diff options
Diffstat (limited to 'benchmarks/CUDA/DG/3rdParty/ParMetis-3.1/METISLib/mkwayfmh.c')
| -rw-r--r-- | benchmarks/CUDA/DG/3rdParty/ParMetis-3.1/METISLib/mkwayfmh.c | 677 |
1 files changed, 677 insertions, 0 deletions
diff --git a/benchmarks/CUDA/DG/3rdParty/ParMetis-3.1/METISLib/mkwayfmh.c b/benchmarks/CUDA/DG/3rdParty/ParMetis-3.1/METISLib/mkwayfmh.c new file mode 100644 index 0000000..69a781a --- /dev/null +++ b/benchmarks/CUDA/DG/3rdParty/ParMetis-3.1/METISLib/mkwayfmh.c @@ -0,0 +1,677 @@ +/* + * mkwayfmh.c + * + * This file contains code that implements the multilevel k-way refinement + * + * Started 7/28/97 + * George + * + * $Id: mkwayfmh.c,v 1.1 2003/07/16 15:55:10 karypis Exp $ + * + */ + +#include <metis.h> + + + +/************************************************************************* +* This function performs k-way refinement +**************************************************************************/ +void MCRandom_KWayEdgeRefineHorizontal(CtrlType *ctrl, GraphType *graph, int nparts, + float *orgubvec, int npasses) +{ + int i, ii, iii, j, jj, k, l, pass, nvtxs, ncon, nmoves, nbnd, myndegrees, same; + int from, me, to, oldcut, gain; + idxtype *xadj, *adjncy, *adjwgt; + idxtype *where, *perm, *bndptr, *bndind; + EDegreeType *myedegrees; + RInfoType *myrinfo; + float *npwgts, *nvwgt, *minwgt, *maxwgt, maxlb, minlb, ubvec[MAXNCON], tvec[MAXNCON]; + + nvtxs = graph->nvtxs; + ncon = graph->ncon; + xadj = graph->xadj; + adjncy = graph->adjncy; + adjwgt = graph->adjwgt; + + bndptr = graph->bndptr; + bndind = graph->bndind; + + where = graph->where; + npwgts = graph->npwgts; + + /* Setup the weight intervals of the various subdomains */ + minwgt = fwspacemalloc(ctrl, nparts*ncon); + maxwgt = fwspacemalloc(ctrl, nparts*ncon); + + /* See if the orgubvec consists of identical constraints */ + maxlb = minlb = orgubvec[0]; + for (i=1; i<ncon; i++) { + minlb = (orgubvec[i] < minlb ? orgubvec[i] : minlb); + maxlb = (orgubvec[i] > maxlb ? orgubvec[i] : maxlb); + } + same = (fabs(maxlb-minlb) < .01 ? 1 : 0); + + + /* Let's not get very optimistic. Let Balancing do the work */ + ComputeHKWayLoadImbalance(ncon, nparts, npwgts, ubvec); + for (i=0; i<ncon; i++) + ubvec[i] = amax(ubvec[i], orgubvec[i]); + + if (!same) { + for (i=0; i<nparts; i++) { + for (j=0; j<ncon; j++) { + maxwgt[i*ncon+j] = ubvec[j]/nparts; + minwgt[i*ncon+j] = 1.0/(ubvec[j]*nparts); + } + } + } + else { + maxlb = ubvec[0]; + for (i=1; i<ncon; i++) + maxlb = (ubvec[i] > maxlb ? ubvec[i] : maxlb); + + for (i=0; i<nparts; i++) { + for (j=0; j<ncon; j++) { + maxwgt[i*ncon+j] = maxlb/nparts; + minwgt[i*ncon+j] = 1.0/(maxlb*nparts); + } + } + } + + + perm = idxwspacemalloc(ctrl, nvtxs); + + if (ctrl->dbglvl&DBG_REFINE) { + printf("Partitions: [%5.4f %5.4f], Nv-Nb[%6d %6d]. Cut: %6d, LB: ", + npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], + graph->nvtxs, graph->nbnd, graph->mincut); + ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec); + for (i=0; i<ncon; i++) + printf("%.3f ", tvec[i]); + printf("\n"); + } + + for (pass=0; pass<npasses; pass++) { + ASSERT(ComputeCut(graph, where) == graph->mincut); + + oldcut = graph->mincut; + nbnd = graph->nbnd; + + RandomPermute(nbnd, perm, 1); + for (nmoves=iii=0; iii<graph->nbnd; iii++) { + ii = perm[iii]; + if (ii >= nbnd) + continue; + i = bndind[ii]; + + myrinfo = graph->rinfo+i; + + if (myrinfo->ed >= myrinfo->id) { /* Total ED is too high */ + from = where[i]; + nvwgt = graph->nvwgt+i*ncon; + + if (myrinfo->id > 0 && AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, -1.0, nvwgt, minwgt+from*ncon)) + continue; /* This cannot be moved! */ + + myedegrees = myrinfo->edegrees; + myndegrees = myrinfo->ndegrees; + + for (k=0; k<myndegrees; k++) { + to = myedegrees[k].pid; + gain = myedegrees[k].ed - myrinfo->id; + if (gain >= 0 && + (AreAllHVwgtsBelow(ncon, 1.0, npwgts+to*ncon, 1.0, nvwgt, maxwgt+to*ncon) || + IsHBalanceBetterFT(ncon, nparts, npwgts+from*ncon, npwgts+to*ncon, nvwgt, ubvec))) + break; + } + if (k == myndegrees) + continue; /* break out if you did not find a candidate */ + + for (j=k+1; j<myndegrees; j++) { + to = myedegrees[j].pid; + if ((myedegrees[j].ed > myedegrees[k].ed && + (AreAllHVwgtsBelow(ncon, 1.0, npwgts+to*ncon, 1.0, nvwgt, maxwgt+to*ncon) || + IsHBalanceBetterFT(ncon, nparts, npwgts+from*ncon, npwgts+to*ncon, nvwgt, ubvec))) || + (myedegrees[j].ed == myedegrees[k].ed && + IsHBalanceBetterTT(ncon, nparts, npwgts+myedegrees[k].pid*ncon, npwgts+to*ncon, nvwgt, ubvec))) + k = j; + } + + to = myedegrees[k].pid; + + if (myedegrees[k].ed-myrinfo->id == 0 + && !IsHBalanceBetterFT(ncon, nparts, npwgts+from*ncon, npwgts+to*ncon, nvwgt, ubvec) + && AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, 0.0, npwgts+from*ncon, maxwgt+from*ncon)) + continue; + + /*===================================================================== + * If we got here, we can now move the vertex from 'from' to 'to' + *======================================================================*/ + graph->mincut -= myedegrees[k].ed-myrinfo->id; + + IFSET(ctrl->dbglvl, DBG_MOVEINFO, printf("\t\tMoving %6d to %3d. Gain: %4d. Cut: %6d\n", i, to, myedegrees[k].ed-myrinfo->id, graph->mincut)); + + /* Update where, weight, and ID/ED information of the vertex you moved */ + saxpy(ncon, 1.0, nvwgt, 1, npwgts+to*ncon, 1); + saxpy(ncon, -1.0, nvwgt, 1, npwgts+from*ncon, 1); + where[i] = to; + myrinfo->ed += myrinfo->id-myedegrees[k].ed; + SWAP(myrinfo->id, myedegrees[k].ed, j); + if (myedegrees[k].ed == 0) + myedegrees[k] = myedegrees[--myrinfo->ndegrees]; + else + myedegrees[k].pid = from; + + if (myrinfo->ed-myrinfo->id < 0) + BNDDelete(nbnd, bndind, bndptr, i); + + /* Update the degrees of adjacent vertices */ + for (j=xadj[i]; j<xadj[i+1]; j++) { + ii = adjncy[j]; + me = where[ii]; + + myrinfo = graph->rinfo+ii; + if (myrinfo->edegrees == NULL) { + myrinfo->edegrees = ctrl->wspace.edegrees+ctrl->wspace.cdegree; + ctrl->wspace.cdegree += xadj[ii+1]-xadj[ii]; + } + myedegrees = myrinfo->edegrees; + + ASSERT(CheckRInfo(myrinfo)); + + if (me == from) { + INC_DEC(myrinfo->ed, myrinfo->id, adjwgt[j]); + + if (myrinfo->ed-myrinfo->id >= 0 && bndptr[ii] == -1) + BNDInsert(nbnd, bndind, bndptr, ii); + } + else if (me == to) { + INC_DEC(myrinfo->id, myrinfo->ed, adjwgt[j]); + + if (myrinfo->ed-myrinfo->id < 0 && bndptr[ii] != -1) + BNDDelete(nbnd, bndind, bndptr, ii); + } + + /* Remove contribution from the .ed of 'from' */ + if (me != from) { + for (k=0; k<myrinfo->ndegrees; k++) { + if (myedegrees[k].pid == from) { + if (myedegrees[k].ed == adjwgt[j]) + myedegrees[k] = myedegrees[--myrinfo->ndegrees]; + else + myedegrees[k].ed -= adjwgt[j]; + break; + } + } + } + + /* Add contribution to the .ed of 'to' */ + if (me != to) { + for (k=0; k<myrinfo->ndegrees; k++) { + if (myedegrees[k].pid == to) { + myedegrees[k].ed += adjwgt[j]; + break; + } + } + if (k == myrinfo->ndegrees) { + myedegrees[myrinfo->ndegrees].pid = to; + myedegrees[myrinfo->ndegrees++].ed = adjwgt[j]; + } + } + + ASSERT(myrinfo->ndegrees <= xadj[ii+1]-xadj[ii]); + ASSERT(CheckRInfo(myrinfo)); + + } + nmoves++; + } + } + + graph->nbnd = nbnd; + + if (ctrl->dbglvl&DBG_REFINE) { + printf("\t [%5.4f %5.4f], Nb: %6d, Nmoves: %5d, Cut: %6d, LB: ", + npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], + nbnd, nmoves, graph->mincut); + ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec); + for (i=0; i<ncon; i++) + printf("%.3f ", tvec[i]); + printf("\n"); + } + + if (graph->mincut == oldcut) + break; + } + + fwspacefree(ctrl, ncon*nparts); + fwspacefree(ctrl, ncon*nparts); + idxwspacefree(ctrl, nvtxs); +} + + + +/************************************************************************* +* This function performs k-way refinement +**************************************************************************/ +void MCGreedy_KWayEdgeBalanceHorizontal(CtrlType *ctrl, GraphType *graph, int nparts, + float *ubvec, int npasses) +{ + int i, ii, iii, j, jj, k, l, pass, nvtxs, ncon, nbnd, myndegrees, oldgain, gain, nmoves; + int from, me, to, oldcut; + idxtype *xadj, *adjncy, *adjwgt; + idxtype *where, *perm, *bndptr, *bndind, *moved; + EDegreeType *myedegrees; + RInfoType *myrinfo; + PQueueType queue; + float *npwgts, *nvwgt, *minwgt, *maxwgt, tvec[MAXNCON]; + + nvtxs = graph->nvtxs; + ncon = graph->ncon; + xadj = graph->xadj; + adjncy = graph->adjncy; + adjwgt = graph->adjwgt; + + bndind = graph->bndind; + bndptr = graph->bndptr; + + where = graph->where; + npwgts = graph->npwgts; + + /* Setup the weight intervals of the various subdomains */ + minwgt = fwspacemalloc(ctrl, ncon*nparts); + maxwgt = fwspacemalloc(ctrl, ncon*nparts); + + for (i=0; i<nparts; i++) { + for (j=0; j<ncon; j++) { + maxwgt[i*ncon+j] = ubvec[j]/nparts; + minwgt[i*ncon+j] = 1.0/(ubvec[j]*nparts); + } + } + + perm = idxwspacemalloc(ctrl, nvtxs); + moved = idxwspacemalloc(ctrl, nvtxs); + + PQueueInit(ctrl, &queue, nvtxs, graph->adjwgtsum[idxamax(nvtxs, graph->adjwgtsum)]); + + if (ctrl->dbglvl&DBG_REFINE) { + printf("Partitions: [%5.4f %5.4f], Nv-Nb[%6d %6d]. Cut: %6d, LB: ", + npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], + graph->nvtxs, graph->nbnd, graph->mincut); + ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec); + for (i=0; i<ncon; i++) + printf("%.3f ", tvec[i]); + printf("[B]\n"); + } + + + for (pass=0; pass<npasses; pass++) { + ASSERT(ComputeCut(graph, where) == graph->mincut); + + /* Check to see if things are out of balance, given the tolerance */ + if (MocIsHBalanced(ncon, nparts, npwgts, ubvec)) + break; + + PQueueReset(&queue); + idxset(nvtxs, -1, moved); + + oldcut = graph->mincut; + nbnd = graph->nbnd; + + RandomPermute(nbnd, perm, 1); + for (ii=0; ii<nbnd; ii++) { + i = bndind[perm[ii]]; + PQueueInsert(&queue, i, graph->rinfo[i].ed - graph->rinfo[i].id); + moved[i] = 2; + } + + nmoves = 0; + for (;;) { + if ((i = PQueueGetMax(&queue)) == -1) + break; + moved[i] = 1; + + myrinfo = graph->rinfo+i; + from = where[i]; + nvwgt = graph->nvwgt+i*ncon; + + if (AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, -1.0, nvwgt, minwgt+from*ncon)) + continue; /* This cannot be moved! */ + + myedegrees = myrinfo->edegrees; + myndegrees = myrinfo->ndegrees; + + for (k=0; k<myndegrees; k++) { + to = myedegrees[k].pid; + if (IsHBalanceBetterFT(ncon, nparts, npwgts+from*ncon, npwgts+to*ncon, nvwgt, ubvec)) + break; + } + if (k == myndegrees) + continue; /* break out if you did not find a candidate */ + + for (j=k+1; j<myndegrees; j++) { + to = myedegrees[j].pid; + if (IsHBalanceBetterTT(ncon, nparts, npwgts+myedegrees[k].pid*ncon, npwgts+to*ncon, nvwgt, ubvec)) + k = j; + } + + to = myedegrees[k].pid; + + j = 0; + if (!AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, 0.0, nvwgt, maxwgt+from*ncon)) + j++; + if (myedegrees[k].ed-myrinfo->id >= 0) + j++; + if (!AreAllHVwgtsAbove(ncon, 1.0, npwgts+to*ncon, 0.0, nvwgt, minwgt+to*ncon) && + AreAllHVwgtsBelow(ncon, 1.0, npwgts+to*ncon, 1.0, nvwgt, maxwgt+to*ncon)) + j++; + if (j == 0) + continue; + +/* DELETE + if (myedegrees[k].ed-myrinfo->id < 0 && + AreAllHVwgtsBelow(ncon, 1.0, npwgts+from*ncon, 0.0, nvwgt, maxwgt+from*ncon) && + AreAllHVwgtsAbove(ncon, 1.0, npwgts+to*ncon, 0.0, nvwgt, minwgt+to*ncon) && + AreAllHVwgtsBelow(ncon, 1.0, npwgts+to*ncon, 1.0, nvwgt, maxwgt+to*ncon)) + continue; +*/ + /*===================================================================== + * If we got here, we can now move the vertex from 'from' to 'to' + *======================================================================*/ + graph->mincut -= myedegrees[k].ed-myrinfo->id; + + IFSET(ctrl->dbglvl, DBG_MOVEINFO, printf("\t\tMoving %6d to %3d. Gain: %4d. Cut: %6d\n", i, to, myedegrees[k].ed-myrinfo->id, graph->mincut)); + + /* Update where, weight, and ID/ED information of the vertex you moved */ + saxpy(ncon, 1.0, nvwgt, 1, npwgts+to*ncon, 1); + saxpy(ncon, -1.0, nvwgt, 1, npwgts+from*ncon, 1); + where[i] = to; + myrinfo->ed += myrinfo->id-myedegrees[k].ed; + SWAP(myrinfo->id, myedegrees[k].ed, j); + if (myedegrees[k].ed == 0) + myedegrees[k] = myedegrees[--myrinfo->ndegrees]; + else + myedegrees[k].pid = from; + + if (myrinfo->ed == 0) + BNDDelete(nbnd, bndind, bndptr, i); + + /* Update the degrees of adjacent vertices */ + for (j=xadj[i]; j<xadj[i+1]; j++) { + ii = adjncy[j]; + me = where[ii]; + + myrinfo = graph->rinfo+ii; + if (myrinfo->edegrees == NULL) { + myrinfo->edegrees = ctrl->wspace.edegrees+ctrl->wspace.cdegree; + ctrl->wspace.cdegree += xadj[ii+1]-xadj[ii]; + } + myedegrees = myrinfo->edegrees; + + ASSERT(CheckRInfo(myrinfo)); + + oldgain = (myrinfo->ed-myrinfo->id); + + if (me == from) { + INC_DEC(myrinfo->ed, myrinfo->id, adjwgt[j]); + + if (myrinfo->ed > 0 && bndptr[ii] == -1) + BNDInsert(nbnd, bndind, bndptr, ii); + } + else if (me == to) { + INC_DEC(myrinfo->id, myrinfo->ed, adjwgt[j]); + + if (myrinfo->ed == 0 && bndptr[ii] != -1) + BNDDelete(nbnd, bndind, bndptr, ii); + } + + /* Remove contribution from the .ed of 'from' */ + if (me != from) { + for (k=0; k<myrinfo->ndegrees; k++) { + if (myedegrees[k].pid == from) { + if (myedegrees[k].ed == adjwgt[j]) + myedegrees[k] = myedegrees[--myrinfo->ndegrees]; + else + myedegrees[k].ed -= adjwgt[j]; + break; + } + } + } + + /* Add contribution to the .ed of 'to' */ + if (me != to) { + for (k=0; k<myrinfo->ndegrees; k++) { + if (myedegrees[k].pid == to) { + myedegrees[k].ed += adjwgt[j]; + break; + } + } + if (k == myrinfo->ndegrees) { + myedegrees[myrinfo->ndegrees].pid = to; + myedegrees[myrinfo->ndegrees++].ed = adjwgt[j]; + } + } + + + /* Update the queue */ + if (me == to || me == from) { + gain = myrinfo->ed-myrinfo->id; + if (moved[ii] == 2) { + if (myrinfo->ed > 0) + PQueueUpdate(&queue, ii, oldgain, gain); + else { + PQueueDelete(&queue, ii, oldgain); + moved[ii] = -1; + } + } + else if (moved[ii] == -1 && myrinfo->ed > 0) { + PQueueInsert(&queue, ii, gain); + moved[ii] = 2; + } + } + + ASSERT(myrinfo->ndegrees <= xadj[ii+1]-xadj[ii]); + ASSERT(CheckRInfo(myrinfo)); + } + nmoves++; + } + + graph->nbnd = nbnd; + + if (ctrl->dbglvl&DBG_REFINE) { + printf("\t [%5.4f %5.4f], Nb: %6d, Nmoves: %5d, Cut: %6d, LB: ", + npwgts[samin(ncon*nparts, npwgts)], npwgts[samax(ncon*nparts, npwgts)], + nbnd, nmoves, graph->mincut); + ComputeHKWayLoadImbalance(ncon, nparts, npwgts, tvec); + for (i=0; i<ncon; i++) + printf("%.3f ", tvec[i]); + printf("\n"); + } + + if (nmoves == 0) + break; + } + + PQueueFree(ctrl, &queue); + + fwspacefree(ctrl, ncon*nparts); + fwspacefree(ctrl, ncon*nparts); + idxwspacefree(ctrl, nvtxs); + idxwspacefree(ctrl, nvtxs); + +} + + + + + +/************************************************************************* +* This function checks if the vertex weights of two vertices are below +* a given set of values +**************************************************************************/ +int AreAllHVwgtsBelow(int ncon, float alpha, float *vwgt1, float beta, float *vwgt2, float *limit) +{ + int i; + + for (i=0; i<ncon; i++) + if (alpha*vwgt1[i] + beta*vwgt2[i] > limit[i]) + return 0; + + return 1; +} + + + +/************************************************************************* +* This function checks if the vertex weights of two vertices are above +* a given set of values +**************************************************************************/ +int AreAllHVwgtsAbove(int ncon, float alpha, float *vwgt1, float beta, float *vwgt2, float *limit) +{ + int i; + + for (i=0; i<ncon; i++) + if (alpha*vwgt1[i] + beta*vwgt2[i] < limit[i]) + return 0; + + return 1; +} + + +/************************************************************************* +* This function