ometis.c

多层权核k均值算法

/*
 * 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,v 1.1 1998/11/27 17:59:27 karypis Exp $
 *
 */

#include <metis.h>


/*************************************************************************
* This function is the entry point for OEMETIS
**************************************************************************/
void METIS_EdgeND(int *nvtxs, idxtype *xadj, idxtype *adjncy, int *numflag, int *options, 
                  idxtype *perm, idxtype *iperm) 
{
  int i, j;
  GraphType graph;
  CtrlType ctrl;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_OEMETIS, *nvtxs, 1, xadj, adjncy, NULL, NULL, 0);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = OEMETIS_CTYPE;
    ctrl.IType = OEMETIS_ITYPE;
    ctrl.RType = OEMETIS_RTYPE;
    ctrl.dbglvl = OEMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }
  ctrl.oflags  = 0;
  ctrl.pfactor = -1;
  ctrl.nseps   = 1;

  ctrl.optype = OP_OEMETIS;
  ctrl.CoarsenTo = 20;
  ctrl.maxvwgt = (int) 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);

  InitRandom(-1);

  AllocateWorkSpace(&ctrl, &graph, 2);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, *nvtxs);

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

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

  FreeWorkSpace(&ctrl, &graph);

  if (*numflag == 1)
    Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);
}


/*************************************************************************
* This function is the entry point for ONCMETIS
**************************************************************************/
void METIS_NodeND(int *nvtxs, idxtype *xadj, idxtype *adjncy, int *numflag, int *options, 
                  idxtype *perm, idxtype *iperm) 
{
  int i, ii, j, l, wflag, nflag;
  GraphType graph;
  CtrlType ctrl;
  idxtype *cptr, *cind, *piperm;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType   = ONMETIS_CTYPE;
    ctrl.IType   = ONMETIS_ITYPE;
    ctrl.RType   = ONMETIS_RTYPE;
    ctrl.dbglvl  = ONMETIS_DBGLVL;
    ctrl.oflags  = ONMETIS_OFLAGS;
    ctrl.pfactor = ONMETIS_PFACTOR;
    ctrl.nseps   = ONMETIS_NSEPS;
  }
  else {
    ctrl.CType   = options[OPTION_CTYPE];
    ctrl.IType   = options[OPTION_ITYPE];
    ctrl.RType   = options[OPTION_RTYPE];
    ctrl.dbglvl  = options[OPTION_DBGLVL];
    ctrl.oflags  = options[OPTION_OFLAGS];
    ctrl.pfactor = options[OPTION_PFACTOR];
    ctrl.nseps   = options[OPTION_NSEPS];
  }
  if (ctrl.nseps < 1)
    ctrl.nseps = 1;

  ctrl.optype = OP_ONMETIS;
  ctrl.CoarsenTo = 100;

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  InitRandom(-1);

  if (ctrl.pfactor > 0) { 
    /*============================================================
    * Prune the dense columns
    ==============================================================*/
    piperm = idxmalloc(*nvtxs, "ONMETIS: piperm");

    PruneGraph(&ctrl, &graph, *nvtxs, xadj, adjncy, piperm, (float)(0.1*ctrl.pfactor));
  }
  else if (ctrl.oflags&OFLAG_COMPRESS) {
    /*============================================================
    * Compress the graph 
    ==============================================================*/
    cptr = idxmalloc(*nvtxs+1, "ONMETIS: cptr");
    cind = idxmalloc(*nvtxs, "ONMETIS: cind");

    CompressGraph(&ctrl, &graph, *nvtxs, xadj, adjncy, cptr, cind);

    if (graph.nvtxs >= COMPRESSION_FRACTION*(*nvtxs)) {
      ctrl.oflags--; /* We actually performed no compression */
      GKfree((void**) &cptr, (void**) &cind, LTERM);
    }
    else if (2*graph.nvtxs < *nvtxs && ctrl.nseps == 1)
      ctrl.nseps = 2;
  }
  else {
    SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, NULL, NULL, 0);
  }


  /*=============================================================
  * Do the nested dissection ordering 
  --=============================================================*/
  ctrl.maxvwgt = (int) 1.5*(idxsum(graph.nvtxs, graph.vwgt)/ctrl.CoarsenTo);
  AllocateWorkSpace(&ctrl, &graph, 2);

  if (ctrl.oflags&OFLAG_CCMP) 
    MlevelNestedDissectionCC(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, graph.nvtxs);
  else
    MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, graph.nvtxs);

  FreeWorkSpace(&ctrl, &graph);

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

    GKfree((void**) (void**) &piperm, LTERM);
  }
  else if (ctrl.oflags&OFLAG_COMPRESS) { /* Uncompress the ordering */
    if (graph.nvtxs < COMPRESSION_FRACTION*(*nvtxs)) { 
      /* construct perm from iperm */
      for (i=0; i<graph.nvtxs; i++)
        perm[iperm[i]] = i; 
      for (l=ii=0; ii<graph.nvtxs; ii++) {
        i = perm[ii];
        for (j=cptr[i]; j<cptr[i+1]; j++)
          iperm[cind[j]] = l++;
      }
    }

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


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

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

  if (*numflag == 1)
    Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);

