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498 lines
16 KiB
498 lines
16 KiB
/*!
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\file
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\brief Functions for the edge-based balancing
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\date Started 7/23/97
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\author George
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\author Copyright 1997-2011, Regents of the University of Minnesota
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\version\verbatim $Id: balance.c 10187 2011-06-13 13:46:57Z karypis $ \endverbatim
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*/
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#include "metislib.h"
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/*************************************************************************
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* This function is the entry poidx_t of the bisection balancing algorithms.
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**************************************************************************/
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void Balance2Way(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
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{
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if (ComputeLoadImbalanceDiff(graph, 2, ctrl->pijbm, ctrl->ubfactors) <= 0)
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return;
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if (graph->ncon == 1) {
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/* return right away if the balance is OK */
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if (rabs(ntpwgts[0]*graph->tvwgt[0]-graph->pwgts[0]) < 3*graph->tvwgt[0]/graph->nvtxs)
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return;
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if (graph->nbnd > 0)
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Bnd2WayBalance(ctrl, graph, ntpwgts);
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else
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General2WayBalance(ctrl, graph, ntpwgts);
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}
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else {
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McGeneral2WayBalance(ctrl, graph, ntpwgts);
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}
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}
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/*************************************************************************
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* This function balances two partitions by moving boundary nodes
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* from the domain that is overweight to the one that is underweight.
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**************************************************************************/
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void Bnd2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
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{
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idx_t i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, tmp;
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idx_t *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
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idx_t *moved, *perm;
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rpq_t *queue;
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idx_t higain, mincut, mindiff;
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idx_t tpwgts[2];
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WCOREPUSH;
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nvtxs = graph->nvtxs;
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xadj = graph->xadj;
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vwgt = graph->vwgt;
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adjncy = graph->adjncy;
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adjwgt = graph->adjwgt;
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where = graph->where;
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id = graph->id;
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ed = graph->ed;
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pwgts = graph->pwgts;
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bndptr = graph->bndptr;
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bndind = graph->bndind;
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moved = iwspacemalloc(ctrl, nvtxs);
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perm = iwspacemalloc(ctrl, nvtxs);
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/* Determine from which domain you will be moving data */
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tpwgts[0] = graph->tvwgt[0]*ntpwgts[0];
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tpwgts[1] = graph->tvwgt[0] - tpwgts[0];
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mindiff = iabs(tpwgts[0]-pwgts[0]);
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from = (pwgts[0] < tpwgts[0] ? 1 : 0);
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to = (from+1)%2;
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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printf("Partitions: [%6"PRIDX" %6"PRIDX"] T[%6"PRIDX" %6"PRIDX"], Nv-Nb[%6"PRIDX" %6"PRIDX"]. ICut: %6"PRIDX" [B]\n",
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pwgts[0], pwgts[1], tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd,
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graph->mincut));
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queue = rpqCreate(nvtxs);
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iset(nvtxs, -1, moved);
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ASSERT(ComputeCut(graph, where) == graph->mincut);
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ASSERT(CheckBnd(graph));
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/* Insert the boundary nodes of the proper partition whose size is OK in the priority queue */
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nbnd = graph->nbnd;
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irandArrayPermute(nbnd, perm, nbnd/5, 1);
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for (ii=0; ii<nbnd; ii++) {
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i = perm[ii];
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ASSERT(ed[bndind[i]] > 0 || id[bndind[i]] == 0);
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ASSERT(bndptr[bndind[i]] != -1);
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if (where[bndind[i]] == from && vwgt[bndind[i]] <= mindiff)
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rpqInsert(queue, bndind[i], ed[bndind[i]]-id[bndind[i]]);
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}
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mincut = graph->mincut;
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for (nswaps=0; nswaps<nvtxs; nswaps++) {
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if ((higain = rpqGetTop(queue)) == -1)
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break;
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ASSERT(bndptr[higain] != -1);
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if (pwgts[to]+vwgt[higain] > tpwgts[to])
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break;
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mincut -= (ed[higain]-id[higain]);
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INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);
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where[higain] = to;
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moved[higain] = nswaps;
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IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
