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342 lines
11 KiB
C
342 lines
11 KiB
C
/*
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* Copyright 1997, Regents of the University of Minnesota
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*
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* mfm.c
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*
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* This file contains code that implements the edge-based FM refinement
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*
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* Started 7/23/97
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* George
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*
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* $Id: NEW_mfm.c,v 1.1 2003/07/16 15:55:13 karypis Exp $
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*/
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#include <metis.h>
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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 MocFM_2WayEdgeRefine(CtrlType *ctrl, GraphType *graph, float *tpwgts, int npasses)
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{
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int i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass, me, limit, tmp, cnum;
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idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind;
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idxtype *moved, *swaps, *perm, *qnum;
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float *nvwgt, *npwgts, mindiff[MAXNCON], origbal, minbal, newbal;
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PQueueType parts[MAXNCON][2];
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int higain, oldgain, mincut, initcut, newcut, mincutorder;
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float rtpwgts[2];
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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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nvwgt = graph->nvwgt;
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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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npwgts = graph->npwgts;
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bndptr = graph->bndptr;
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bndind = graph->bndind;
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moved = idxwspacemalloc(ctrl, nvtxs);
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swaps = idxwspacemalloc(ctrl, nvtxs);
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perm = idxwspacemalloc(ctrl, nvtxs);
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qnum = idxwspacemalloc(ctrl, nvtxs);
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limit = amin(amax(0.01*nvtxs, 25), 150);
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/* Initialize the queues */
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for (i=0; i<ncon; i++) {
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PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1);
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PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1);
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}
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for (i=0; i<nvtxs; i++)
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qnum[i] = samax(ncon, nvwgt+i*ncon);
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origbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts);
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rtpwgts[0] = origbal*tpwgts[0];
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rtpwgts[1] = origbal*tpwgts[1];
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if (ctrl->dbglvl&DBG_REFINE) {
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printf("Parts: [");
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for (l=0; l<ncon; l++)
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printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
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printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: %.3f\n", tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut, origbal);
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}
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idxset(nvtxs, -1, moved);
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for (pass=0; pass<npasses; pass++) { /* Do a number of passes */
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for (i=0; i<ncon; i++) {
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PQueueReset(&parts[i][0]);
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PQueueReset(&parts[i][1]);
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}
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mincutorder = -1;
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newcut = mincut = initcut = graph->mincut;
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for (i=0; i<ncon; i++)
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mindiff[i] = fabs(tpwgts[0]-npwgts[i]);
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minbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts);
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ASSERT(ComputeCut(graph, where) == graph->mincut);
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ASSERT(CheckBnd(graph));
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/* Insert boundary nodes in the priority queues */
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nbnd = graph->nbnd;
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RandomPermute(nbnd, perm, 1);
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for (ii=0; ii<nbnd; ii++) {
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i = bndind[perm[ii]];
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ASSERT(ed[i] > 0 || id[i] == 0);
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ASSERT(bndptr[i] != -1);
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PQueueInsert(&parts[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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SelectQueue(ncon, npwgts, rtpwgts, &from, &cnum, parts);
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to = (from+1)%2;
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if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1)
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break;
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ASSERT(bndptr[higain] != -1);
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saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
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saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1);
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newcut -= (ed[higain]-id[higain]);
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newbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts);
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if ((newcut < mincut && newbal-origbal <= .00001) ||
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(newcut == mincut && (newbal < minbal ||
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(newbal == minbal && BetterBalance(ncon, npwgts, tpwgts, mindiff))))) {
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mincut = newcut;
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minbal = newbal;
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mincutorder = nswaps;
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for (i=0; i<ncon; i++)
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mindiff[i] = fabs(tpwgts[0]-npwgts[i]);
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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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saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1);
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saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+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&DBG_MOVEINFO) {
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printf("Moved %6d from %d(%d). Gain: %5d, Cut: %5d, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut);
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for (l=0; l<ncon; l++)
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printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
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printf(", %.3f LB: %.3f\n", minbal, newbal);
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}
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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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oldgain = ed[k]-id[k];
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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) /* Remove it if in the queues */
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PQueueDelete(&parts[qnum[k]][where[k]], k, oldgain);
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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)
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PQueueUpdate(&parts[qnum[k]][where[k]], k, oldgain, 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)
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PQueueInsert(&parts[qnum[k]][where[k]], 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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/****************************************************************
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* Roll back computations
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*****************************************************************/
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for (i=0; i<nswaps; i++)
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moved[swaps[i]] = -1; /* reset moved array */
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for (nswaps--; nswaps>mincutorder; nswaps--) {
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higain = swaps[nswaps];
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to = where[higain] = (where[higain]+1)%2;
