/* * Copyright 1997, Regents of the University of Minnesota * * balance.c * * This file contains code that is used to forcefully balance either * bisections or k-sections * * Started 7/29/97 * George * * $Id: balance.c 2501 2007-11-20 02:33:29Z benkirk $ * */#include <metis.h>/************************************************************************** This function is the entry point of the bisection balancing algorithms.**************************************************************************/void Balance2Way(CtrlType *ctrl, GraphType *graph, int *tpwgts, float ubfactor){  int i, j, nvtxs, from, imax, gain, mindiff;  idxtype *id, *ed;  /* Return right away if the balance is OK */  mindiff = abs(tpwgts[0]-graph->pwgts[0]);  if (mindiff < 3*(graph->pwgts[0]+graph->pwgts[1])/graph->nvtxs)    return;  if (graph->pwgts[0] > tpwgts[0] && graph->pwgts[0] < (int)(ubfactor*tpwgts[0]))    return;  if (graph->pwgts[1] > tpwgts[1] && graph->pwgts[1] < (int)(ubfactor*tpwgts[1]))    return;  if (graph->nbnd > 0)    Bnd2WayBalance(ctrl, graph, tpwgts);  else    General2WayBalance(ctrl, graph, tpwgts);}/************************************************************************** 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 {        if (ed[k] > 0) {  /* It will now become a boundary vertex */          BNDInsert(nbnd, bndind, bndptr, k);          if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)             PQueueInsert(&parts, k, ed[k]-id[k]);        }      }    }  }  IFSET(ctrl->dbglvl, DBG_REFINE,     printf("\tMinimum cut: %6d, PWGTS: [%6d %6d], NBND: %6d\n", mincut, pwgts[0], pwgts[1], nbnd));  graph->mincut = mincut;  graph->nbnd = nbnd;  PQueueFree(ctrl, &parts);  idxwspacefree(ctrl, nvtxs);  idxwspacefree(ctrl, nvtxs);}/************************************************************************** This function balances two partitions by moving the highest gain * (including negative gain) vertices to the other domain.* It is used only when tha unbalance is due to non contigous* subdomains. That is, the are no boundary vertices.* It moves vertices from the domain that is overweight to the one that * is underweight.**************************************************************************/void General2WayBalance(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 nodes of the proper partition whose size is OK in the priority queue */  RandomPermute(nvtxs, perm, 1);  for (ii=0; ii<nvtxs; ii++) {    i = perm[ii];    if (where[i] == from && vwgt[i] <= mindiff)      PQueueInsert(&parts, i, ed[i]-id[i]);  }  mincut = graph->mincut;  nbnd = graph->nbnd;  for (nswaps=0; nswaps<nvtxs; nswaps++) {    if ((higain = PQueueGetMax(&parts)) == -1)      break;    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 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])       BNDDelete(nbnd, bndind,  bndptr, higain);    if (ed[higain] > 0 && bndptr[higain] == -1)      BNDInsert(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 the queue position */      if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)        PQueueUpdate(&parts, k, oldgain, ed[k]-id[k]);      /* Update its boundary information */      if (ed[k] == 0 && bndptr[k] != -1)         BNDDelete(nbnd, bndind, bndptr, k);      else if (ed[k] > 0 && bndptr[k] == -1)          BNDInsert(nbnd, bndind, bndptr, k);    }  }  IFSET(ctrl->dbglvl, DBG_REFINE,     printf("\tMinimum cut: %6d, PWGTS: [%6d %6d], NBND: %6d\n", mincut, pwgts[0], pwgts[1], nbnd));  graph->mincut = mincut;  graph->nbnd = nbnd;  PQueueFree(ctrl, &parts);  idxwspacefree(ctrl, nvtxs);  idxwspacefree(ctrl, nvtxs);}