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543 lines
18 KiB
543 lines
18 KiB
/*!
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\file
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\brief Functions for the edge-based FM refinement
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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: fm.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 performs an edge-based FM refinement
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**************************************************************************/
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void FM_2WayRefine(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts, idx_t niter)
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{
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if (graph->ncon == 1)
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FM_2WayCutRefine(ctrl, graph, ntpwgts, niter);
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else
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FM_Mc2WayCutRefine(ctrl, graph, ntpwgts, niter);
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}
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/*************************************************************************/
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/*! This function performs a cut-focused FM refinement */
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/*************************************************************************/
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void FM_2WayCutRefine(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts, idx_t niter)
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{
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idx_t i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, limit, tmp;
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idx_t *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
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idx_t *moved, *swaps, *perm;
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rpq_t *queues[2];
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idx_t higain, mincut, mindiff, origdiff, initcut, newcut, mincutorder, avgvwgt;
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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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swaps = iwspacemalloc(ctrl, nvtxs);
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perm = iwspacemalloc(ctrl, nvtxs);
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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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limit = gk_min(gk_max(0.01*nvtxs, 15), 100);
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avgvwgt = gk_min((pwgts[0]+pwgts[1])/20, 2*(pwgts[0]+pwgts[1])/nvtxs);
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queues[0] = rpqCreate(nvtxs);
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queues[1] = rpqCreate(nvtxs);
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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Print2WayRefineStats(ctrl, graph, ntpwgts, 0, -2));
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origdiff = iabs(tpwgts[0]-pwgts[0]);
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iset(nvtxs, -1, moved);
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for (pass=0; pass<niter; pass++) { /* Do a number of passes */
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rpqReset(queues[0]);
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rpqReset(queues[1]);
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mincutorder = -1;
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newcut = mincut = initcut = graph->mincut;
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mindiff = iabs(tpwgts[0]-pwgts[0]);
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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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irandArrayPermute(nbnd, perm, nbnd, 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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rpqInsert(queues[where[bndind[i]]], bndind[i], ed[bndind[i]]-id[bndind[i]]);
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}
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for (nswaps=0; nswaps<nvtxs; nswaps++) {
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from = (tpwgts[0]-pwgts[0] < tpwgts[1]-pwgts[1] ? 0 : 1);
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to = (from+1)%2;
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if ((higain = rpqGetTop(queues[from])) == -1)
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break;
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ASSERT(bndptr[higain] != -1);
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newcut -= (ed[higain]-id[higain]);
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INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);
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if ((newcut < mincut && iabs(tpwgts[0]-pwgts[0]) <= origdiff+avgvwgt) ||
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(newcut == mincut && iabs(tpwgts[0]-pwgts[0]) < mindiff)) {
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mincut = newcut;
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mindiff = iabs(tpwgts[0]-pwgts[0]);
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mincutorder = nswaps;
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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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INC_DEC(pwgts[from], pwgts[to], vwgt[higain]);
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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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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], newcut, 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) /* Remove it if in the queues */
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rpqDelete(queues[where[k]], 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)
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rpqUpdate(queues[where[k]], 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)
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rpqInsert(queues[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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INC_DEC(pwgts[to], pwgts[(to+1)%2], vwgt[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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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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graph->mincut = mincut;
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graph->nbnd = nbnd;
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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Print2WayRefineStats(ctrl, graph, ntpwgts, 0, mincutorder));
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if (mincutorder <= 0 || mincut == initcut)
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break;
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}
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rpqDestroy(queues[0]);
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rpqDestroy(queues[1]);
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WCOREPOP;
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}
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/*************************************************************************/
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/*! This function performs a cut-focused multi-constraint FM refinement */
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/*************************************************************************/
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void FM_Mc2WayCutRefine(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts, idx_t niter)
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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, *pwgts, *where, *id, *ed,
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*bndptr, *bndind;