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printf("Moved %6"PRIDX" from %"PRIDX". [%3"PRIDX" %3"PRIDX"] %5"PRIDX" [%4"PRIDX" %4"PRIDX"]\n", higain, from, ed[higain]-id[higain], vwgt[higain], mincut, pwgts[0], pwgts[1]));
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/**************************************************************
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* Update the id[i]/ed[i] values of the affected nodes
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***************************************************************/
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SWAP(id[higain], ed[higain], tmp);
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if (ed[higain] == 0 && xadj[higain] < xadj[higain+1])
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BNDDelete(nbnd, bndind, bndptr, higain);
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for (j=xadj[higain]; j<xadj[higain+1]; j++) {
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k = adjncy[j];
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kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
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INC_DEC(id[k], ed[k], kwgt);
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/* Update its boundary information and queue position */
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if (bndptr[k] != -1) { /* If k was a boundary vertex */
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if (ed[k] == 0) { /* Not a boundary vertex any more */
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BNDDelete(nbnd, bndind, bndptr, k);
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if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff) /* Remove it if in the queues */
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rpqDelete(queue, k);
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}
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else { /* If it has not been moved, update its position in the queue */
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if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
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rpqUpdate(queue, k, ed[k]-id[k]);
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}
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}
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else {
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if (ed[k] > 0) { /* It will now become a boundary vertex */
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BNDInsert(nbnd, bndind, bndptr, k);
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if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
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rpqInsert(queue, k, ed[k]-id[k]);
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}
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}
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}
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}
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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printf("\tMinimum cut: %6"PRIDX", PWGTS: [%6"PRIDX" %6"PRIDX"], NBND: %6"PRIDX"\n", mincut, pwgts[0], pwgts[1], nbnd));
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graph->mincut = mincut;
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graph->nbnd = nbnd;
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rpqDestroy(queue);
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WCOREPOP;
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}
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/*************************************************************************
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* This function balances two partitions by moving the highest gain
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* (including negative gain) vertices to the other domain.
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* It is used only when the unbalance is due to non contiguous
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* subdomains. That is, the are no boundary vertices.
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* It moves vertices from the domain that is overweight to the one that
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* is underweight.
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**************************************************************************/
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void General2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
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{
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idx_t i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, tmp;
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idx_t *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
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idx_t *moved, *perm;
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rpq_t *queue;
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idx_t higain, mincut, mindiff;
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idx_t tpwgts[2];
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WCOREPUSH;
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nvtxs = graph->nvtxs;
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xadj = graph->xadj;
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vwgt = graph->vwgt;
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adjncy = graph->adjncy;
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adjwgt = graph->adjwgt;
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where = graph->where;
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id = graph->id;
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ed = graph->ed;
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pwgts = graph->pwgts;
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bndptr = graph->bndptr;
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bndind = graph->bndind;
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moved = iwspacemalloc(ctrl, nvtxs);
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perm = iwspacemalloc(ctrl, nvtxs);
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/* Determine from which domain you will be moving data */
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tpwgts[0] = graph->tvwgt[0]*ntpwgts[0];
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tpwgts[1] = graph->tvwgt[0] - tpwgts[0];
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mindiff = iabs(tpwgts[0]-pwgts[0]);
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from = (pwgts[0] < tpwgts[0] ? 1 : 0);
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to = (from+1)%2;
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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printf("Partitions: [%6"PRIDX" %6"PRIDX"] T[%6"PRIDX" %6"PRIDX"], Nv-Nb[%6"PRIDX" %6"PRIDX"]. ICut: %6"PRIDX" [B]\n",
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pwgts[0], pwgts[1], tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));
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queue = rpqCreate(nvtxs);
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iset(nvtxs, -1, moved);
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ASSERT(ComputeCut(graph, where) == graph->mincut);
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ASSERT(CheckBnd(graph));
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/* Insert the nodes of the proper partition whose size is OK in the priority queue */
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irandArrayPermute(nvtxs, perm, nvtxs/5, 1);
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for (ii=0; ii<nvtxs; ii++) {
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i = perm[ii];
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if (where[i] == from && vwgt[i] <= mindiff)
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rpqInsert(queue, i, ed[i]-id[i]);
