/************************************************************************* * This function is the entry point of the bisection balancing algorithms. **************************************************************************/ void MocBalance2Way(CtrlType *ctrl, GraphType *graph, float *tpwgts, float lbfactor) { if (Compute2WayHLoadImbalance(graph->ncon, graph->npwgts, tpwgts) < lbfactor) return; MocGeneral2WayBalance(ctrl, graph, tpwgts, lbfactor); }
/************************************************************************* * 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 MocInit2WayBalance(CtrlType *ctrl, GraphType *graph, float *tpwgts) { int i, ii, j, k, l, kwgt, nvtxs, nbnd, ncon, nswaps, from, to, pass, me, cnum, tmp; idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind; idxtype *perm, *qnum; float *nvwgt, *npwgts; PQueueType parts[MAXNCON][2]; int higain, oldgain, mincut; nvtxs = graph->nvtxs; ncon = graph->ncon; xadj = graph->xadj; adjncy = graph->adjncy; nvwgt = graph->nvwgt; adjwgt = graph->adjwgt; where = graph->where; id = graph->id; ed = graph->ed; npwgts = graph->npwgts; bndptr = graph->bndptr; bndind = graph->bndind; perm = idxwspacemalloc(ctrl, nvtxs); qnum = idxwspacemalloc(ctrl, nvtxs); /* This is called for initial partitioning so we know from where to pick nodes */ from = 1; to = (from+1)%2; if (ctrl->dbglvl&DBG_REFINE) { printf("Parts: ["); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: %.3f [B]\n", tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut, Compute2WayHLoadImbalance(ncon, npwgts, tpwgts)); } for (i=0; i<ncon; i++) { PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1); PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1); } ASSERT(ComputeCut(graph, where) == graph->mincut); ASSERT(CheckBnd(graph)); ASSERT(CheckGraph(graph)); /* Compute the queues in which each vertex will be assigned to */ for (i=0; i<nvtxs; i++) qnum[i] = samax(ncon, nvwgt+i*ncon); /* Insert the nodes of the proper partition in the appropriate priority queue */ RandomPermute(nvtxs, perm, 1); for (ii=0; ii<nvtxs; ii++) { i = perm[ii]; if (where[i] == from) { if (ed[i] > 0) PQueueInsert(&parts[qnum[i]][0], i, ed[i]-id[i]); else PQueueInsert(&parts[qnum[i]][1], i, ed[i]-id[i]); } } mincut = graph->mincut; nbnd = graph->nbnd; for (nswaps=0; nswaps<nvtxs; nswaps++) { if (AreAnyVwgtsBelow(ncon, 1.0, npwgts+from*ncon, 0.0, nvwgt, tpwgts[from])) break; if ((cnum = SelectQueueOneWay(ncon, npwgts, tpwgts, from, parts)) == -1) break; if ((higain = PQueueGetMax(&parts[cnum][0])) == -1) higain = PQueueGetMax(&parts[cnum][1]); mincut -= (ed[higain]-id[higain]); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); where[higain] = to; if (ctrl->dbglvl&DBG_MOVEINFO) { printf("Moved %6d from %d(%d). [%5d] %5d, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], mincut); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf(", LB: %.3f\n", Compute2WayHLoadImbalance(ncon, npwgts, tpwgts)); if (ed[higain] == 0 && id[higain] > 0) printf("\t Pulled from the interior!\n"); } /************************************************************** * 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 (where[k] == from) { if (ed[k] > 0 && bndptr[k] == -1) { /* It moves in boundary */ PQueueDelete(&parts[qnum[k]][1], k, oldgain); PQueueInsert(&parts[qnum[k]][0], k, ed[k]-id[k]); } else { /* It must be in the boundary already */ if (bndptr[k] == -1) printf("What you thought was wrong!\n"); PQueueUpdate(&parts[qnum[k]][0], 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); } ASSERTP(ComputeCut(graph, where) == mincut, ("%d != %d\n", ComputeCut(graph, where), mincut)); } if (ctrl->dbglvl&DBG_REFINE) { printf("\tMincut: %6d, NBND: %6d, NPwgts: ", mincut, nbnd); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf(", LB: %.3f\n", Compute2WayHLoadImbalance(ncon, npwgts, tpwgts)); } graph->mincut = mincut; graph->nbnd = nbnd; for (i=0; i<ncon; i++) { PQueueFree(ctrl, &parts[i][0]); PQueueFree(ctrl, &parts[i][1]); } ASSERT(ComputeCut(graph, where) == graph->mincut); ASSERT(CheckBnd(graph)); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }