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idx_t *moved, *swaps, *perm, *qnum;
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idx_t higain, mincut, initcut, newcut, mincutorder;
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real_t *invtvwgt, *ubfactors, *minbalv, *newbalv;
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real_t origbal, minbal, newbal, rgain, ffactor;
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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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ubfactors = rwspacemalloc(ctrl, ncon);
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newbalv = rwspacemalloc(ctrl, ncon);
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minbalv = rwspacemalloc(ctrl, ncon);
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limit = gk_min(gk_max(0.01*nvtxs, 25), 150);
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/* Determine a fudge factor to allow the refinement routines to get out
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of tight balancing constraints. */
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ffactor = .5/gk_max(20, nvtxs);
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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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for (i=0; i<nvtxs; i++)
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qnum[i] = iargmax_nrm(ncon, vwgt+i*ncon, invtvwgt);
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/* Determine the unbalance tolerance for each constraint. The tolerance is
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equal to the maximum of the original load imbalance and the user-supplied
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allowed tolerance. The rationale behind this approach is to allow the
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refinement routine to improve the cut, without having to worry about fixing
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load imbalance problems. The load imbalance is addressed by the balancing
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routines. */
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origbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ctrl->ubfactors, ubfactors);
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for (i=0; i<ncon; i++)
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ubfactors[i] = (ubfactors[i] > 0 ? ctrl->ubfactors[i]+ubfactors[i] : ctrl->ubfactors[i]);
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IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
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Print2WayRefineStats(ctrl, graph, ntpwgts, origbal, -2));
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iset(nvtxs, -1, moved);
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for (pass=0; pass<niter; pass++) { /* Do a number of passes */
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for (i=0; i<2*ncon; i++)
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rpqReset(queues[i]);
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mincutorder = -1;
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newcut = mincut = initcut = graph->mincut;
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minbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ubfactors, minbalv);
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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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irandArrayPermute(nbnd, perm, nbnd/5, 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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//rgain = 1.0*(ed[i]-id[i])/sqrt(vwgt[i*ncon+qnum[i]]+1);
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//rgain = (ed[i]-id[i] > 0 ? 1.0*(ed[i]-id[i])/sqrt(vwgt[i*ncon+qnum[i]]+1) : ed[i]-id[i]);
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rgain = ed[i]-id[i];
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rpqInsert(queues[2*qnum[i]+where[i]], i, rgain);
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}
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for (nswaps=0; nswaps<nvtxs; nswaps++) {
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SelectQueue(graph, ctrl->pijbm, 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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ASSERT(bndptr[higain] != -1);
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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, ubfactors, newbalv);
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if ((newcut < mincut && newbal <= ffactor) ||
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(newcut == mincut && (newbal < minbal ||
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(newbal == minbal && 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++)
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printf("(%.3"PRREAL" %.3"PRREAL")", pwgts[l]*invtvwgt[l], pwgts[ncon+l]*invtvwgt[l]);
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printf(" %+.3"PRREAL" LB: %.3"PRREAL"(%+.3"PRREAL")\n",
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minbal, ComputeLoadImbalance(graph, 2, ctrl->pijbm), 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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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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rpqDelete(queues[2*qnum[k]+where[k]], 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) {
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//rgain = 1.0*(ed[k]-id[k])/sqrt(vwgt[k*ncon+qnum[k]]+1);
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//rgain = (ed[k]-id[k] > 0 ?
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// 1.0*(ed[k]-id[k])/sqrt(vwgt[k*ncon+qnum[k]]+1) : ed[k]-id[k]);
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rgain = ed[k]-id[k];
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rpqUpdate(queues[2*qnum[k]+where[k]], k, rgain);
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}
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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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//rgain = 1.0*(ed[k]-id[k])/sqrt(vwgt[k*ncon+qnum[k]]+1);
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//rgain = (ed[k]-id[k] > 0 ?
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// 1.0*(ed[k]-id[k])/sqrt(vwgt[k*ncon+qnum[k]]+1) : ed[k]-id[k]);
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rgain = ed[k]-id[k];
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rpqInsert(queues[2*qnum[k]+where[k]], k, rgain);
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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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* 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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iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
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iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+((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)
|
|
BNDDelete(nbnd, bndind, bndptr, k);
|
|
if (bndptr[k] == -1 && ed[k] > 0)
|
|
BNDInsert(nbnd, bndind, bndptr, k);
|
|
}
|
|
}
|
|
|
|
graph->mincut = mincut;
|
|
graph->nbnd = nbnd;
|
|
|
|
IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
|
|
Print2WayRefineStats(ctrl, graph, ntpwgts, minbal, mincutorder));
|
|
|
|
if (mincutorder <= 0 || mincut == initcut)
|
|
break;
|
|
}
|
|
|
|
for (i=0; i<2*ncon; i++)
|
|
rpqDestroy(queues[i]);
|
|
|
|
WCOREPOP;
|
|
}
|
|
|
|
|
|
/*************************************************************************/
|
|
/*! This function selects the partition number and the queue from which
|
|
we will move vertices out. */
|
|
/*************************************************************************/
|
|
void SelectQueue(graph_t *graph, real_t *pijbm, real_t *ubfactors,
|
|
rpq_t **queues, idx_t *from, idx_t *cnum)
|
|
{
|
|
idx_t ncon, i, part;
|
|
real_t max, tmp;
|
|
|
|
ncon = graph->ncon;
|
|
|
|
*from = -1;
|
|
*cnum = -1;
|
|
|
|
/* First determine the side and the queue, irrespective of the presence of nodes.
|
|
The side & queue is determined based on the most violated balancing constraint. */
|
|
for (max=0.0, part=0; part<2; part++) {
|
|
for (i=0; i<ncon; i++) {
|
|
tmp = graph->pwgts[part*ncon+i]*pijbm[part*ncon+i] - ubfactors[i];
|
|
/* the '=' in the test below is to ensure that under tight constraints
|
|
the partition that is at the max is selected */
|
|
if (tmp >= max) {
|
|
max = tmp;
|
|
*from = part;
|
|
*cnum = i;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
if (*from != -1) {
|
|
/* in case the desired queue is empty, select a queue from the same side */
|
|
if (rpqLength(queues[2*(*cnum)+(*from)]) == 0) {
|
|
for (i=0; i<ncon; i++) {
|
|
if (rpqLength(queues[2*i+(*from)]) > 0) {
|
|
max = graph->pwgts[(*from)*ncon+i]*pijbm[(*from)*ncon+i] - ubfactors[i];
|
|
*cnum = i;
|
|
break;
|
|
}
|
|
}
|
|
|
|
for (i++; i<ncon; i++) {
|
|
tmp = graph->pwgts[(*from)*ncon+i]*pijbm[(*from)*ncon+i] - ubfactors[i];
|
|
if (tmp > max && rpqLength(queues[2*i+(*from)]) > 0) {
|
|
max = tmp;
|
|
*cnum = i;
|
|
}
|
|
}
|
|
}
|
|
|
|
/*
|
|
printf("Selected1 %"PRIDX"(%"PRIDX") -> %"PRIDX" [%5"PRREAL"]\n",
|
|
*from, *cnum, rpqLength(queues[2*(*cnum)+(*from)]), max);
|
|
*/
|
|
}
|
|
else {
|
|
/* the partitioning does not violate balancing constraints, in which case select
|
|
a queue based on cut criteria */
|
|
for (part=0; part<2; part++) {
|
|
for (i=0; i<ncon; i++) {
|
|
if (rpqLength(queues[2*i+part]) > 0 &&
|
|
(*from == -1 || rpqSeeTopKey(queues[2*i+part]) > max)) {
|
|
max = rpqSeeTopKey(queues[2*i+part]);
|
|
*from = part;
|
|
*cnum = i;
|
|
}
|
|
}
|
|
}
|
|
/*
|
|
printf("Selected2 %"PRIDX"(%"PRIDX") -> %"PRIDX"\n",
|
|
*from, *cnum, rpqLength(queues[2*(*cnum)+(*from)]), max);
|
|
*/
|
|
}
|
|
}
|
|
|
|
|
|
/*************************************************************************/
|
|
/*! Prints statistics about the refinement */
|
|
/*************************************************************************/
|
|
void Print2WayRefineStats(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts,
|
|
real_t deltabal, idx_t mincutorder)
|
|
{
|
|
int i;
|
|
|
|
if (mincutorder == -2) {
|
|
printf("Parts: ");
|
|
printf("Nv-Nb[%5"PRIDX" %5"PRIDX"] ICut: %6"PRIDX,
|
|
graph->nvtxs, graph->nbnd, graph->mincut);
|
|
printf(" [");
|
|
for (i=0; i<graph->ncon; i++)
|
|
printf("(%.3"PRREAL" %.3"PRREAL" T:%.3"PRREAL" %.3"PRREAL")",
|
|
graph->pwgts[i]*graph->invtvwgt[i],
|
|
graph->pwgts[graph->ncon+i]*graph->invtvwgt[i],
|
|
ntpwgts[i], ntpwgts[graph->ncon+i]);
|
|
printf("] LB: %.3"PRREAL"(%+.3"PRREAL")\n",
|
|
ComputeLoadImbalance(graph, 2, ctrl->pijbm), deltabal);
|
|
}
|
|
else {
|
|
printf("\tMincut: %6"PRIDX" at %5"PRIDX" NBND %6"PRIDX" NPwgts: [",
|
|
graph->mincut, mincutorder, graph->nbnd);
|
|
for (i=0; i<graph->ncon; i++)
|
|
printf("(%.3"PRREAL" %.3"PRREAL")",
|
|
graph->pwgts[i]*graph->invtvwgt[i], graph->pwgts[graph->ncon+i]*graph->invtvwgt[i]);
|
|
printf("] LB: %.3"PRREAL"(%+.3"PRREAL")\n",
|
|
ComputeLoadImbalance(graph, 2, ctrl->pijbm), deltabal);
|
|
}
|
|
}
|
|
|
|
|