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}
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mincut = graph->mincut;
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nbnd = graph->nbnd;
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for (nswaps=0; nswaps<nvtxs; nswaps++) {
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if ((higain = rpqGetTop(queue)) == -1)
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break;
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if (pwgts[to]+vwgt[higain] > tpwgts[to])
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break;
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mincut -= (ed[higain]-id[higain]);
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INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);
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where[higain] = to;
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moved[higain] = nswaps;
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IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
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printf("Moved %6"PRIDX" from %"PRIDX". [%3"PRIDX" %3"PRIDX"] %5"PRIDX" [%4"PRIDX" %4"PRIDX"]\n", higain, from, ed[higain]-id[higain], vwgt[higain], mincut, pwgts[0], pwgts[1]));
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/**************************************************************
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* Update the id[i]/ed[i] values of the affected nodes
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***************************************************************/
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SWAP(id[higain], ed[higain], tmp);
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if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])
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BNDDelete(nbnd, bndind, bndptr, higain);
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if (ed[higain] > 0 && bndptr[higain] == -1)
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BNDInsert(nbnd, bndind, bndptr, higain);
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for (j=xadj[higain]; j<xadj[higain+1]; j++) {
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k = adjncy[j];
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kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
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INC_DEC(id[k], ed[k], kwgt);
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/* Update the queue position */
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if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
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rpqUpdate(queue, k, ed[k]-id[k]);
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/* Update its boundary information */
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if (ed[k] == 0 && bndptr[k] != -1)
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BNDDelete(nbnd, bndind, bndptr, k);
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else if (ed[k] > 0 && bndptr[k] == -1)
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BNDInsert(nbnd, bndind, bndptr, k);
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}
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}
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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printf("\tMinimum cut: %6"PRIDX", PWGTS: [%6"PRIDX" %6"PRIDX"], NBND: %6"PRIDX"\n", mincut, pwgts[0], pwgts[1], nbnd));
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graph->mincut = mincut;
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graph->nbnd = nbnd;
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rpqDestroy(queue);
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WCOREPOP;
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}
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/*************************************************************************
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* This function performs an edge-based FM refinement
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**************************************************************************/
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void McGeneral2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
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{
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idx_t i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass,
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me, limit, tmp, cnum;
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idx_t *xadj, *adjncy, *vwgt, *adjwgt, *where, *pwgts, *id, *ed, *bndptr, *bndind;
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idx_t *moved, *swaps, *perm, *qnum, *qsizes;
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idx_t higain, mincut, newcut, mincutorder;
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real_t *invtvwgt, *minbalv, *newbalv, minbal, newbal;
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rpq_t **queues;
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WCOREPUSH;
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nvtxs = graph->nvtxs;
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ncon = graph->ncon;
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xadj = graph->xadj;
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vwgt = graph->vwgt;
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adjncy = graph->adjncy;
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adjwgt = graph->adjwgt;
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invtvwgt = graph->invtvwgt;
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where = graph->where;
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id = graph->id;
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ed = graph->ed;
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pwgts = graph->pwgts;
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bndptr = graph->bndptr;
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bndind = graph->bndind;
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moved = iwspacemalloc(ctrl, nvtxs);
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swaps = iwspacemalloc(ctrl, nvtxs);
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perm = iwspacemalloc(ctrl, nvtxs);
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qnum = iwspacemalloc(ctrl, nvtxs);
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newbalv = rwspacemalloc(ctrl, ncon);
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minbalv = rwspacemalloc(ctrl, ncon);
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qsizes = iwspacemalloc(ctrl, 2*ncon);
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limit = gk_min(gk_max(0.01*nvtxs, 15), 100);
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/* Initialize the queues */
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queues = (rpq_t **)wspacemalloc(ctrl, 2*ncon*sizeof(rpq_t *));
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for (i=0; i<2*ncon; i++) {
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queues[i] = rpqCreate(nvtxs);
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qsizes[i] = 0;
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}
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for (i=0; i<nvtxs; i++) {
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qnum[i] = iargmax_nrm(ncon, vwgt+i*ncon, invtvwgt);
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qsizes[2*qnum[i]+where[i]]++;
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}
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/* for the empty queues, move into them vertices from other queues */
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for (from=0; from<2; from++) {
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for (j=0; j<ncon; j++) {
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if (qsizes[2*j+from] == 0) {