}


/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_NodeWND(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt, int *numflag, 
                   int *options, idxtype *perm, idxtype *iperm) 
{
  int i, j, tvwgt;
  GraphType graph;
  CtrlType ctrl;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, NULL, 2);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = ONMETIS_CTYPE;
    ctrl.IType = ONMETIS_ITYPE;
    ctrl.RType = ONMETIS_RTYPE;
    ctrl.dbglvl = ONMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }

  ctrl.oflags  = OFLAG_COMPRESS;
  ctrl.pfactor = 0;
  ctrl.nseps = 2;
  ctrl.optype = OP_ONMETIS;
  ctrl.CoarsenTo = 100;
  ctrl.maxvwgt = (int) 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);

  InitRandom(-1);

  AllocateWorkSpace(&ctrl, &graph, 2);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, *nvtxs);

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

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

  FreeWorkSpace(&ctrl, &graph);

  if (*numflag == 1)
    Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);
}




/*************************************************************************
* This function takes a graph and produces a bisection of it
**************************************************************************/
void MlevelNestedDissection(CtrlType *ctrl, GraphType *graph, idxtype *order, float ubfactor, int lastvtx)
{
  int i, j, nvtxs, nbnd, tvwgt, tpwgts2[2];
  idxtype *label, *bndind;
  GraphType lgraph, rgraph;

  nvtxs = graph->nvtxs;

  /* Determine the weights of the partitions */
  tvwgt = idxsum(nvtxs, graph->vwgt);
  tpwgts2[0] = tvwgt/2;
  tpwgts2[1] = tvwgt-tpwgts2[0];

  switch (ctrl->optype) {
    case OP_OEMETIS:
      MlevelEdgeBisection(ctrl, graph, tpwgts2, ubfactor);

      IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->SepTmr));
      ConstructMinCoverSeparator(ctrl, graph, ubfactor);
      IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->SepTmr));

      break;
    case OP_ONMETIS:
      MlevelNodeBisectionMultiple(ctrl, graph, tpwgts2, ubfactor);

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

      break;
  }

  /* 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 */
  GKfree((void**) &graph->gdata, (void**) &graph->rdata, (void**) &graph->label, LTERM);

  if (rgraph.nvtxs > MMDSWITCH) 
    MlevelNestedDissection(ctrl, &rgraph, order, ubfactor, lastvtx);
  else {
    MMDOrder(ctrl, &rgraph, order, lastvtx); 
    GKfree((void**) &rgraph.gdata, (void**) &rgraph.rdata, (void**) &rgraph.label, LTERM);
  }
  if (lgraph.nvtxs > MMDSWITCH) 
    MlevelNestedDissection(ctrl, &lgraph, order, ubfactor, lastvtx-rgraph.nvtxs);
  else {
    MMDOrder(ctrl, &lgraph, order, lastvtx-rgraph.nvtxs); 
    GKfree((void**) &lgraph.gdata, (void**) &lgraph.rdata, (void**) &lgraph.label, LTERM);
  }
}


/*************************************************************************
* This function takes a graph and produces a bisection of it
**************************************************************************/
void MlevelNestedDissectionCC(CtrlType *ctrl, GraphType *graph, idxtype *order, float ubfactor, int lastvtx)
{
  int i, j, nvtxs, nbnd, tvwgt, tpwgts2[2], nsgraphs, ncmps, rnvtxs;
  idxtype *label, *bndind;
  idxtype *cptr, *cind;
  GraphType *sgraphs;

  nvtxs = graph->nvtxs;

  /* Determine the weights of the partitions */
  tvwgt = idxsum(nvtxs, graph->vwgt);
  tpwgts2[0] = tvwgt/2;
  tpwgts2[1] = tvwgt-tpwgts2[0];

  MlevelNodeBisectionMultiple(ctrl, graph, tpwgts2, ubfactor);
  IFSET(ctrl->dbglvl, DBG_SEPINFO, printf("Nvtxs: %6d, [%6d %6d %6d]\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;

  cptr = idxmalloc(nvtxs, "MlevelNestedDissectionCC: cptr");
  cind = idxmalloc(nvtxs, "MlevelNestedDissectionCC: cind");
  ncmps = FindComponents(ctrl, graph, cptr, cind);

/*
  if (ncmps > 2)
    printf("[%5d] has %3d components\n", nvtxs, ncmps);
*/

  sgraphs = (GraphType *)GKmalloc(ncmps*sizeof(GraphType), "MlevelNestedDissectionCC: sgraphs");

  nsgraphs = SplitGraphOrderCC(ctrl, graph, sgraphs, ncmps, cptr, cind);

  GKfree((void**) &cptr, (void**) &cind, LTERM);

  /* Free the memory of the top level graph */
  GKfree((void**) &graph->gdata, (void**) &graph->rdata, (void**) &graph->label, LTERM);

  /* Go and process the subgraphs */
  for (rnvtxs=i=0; i<nsgraphs; i++) {
    if (sgraphs[i].adjwgt == NULL) {
      MMDOrder(ctrl, sgraphs+i, order, lastvtx-rnvtxs);
      GKfree((void**) &sgraphs[i].gdata, (void**) &sgraphs[i].label, LTERM);
    }
    else {
      MlevelNestedDissectionCC(ctrl, sgraphs+i, order, ubfactor, lastvtx-rnvtxs);
    }
    rnvtxs += sgraphs[i].nvtxs;
  }

  free(sgraphs);
}



/*************************************************************************
* This function performs multilevel bisection. It performs multiple