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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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else if (ed[higain] > 0 && bndptr[higain] == -1)
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BNDInsert(nbnd, bndind, bndptr, higain);
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saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
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saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+((to+1)%2)*ncon, 1);
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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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if (bndptr[k] != -1 && ed[k] == 0)
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BNDDelete(nbnd, bndind, bndptr, k);
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if (bndptr[k] == -1 && ed[k] > 0)
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BNDInsert(nbnd, bndind, bndptr, k);
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}
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}
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if (ctrl->dbglvl&DBG_REFINE) {
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printf("\tMincut: %6d at %5d, NBND: %6d, NPwgts: [", mincut, mincutorder, nbnd);
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for (l=0; l<ncon; l++)
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printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
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printf("], LB: %.3f\n", Compute2WayHLoadImbalance(ncon, npwgts, tpwgts));
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}
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graph->mincut = mincut;
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graph->nbnd = nbnd;
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if (mincutorder == -1 || mincut == initcut)
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break;
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}
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for (i=0; i<ncon; i++) {
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PQueueFree(ctrl, &parts[i][0]);
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PQueueFree(ctrl, &parts[i][1]);
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}
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idxwspacefree(ctrl, nvtxs);
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idxwspacefree(ctrl, nvtxs);
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idxwspacefree(ctrl, nvtxs);
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idxwspacefree(ctrl, nvtxs);
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}
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/*************************************************************************
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* This function selects the partition number and the queue from which
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* we will move vertices out
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**************************************************************************/
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void SelectQueue(int ncon, float *npwgts, float *tpwgts, int *from, int *cnum, PQueueType queues[MAXNCON][2])
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{
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int i, part, maxgain=0;
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float max, maxdiff=0.0;
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*from = -1;
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*cnum = -1;
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/* First determine the side and the queue, irrespective of the presence of nodes */
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for (part=0; part<2; part++) {
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for (i=0; i<ncon; i++) {
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if (npwgts[part*ncon+i]-tpwgts[part] >= maxdiff) {
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maxdiff = npwgts[part*ncon+i]-tpwgts[part];
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*from = part;
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*cnum = i;
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}
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}
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}
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/* printf("Selected %d(%d) -> %d\n", *from, *cnum, PQueueGetSize(&queues[*cnum][*from])); */
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if (*from != -1 && PQueueGetSize(&queues[*cnum][*from]) == 0) {
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/* The desired queue is empty, select a node from that side anyway */
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for (i=0; i<ncon; i++) {
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if (PQueueGetSize(&queues[i][*from]) > 0) {
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max = npwgts[(*from)*ncon + i];
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*cnum = i;
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break;
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}
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}
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for (i++; i<ncon; i++) {
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if (npwgts[(*from)*ncon + i] > max && PQueueGetSize(&queues[i][*from]) > 0) {
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max = npwgts[(*from)*ncon + i];
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*cnum = i;
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}
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}
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}
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/* Check to see if you can focus on the cut */
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if (maxdiff <= 0.0 || *from == -1) {
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maxgain = -100000;
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for (part=0; part<2; part++) {
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for (i=0; i<ncon; i++) {
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if (PQueueGetSize(&queues[i][part]) > 0 && PQueueGetKey(&queues[i][part]) > maxgain) {
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maxgain = PQueueGetKey(&queues[i][part]);
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*from = part;
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*cnum = i;
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}
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}
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}
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}
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}
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/*************************************************************************
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* This function checks if the balance achieved is better than the diff
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* For now, it uses a 2-norm measure
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**************************************************************************/
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int BetterBalance(int ncon, float *npwgts, float *tpwgts, float *diff)
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{
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int i;
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float ndiff[MAXNCON];
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for (i=0; i<ncon; i++)
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ndiff[i] = fabs(tpwgts[0]-npwgts[i]);
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return snorm2(ncon, ndiff) < snorm2(ncon, diff);
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}
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/*************************************************************************
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* This function computes the load imbalance over all the constrains
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**************************************************************************/
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float Compute2WayHLoadImbalance(int ncon, float *npwgts, float *tpwgts)
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{
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int i;
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float max=0.0, temp;
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for (i=0; i<ncon; i++) {
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/* temp = amax(npwgts[i]/tpwgts[0], npwgts[ncon+i]/tpwgts[1]); */
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temp = fabs(tpwgts[0]-npwgts[i])/tpwgts[0];
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max = (max < temp ? temp : max);
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}
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return 1.0+max;
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}
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/*************************************************************************
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* This function computes the load imbalance over all the constrains
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* For now assume that we just want balanced partitionings
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**************************************************************************/
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void Compute2WayHLoadImbalanceVec(int ncon, float *npwgts, float *tpwgts, float *lbvec)
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{
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int i;
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for (i=0; i<ncon; i++)
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lbvec[i] = 1.0 + fabs(tpwgts[0]-npwgts[i])/tpwgts[0];
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}
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