computes the load imbalance over all the constrains +* For now assume that we just want balanced partitionings +**************************************************************************/ +void ComputeHKWayLoadImbalance(int ncon, int nparts, float *npwgts, float *lbvec) +{ + int i, j; + float max; + + for (i=0; i<ncon; i++) { + max = 0.0; + for (j=0; j<nparts; j++) { + if (npwgts[j*ncon+i] > max) + max = npwgts[j*ncon+i]; + } + + lbvec[i] = max*nparts; + } +} + + +/************************************************************************* +* This function determines if a partitioning is horizontally balanced +**************************************************************************/ +int MocIsHBalanced(int ncon, int nparts, float *npwgts, float *ubvec) +{ + int i, j; + float max; + + for (i=0; i<ncon; i++) { + max = 0.0; + for (j=0; j<nparts; j++) { + if (npwgts[j*ncon+i] > max) + max = npwgts[j*ncon+i]; + } + + if (ubvec[i] < max*nparts) + return 0; + } + + return 1; +} + + + + + +/************************************************************************* +* This function checks if the pairwise balance of the between the two +* partitions will improve by moving the vertex v from pfrom to pto, +* subject to the target partition weights of tfrom, and tto respectively +**************************************************************************/ +int IsHBalanceBetterFT(int ncon, int nparts, float *pfrom, float *pto, float *vwgt, float *ubvec) +{ + int i, j, k; + float blb1=0.0, alb1=0.0, sblb=0.0, salb=0.0; + float blb2=0.0, alb2=0.0; + float temp; + + for (i=0; i<ncon; i++) { + temp = amax(pfrom[i], pto[i])*nparts/ubvec[i]; + if (blb1 < temp) { + blb2 = blb1; + blb1 = temp; + } + else if (blb2 < temp) + blb2 = temp; + sblb += temp; + + temp = amax(pfrom[i]-vwgt[i], pto[i]+vwgt[i])*nparts/ubvec[i]; + if (alb1 < temp) { + alb2 = alb1; + alb1 = temp; + } + else if (alb2 < temp) + alb2 = temp; + salb += temp; + } + + if (alb1 < blb1) + return 1; + if (blb1 < alb1) + return 0; + if (alb2 < blb2) + return 1; + if (blb2 < alb2) + return 0; + + return salb < sblb; + +} + + + + +/************************************************************************* +* This function checks if it will be better to move a vertex to pt2 than +* to pt1 subject to their target weights of tt1 and tt2, respectively +* This routine takes into account the weight of the vertex in question +**************************************************************************/ +int IsHBalanceBetterTT(int ncon, int nparts, float *pt1, float *pt2, float *vwgt, float *ubvec) +{ + int i; + float m11=0.0, m12=0.0, m21=0.0, m22=0.0, sm1=0.0, sm2=0.0, temp; + + for (i=0; i<ncon; i++) { + temp = (pt1[i]+vwgt[i])*nparts/ubvec[i]; + if (m11 < temp) { + m12 = m11; + m11 = temp; + } + else if (m12 < temp) + m12 = temp; + sm1 += temp; + + temp = (pt2[i]+vwgt[i])*nparts/ubvec[i]; + if (m21 < temp) { + m22 = m21; + m21 = temp; + } + else if (m22 < temp) + m22 = temp; + sm2 += temp; + } + + if (m21 < m11) + return 1; + if (m21 > m11) + return 0; + if (m22 < m12) + return 1; + if (m22 > m12) + return 0; + + return sm2 < sm1; +} + |