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for (i=0; i<nvtxs; i++) {
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if (where[i] != from)
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continue;
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k = iargmax2_nrm(ncon, vwgt+i*ncon, invtvwgt);
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if (k == j &&
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qsizes[2*qnum[i]+from] > qsizes[2*j+from] &&
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vwgt[i*ncon+qnum[i]]*invtvwgt[qnum[i]] < 1.3*vwgt[i*ncon+j]*invtvwgt[j]) {
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qsizes[2*qnum[i]+from]--;
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qsizes[2*j+from]++;
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qnum[i] = j;
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}
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}
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}
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}
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}
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minbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ctrl->ubfactors, minbalv);
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ASSERT(minbal > 0.0);
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newcut = mincut = graph->mincut;
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mincutorder = -1;
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if (ctrl->dbglvl&METIS_DBG_REFINE) {
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printf("Parts: [");
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for (l=0; l<ncon; l++)
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printf("(%6"PRIDX" %6"PRIDX" %.3"PRREAL" %.3"PRREAL") ",
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pwgts[l], pwgts[ncon+l], ntpwgts[l], ntpwgts[ncon+l]);
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printf("] Nv-Nb[%5"PRIDX", %5"PRIDX"]. ICut: %6"PRIDX", LB: %+.3"PRREAL" [B]\n",
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graph->nvtxs, graph->nbnd, graph->mincut, minbal);
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}
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iset(nvtxs, -1, moved);
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ASSERT(ComputeCut(graph, where) == graph->mincut);
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ASSERT(CheckBnd(graph));
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/* Insert all nodes in the priority queues */
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nbnd = graph->nbnd;
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irandArrayPermute(nvtxs, perm, nvtxs/10, 1);
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for (ii=0; ii<nvtxs; ii++) {
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i = perm[ii];
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rpqInsert(queues[2*qnum[i]+where[i]], i, ed[i]-id[i]);
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}
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for (nswaps=0; nswaps<nvtxs; nswaps++) {
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if (minbal <= 0.0)
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break;
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SelectQueue(graph, ctrl->pijbm, ctrl->ubfactors, queues, &from, &cnum);
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to = (from+1)%2;
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if (from == -1 || (higain = rpqGetTop(queues[2*cnum+from])) == -1)
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break;
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newcut -= (ed[higain]-id[higain]);
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iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
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iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+from*ncon, 1);
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newbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ctrl->ubfactors, newbalv);
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if (newbal < minbal || (newbal == minbal &&
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(newcut < mincut ||
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(newcut == mincut && BetterBalance2Way(ncon, minbalv, newbalv))))) {
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mincut = newcut;
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minbal = newbal;
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mincutorder = nswaps;
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rcopy(ncon, newbalv, minbalv);
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}
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else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */
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newcut += (ed[higain]-id[higain]);
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iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+from*ncon, 1);
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iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
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break;
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}
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where[higain] = to;
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moved[higain] = nswaps;
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swaps[nswaps] = higain;
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if (ctrl->dbglvl&METIS_DBG_MOVEINFO) {
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printf("Moved %6"PRIDX" from %"PRIDX"(%"PRIDX"). Gain: %5"PRIDX", "
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"Cut: %5"PRIDX", NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut);
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for (l=0; l<ncon; l++)
|
|
printf("(%6"PRIDX", %6"PRIDX") ", pwgts[l], pwgts[ncon+l]);
|
|
printf(", %+.3"PRREAL" LB: %+.3"PRREAL"\n", minbal, newbal);
|
|
}
|
|
|
|
|
|
/**************************************************************
|
|
* 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];
|
|
|
|
kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
|
|
INC_DEC(id[k], ed[k], kwgt);
|
|
|
|
/* Update the queue position */
|
|
if (moved[k] == -1)
|
|
rpqUpdate(queues[2*qnum[k]+where[k]], k, 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);
|
|
}
|
|
}
|
|
|
|
|
|
|
|
/****************************************************************
|
|
* Roll back computations
|
|
*****************************************************************/
|
|
for (nswaps--; nswaps>mincutorder; nswaps--) {
|
|
higain = swaps[nswaps];
|
|
|
|
to = where[higain] = (where[higain]+1)%2;
|
|
SWAP(id[higain], ed[higain], tmp);
|
|
if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])
|
|
BNDDelete(nbnd, bndind, bndptr, higain);
|
|
else if (ed[higain] > 0 && bndptr[higain] == -1)
|
|
BNDInsert(nbnd, bndind, bndptr, higain);
|
|
|
|
iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
|
|
iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+((to+1)%2)*ncon, 1);
|
|
for (j=xadj[higain]; j<xadj[higain+1]; j++) {
|
|
k = adjncy[j];
|
|
|
|
kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
|
|
INC_DEC(id[k], ed[k], kwgt);
|
|
|
|
if (bndptr[k] != -1 && ed[k] == 0)
|
|
BNDDelete(nbnd, bndind, bndptr, k);
|
|
if (bndptr[k] == -1 && ed[k] > 0)
|
|
BNDInsert(nbnd, bndind, bndptr, k);
|
|
}
|
|
}
|
|
|
|
if (ctrl->dbglvl&METIS_DBG_REFINE) {
|
|
printf("\tMincut: %6"PRIDX" at %5"PRIDX", NBND: %6"PRIDX", NPwgts: [",
|
|
mincut, mincutorder, nbnd);
|
|
for (l=0; l<ncon; l++)
|
|
printf("(%6"PRIDX", %6"PRIDX") ", pwgts[l], pwgts[ncon+l]);
|
|
printf("], LB: %.3"PRREAL"\n", ComputeLoadImbalance(graph, 2, ctrl->pijbm));
|
|
}
|
|
|
|
graph->mincut = mincut;
|
|
graph->nbnd = nbnd;
|
|
|
|
|
|
for (i=0; i<2*ncon; i++)
|
|
rpqDestroy(queues[i]);
|
|
|
|
WCOREPOP;
|
|
}
|
|
|
|
|