/************************************************************************* * This function performs an edge-based FM refinement **************************************************************************/ void MocGeneral2WayBalance(CtrlType *ctrl, GraphType *graph, float *tpwgts, float lbfactor) { int i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass, me, limit, tmp, cnum; idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind; idxtype *moved, *swaps, *perm, *qnum; float *nvwgt, *npwgts, mindiff[MAXNCON], origbal, minbal, newbal; PQueueType parts[MAXNCON][2]; int higain, oldgain, mincut, newcut, mincutorder; int qsizes[MAXNCON][2]; nvtxs = graph->nvtxs; ncon = graph->ncon; xadj = graph->xadj; nvwgt = graph->nvwgt; adjncy = graph->adjncy; adjwgt = graph->adjwgt; where = graph->where; id = graph->id; ed = graph->ed; npwgts = graph->npwgts; bndptr = graph->bndptr; bndind = graph->bndind; moved = idxwspacemalloc(ctrl, nvtxs); swaps = idxwspacemalloc(ctrl, nvtxs); perm = idxwspacemalloc(ctrl, nvtxs); qnum = idxwspacemalloc(ctrl, nvtxs); limit = amin(amax(0.01*nvtxs, 15), 100); /* Initialize the queues */ for (i=0; i<ncon; i++) { PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1); PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1); qsizes[i][0] = qsizes[i][1] = 0; } for (i=0; i<nvtxs; i++) { qnum[i] = samax(ncon, nvwgt+i*ncon); qsizes[qnum[i]][where[i]]++; } /* printf("Weight Distribution: \t"); for (i=0; i<ncon; i++) printf(" [%d %d]", qsizes[i][0], qsizes[i][1]); printf("\n"); */ for (from=0; from<2; from++) { for (j=0; j<ncon; j++) { if (qsizes[j][from] == 0) { for (i=0; i<nvtxs; i++) { if (where[i] != from) continue; k = samax2(ncon, nvwgt+i*ncon); if (k == j && qsizes[qnum[i]][from] > qsizes[j][from] && nvwgt[i*ncon+qnum[i]] < 1.3*nvwgt[i*ncon+j]) { qsizes[qnum[i]][from]--; qsizes[j][from]++; qnum[i] = j; } } } } } /* printf("Weight Distribution (after):\t "); for (i=0; i<ncon; i++) printf(" [%d %d]", qsizes[i][0], qsizes[i][1]); printf("\n"); */ for (i=0; i<ncon; i++) mindiff[i] = fabs(tpwgts[0]-npwgts[i]); minbal = origbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts); newcut = mincut = graph->mincut; mincutorder = -1; if (ctrl->dbglvl&DBG_REFINE) { printf("Parts: ["); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: %.3f [B]\n", tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut, origbal); } idxset(nvtxs, -1, moved); ASSERT(ComputeCut(graph, where) == graph->mincut); ASSERT(CheckBnd(graph)); /* Insert all nodes in the priority queues */ nbnd = graph->nbnd; RandomPermute(nvtxs, perm, 1); for (ii=0; ii<nvtxs; ii++) { i = perm[ii]; PQueueInsert(&parts[qnum[i]][where[i]], i, ed[i]-id[i]); } for (nswaps=0; nswaps<nvtxs; nswaps++) { if (minbal < lbfactor) break; SelectQueue(ncon, npwgts, tpwgts, &from, &cnum, parts); to = (from+1)%2; if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1) break; saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); newcut -= (ed[higain]-id[higain]); newbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts); if (newbal < minbal || (newbal == minbal && (newcut < mincut || (newcut == mincut && BetterBalance(ncon, npwgts, tpwgts, mindiff))))) { mincut = newcut; minbal = newbal; mincutorder = nswaps; for (i=0; i<ncon; i++) mindiff[i] = fabs(tpwgts[0]-npwgts[i]); } else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */ newcut += (ed[higain]-id[higain]); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); break; } where[higain] = to; moved[higain] = nswaps; swaps[nswaps] = higain; if (ctrl->dbglvl&DBG_MOVEINFO) { printf("Moved %6d from %d(%d). Gain: %5d, Cut: %5d, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf(", %.3f LB: %.3f\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]; 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) PQueueUpdate(&parts[qnum[k]][where[k]], 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); } } /**************************************************************** * 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); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+((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&DBG_REFINE) { printf("\tMincut: %6d at %5d, NBND: %6d, NPwgts: [", mincut, mincutorder, nbnd); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf("], LB: %.3f\n", Compute2WayHLoadImbalance(ncon, npwgts, tpwgts)); } graph->mincut = mincut; graph->nbnd = nbnd; for (i=0; i<ncon; i++) { PQueueFree(ctrl, &parts[i][0]); PQueueFree(ctrl, &parts[i][1]); } idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }
/************************************************************************* * This function performs an edge-based FM refinement **************************************************************************/ void MocFM_2WayEdgeRefine(CtrlType *ctrl, GraphType *graph, float *tpwgts, int npasses) { int i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass, me, limit, tmp, cnum; idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind; idxtype *moved, *swaps, *perm, *qnum; float *nvwgt, *npwgts, mindiff[MAXNCON], origbal, minbal, newbal; PQueueType parts[MAXNCON][2]; int higain, oldgain, mincut, initcut, newcut, mincutorder; float rtpwgts[2]; nvtxs = graph->nvtxs; ncon = graph->ncon; xadj = graph->xadj; nvwgt = graph->nvwgt; adjncy = graph->adjncy; adjwgt = graph->adjwgt; where = graph->where; id = graph->id; ed = graph->ed; npwgts = graph->npwgts; bndptr = graph->bndptr; bndind = graph->bndind; moved = idxwspacemalloc(ctrl, nvtxs); swaps = idxwspacemalloc(ctrl, nvtxs); perm = idxwspacemalloc(ctrl, nvtxs); qnum = idxwspacemalloc(ctrl, nvtxs); limit = amin(amax(0.01*nvtxs, 25), 150); /* Initialize the queues */ for (i=0; i<ncon; i++) { PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1); PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1); } for (i=0; i<nvtxs; i++) qnum[i] = samax(ncon, nvwgt+i*ncon); origbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts); rtpwgts[0] = origbal*tpwgts[0]; rtpwgts[1] = origbal*tpwgts[1]; /* if (ctrl->dbglvl&DBG_REFINE) { printf("Parts: ["); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf("] T[%.3f %.3f], Nv-Nb[%5d, %5d]. ICut: %6d, LB: %.3f\n", tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut, origbal); } */ idxset(nvtxs, -1, moved); for (pass=0; pass<npasses; pass++) { /* Do a number of passes */ for (i=0; i<ncon; i++) { PQueueReset(&parts[i][0]); PQueueReset(&parts[i][1]); } mincutorder = -1; newcut = mincut = initcut = graph->mincut; for (i=0; i<ncon; i++) mindiff[i] = fabs(tpwgts[0]-npwgts[i]); minbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts); ASSERT(ComputeCut(graph, where) == graph->mincut); ASSERT(CheckBnd(graph)); /* Insert boundary nodes in the priority queues */ nbnd = graph->nbnd; RandomPermute(nbnd, perm, 1); for (ii=0; ii<nbnd; ii++) { i = bndind[perm[ii]]; ASSERT(ed[i] > 0 || id[i] == 0); ASSERT(bndptr[i] != -1); PQueueInsert(&parts[qnum[i]][where[i]], i, ed[i]-id[i]); } for (nswaps=0; nswaps<nvtxs; nswaps++) { SelectQueue(ncon, npwgts, rtpwgts, &from, &cnum, parts); to = (from+1)%2; if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1) break; ASSERT(bndptr[higain] != -1); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); newcut -= (ed[higain]-id[higain]); newbal = Compute2WayHLoadImbalance(ncon, npwgts, tpwgts); if ((newcut < mincut && newbal-origbal <= .00001) || (newcut == mincut && (newbal < minbal || (newbal == minbal && BetterBalance(ncon, npwgts, tpwgts, mindiff))))) { mincut = newcut; minbal = newbal; mincutorder = nswaps; for (i=0; i<ncon; i++) mindiff[i] = fabs(tpwgts[0]-npwgts[i]); } else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */ newcut += (ed[higain]-id[higain]); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); break; } where[higain] = to; moved[higain] = nswaps; swaps[nswaps] = higain; /* if (ctrl->dbglvl&DBG_MOVEINFO) { printf("Moved %6d from %d(%d). Gain: %5d, Cut: %5d, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf(", %.3f LB: %.3f\n", minbal, newbal); } */ /************************************************************** * 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) /* Remove it if in the queues */ PQueueDelete(&parts[qnum[k]][where[k]], k, oldgain); } else { /* If it has not been moved, update its position in the queue */ if (moved[k] == -1) PQueueUpdate(&parts[qnum[k]][where[k]], 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) PQueueInsert(&parts[qnum[k]][where[k]], k, ed[k]-id[k]); } } } } /**************************************************************** * Roll back computations *****************************************************************/ for (i=0; i<nswaps; i++) moved[swaps[i]] = -1; /* reset moved array */ 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); saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1); saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+((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&DBG_REFINE) { printf("\tMincut: %6d at %5d, NBND: %6d, NPwgts: [", mincut, mincutorder, nbnd); for (l=0; l<ncon; l++) printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]); printf("], LB: %.3f\n", Compute2WayHLoadImbalance(ncon, npwgts, tpwgts)); } */ graph->mincut = mincut; graph->nbnd = nbnd; if (mincutorder == -1 || mincut == initcut) break; } for (i=0; i<ncon; i++) { PQueueFree(ctrl, &parts[i][0]); PQueueFree(ctrl, &parts[i][1]); } idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }