedges;

    SetupGraph_tvwgt(sgraphs[iii]);
  }

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->SplitTmr));

  WCOREPOP;

  return sgraphs;
}


/*************************************************************************/
/*************************************************************************/
void MMDOrder(ctrl_t *ctrl, graph_t *graph, idx_t *order, idx_t lastvtx)
{
  idx_t i, j, k, nvtxs, nofsub, firstvtx;
  idx_t *xadj, *adjncy, *label;
  idx_t *perm, *iperm, *head, *qsize, *list, *marker;

  WCOREPUSH;

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

  /* Relabel the vertices so that it starts from 1 */
  k = xadj[nvtxs];
  for (i=0; i<k; i++)
    adjncy[i]++;
  for (i=0; i<nvtxs+1; i++)
    xadj[i]++;

  perm   = iwspacemalloc(ctrl, nvtxs+5);
  iperm  = iwspacemalloc(ctrl, nvtxs+5);
  head   = iwspacemalloc(ctrl, nvtxs+5);
  qsize  = iwspacemalloc(ctrl, nvtxs+5);
  list   = iwspacemalloc(ctrl, nvtxs+5);
  marker = iwspacemalloc(ctrl, nvtxs+5);

  genmmd(nvtxs, xadj, adjncy, iperm, perm, 1, head, qsize, list, marker, IDX_MAX, &nofsub);

  label = graph->label;
  firstvtx = lastvtx-nvtxs;
  for (i=0; i<nvtxs; i++)
    order[label[i]] = firstvtx+iperm[i]-1;

  /* Relabel the vertices so that it starts from 0 */
  for (i=0; i<nvtxs+1; i++)
    xadj[i]--;
  k = xadj[nvtxs];
  for (i=0; i<k; i++)
    adjncy[i]--;

  WCOREPOP;
}