/************************************************************************* * This function performs a node-based FM refinement. This is the * one-way version **************************************************************************/ void FM_2WayNodeRefine_OneSided(CtrlType *ctrl, GraphType *graph, float ubfactor, idxtype npasses) { idxtype i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps, nmind; idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr; idxtype *mptr, *mind, *swaps, *perm; PQueueType parts; NRInfoType *rinfo; idxtype higain, oldgain, mincut, initcut, mincutorder; idxtype pass, to, other, limit; idxtype badmaxpwgt, mindiff, newdiff; nvtxs = graph->nvtxs; xadj = graph->xadj; adjncy = graph->adjncy; vwgt = graph->vwgt; bndind = graph->bndind; bndptr = graph->bndptr; where = graph->where; pwgts = graph->pwgts; rinfo = graph->nrinfo; PQueueInit(ctrl, &parts, nvtxs, ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt)); perm = idxwspacemalloc(ctrl, nvtxs); swaps = idxwspacemalloc(ctrl, nvtxs); mptr = idxwspacemalloc(ctrl, nvtxs+1); mind = idxwspacemalloc(ctrl, nvtxs); IFSET(ctrl->dbglvl, DBG_REFINE, mprintf("Partitions-N1: [%6D %6D] Nv-Nb[%6D %6D]. ISep: %6D\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, graph->mincut)); badmaxpwgt = (int)(ubfactor*(pwgts[0]+pwgts[1]+pwgts[2])/2); to = (pwgts[0] < pwgts[1] ? 1 : 0); for (pass=0; pass<npasses; pass++) { other = to; to = (to+1)%2; PQueueReset(&parts); mincutorder = -1; initcut = mincut = graph->mincut; nbnd = graph->nbnd; RandomPermute(nbnd, perm, 1); for (ii=0; ii<nbnd; ii++) { i = bndind[perm[ii]]; ASSERT(where[i] == 2); PQueueInsert(&parts, i, vwgt[i]-rinfo[i].edegrees[other]); } ASSERT(CheckNodeBnd(graph, nbnd)); ASSERT(CheckNodePartitionParams(graph)); limit = (ctrl->oflags&OFLAG_COMPRESS ? amin(5*nbnd, 400) : amin(2*nbnd, 300)); /****************************************************** * Get into the FM loop *******************************************************/ mptr[0] = nmind = 0; mindiff = idxtype_abs(pwgts[0]-pwgts[1]); for (nswaps=0; nswaps<nvtxs; nswaps++) { if ((higain = PQueueGetMax(&parts)) == -1) break; ASSERT(bndptr[higain] != -1); if (pwgts[to]+vwgt[higain] > badmaxpwgt) break; /* No point going any further. Balance will be bad */ pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[other]); newdiff = idxtype_abs(pwgts[to]+vwgt[higain] - (pwgts[other]-rinfo[higain].edegrees[other])); if (pwgts[2] < mincut || (pwgts[2] == mincut && newdiff < mindiff)) { mincut = pwgts[2]; mincutorder = nswaps; mindiff = newdiff; } else { if (nswaps - mincutorder > limit) { pwgts[2] += (vwgt[higain]-rinfo[higain].edegrees[other]); break; /* No further improvement, break out */ } } BNDDelete(nbnd, bndind, bndptr, higain); pwgts[to] += vwgt[higain]; where[higain] = to; swaps[nswaps] = higain; /********************************************************** * Update the degrees of the affected nodes ***********************************************************/ for (j=xadj[higain]; j<xadj[higain+1]; j++) { k = adjncy[j]; if (where[k] == 2) { /* For the in-separator vertices modify their edegree[to] */ rinfo[k].edegrees[to] += vwgt[higain]; } else if (where[k] == other) { /* This vertex is pulled into the separator */ ASSERTP(bndptr[k] == -1, ("%d %d %d\n", k, bndptr[k], where[k])); BNDInsert(nbnd, bndind, bndptr, k); mind[nmind++] = k; /* Keep track for rollback */ where[k] = 2; pwgts[other] -= vwgt[k]; edegrees = rinfo[k].edegrees; edegrees[0] = edegrees[1] = 0; for (jj=xadj[k]; jj<xadj[k+1]; jj++) { kk = adjncy[jj]; if (where[kk] != 2) edegrees[where[kk]] += vwgt[kk]; else { oldgain = vwgt[kk]-rinfo[kk].edegrees[other]; rinfo[kk].edegrees[other] -= vwgt[k]; /* Since the moves are one-sided this vertex has not been moved yet */ PQueueUpdateUp(&parts, kk, oldgain, oldgain+vwgt[k]); } } /* Insert the new vertex into the priority queue. Safe due to one-sided moves */ PQueueInsert(&parts, k, vwgt[k]-edegrees[other]); } } mptr[nswaps+1] = nmind; IFSET(ctrl->dbglvl, DBG_MOVEINFO, mprintf("Moved %6D to %3D, Gain: %5D [%5D] \t[%5D %5D %5D] [%3D %2D]\n", higain, to, (vwgt[higain]-rinfo[higain].edegrees[other]), vwgt[higain], pwgts[0], pwgts[1], pwgts[2], nswaps, limit)); } /**************************************************************** * Roll back computation *****************************************************************/ for (nswaps--; nswaps>mincutorder; nswaps--) { higain = swaps[nswaps]; ASSERT(CheckNodePartitionParams(graph)); ASSERT(where[higain] == to); INC_DEC(pwgts[2], pwgts[to], vwgt[higain]); where[higain] = 2; BNDInsert(nbnd, bndind, bndptr, higain); edegrees = rinfo[higain].edegrees; edegrees[0] = edegrees[1] = 0; for (j=xadj[higain]; j<xadj[higain+1]; j++) { k = adjncy[j]; if (where[k] == 2) rinfo[k].edegrees[to] -= vwgt[higain]; else edegrees[where[k]] += vwgt[k]; } /* Push nodes out of the separator */ for (j=mptr[nswaps]; j<mptr[nswaps+1]; j++) { k = mind[j]; ASSERT(where[k] == 2); where[k] = other; INC_DEC(pwgts[other], pwgts[2], vwgt[k]); BNDDelete(nbnd, bndind, bndptr, k); for (jj=xadj[k]; jj<xadj[k+1]; jj++) { kk = adjncy[jj]; if (where[kk] == 2) rinfo[kk].edegrees[other] += vwgt[k]; } } } ASSERT(mincut == pwgts[2]); IFSET(ctrl->dbglvl, DBG_REFINE, mprintf("\tMinimum sep: %6D at %5D, PWGTS: [%6D %6D], NBND: %6D\n", mincut, mincutorder, pwgts[0], pwgts[1], nbnd)); graph->mincut = mincut; graph->nbnd = nbnd; if (pass%2 == 1 && (mincutorder == -1 || mincut >= initcut)) break; } PQueueFree(ctrl, &parts); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs+1); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }
/************************************************************************* * This function performs a node-based FM refinement **************************************************************************/ void FM_2WayNodeBalance(CtrlType *ctrl, GraphType *graph, float ubfactor) { idxtype i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps; idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr; idxtype *perm, *moved; PQueueType parts; NRInfoType *rinfo; idxtype higain, oldgain; idxtype pass, to, other; nvtxs = graph->nvtxs; xadj = graph->xadj; adjncy = graph->adjncy; vwgt = graph->vwgt; bndind = graph->bndind; bndptr = graph->bndptr; where = graph->where; pwgts = graph->pwgts; rinfo = graph->nrinfo; if (idxtype_abs(pwgts[0]-pwgts[1]) < (int)((ubfactor-1.0)*(pwgts[0]+pwgts[1]))) return; if (idxtype_abs(pwgts[0]-pwgts[1]) < 3*idxsum(nvtxs, vwgt, 1)/nvtxs) return; to = (pwgts[0] < pwgts[1] ? 0 : 1); other = (to+1)%2; PQueueInit(ctrl, &parts, nvtxs, ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt)); perm = idxwspacemalloc(ctrl, nvtxs); moved = idxset(nvtxs, -1, idxwspacemalloc(ctrl, nvtxs)); IFSET(ctrl->dbglvl, DBG_REFINE, mprintf("Partitions: [%6D %6D] Nv-Nb[%6D %6D]. ISep: %6D [B]\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, graph->mincut)); nbnd = graph->nbnd; RandomPermute(nbnd, perm, 1); for (ii=0; ii<nbnd; ii++) { i = bndind[perm[ii]]; ASSERT(where[i] == 2); PQueueInsert(&parts, i, vwgt[i]-rinfo[i].edegrees[other]); } ASSERT(CheckNodeBnd(graph, nbnd)); ASSERT(CheckNodePartitionParams(graph)); /****************************************************** * Get into the FM loop *******************************************************/ for (nswaps=0; nswaps<nvtxs; nswaps++) { if ((higain = PQueueGetMax(&parts)) == -1) break; moved[higain] = 1; if (pwgts[other] - rinfo[higain].edegrees[other] < (pwgts[0]+pwgts[1])/2) continue; #ifdef XXX if (pwgts[other] - rinfo[higain].edegrees[other] < pwgts[to]+vwgt[higain]) break; #endif ASSERT(bndptr[higain] != -1); pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[other]); BNDDelete(nbnd, bndind, bndptr, higain); pwgts[to] += vwgt[higain]; where[higain] = to; IFSET(ctrl->dbglvl, DBG_MOVEINFO, mprintf("Moved %6D to %3D, Gain: %3D, \t[%5D %5D %5D]\n", higain, to, vwgt[higain]-rinfo[higain].edegrees[other], pwgts[0], pwgts[1], pwgts[2])); /********************************************************** * Update the degrees of the affected nodes ***********************************************************/ for (j=xadj[higain]; j<xadj[higain+1]; j++) { k = adjncy[j]; if (where[k] == 2) { /* For the in-separator vertices modify their edegree[to] */ rinfo[k].edegrees[to] += vwgt[higain]; } else if (where[k] == other) { /* This vertex is pulled into the separator */ ASSERTP(bndptr[k] == -1, ("%d %d %d\n", k, bndptr[k], where[k])); BNDInsert(nbnd, bndind, bndptr, k); where[k] = 2; pwgts[other] -= vwgt[k]; edegrees = rinfo[k].edegrees; edegrees[0] = edegrees[1] = 0; for (jj=xadj[k]; jj<xadj[k+1]; jj++) { kk = adjncy[jj]; if (where[kk] != 2) edegrees[where[kk]] += vwgt[kk]; else { ASSERT(bndptr[kk] != -1); oldgain = vwgt[kk]-rinfo[kk].edegrees[other]; rinfo[kk].edegrees[other] -= vwgt[k]; if (moved[kk] == -1) PQueueUpdateUp(&parts, kk, oldgain, oldgain+vwgt[k]); } } /* Insert the new vertex into the priority queue */ PQueueInsert(&parts, k, vwgt[k]-edegrees[other]); } } if (pwgts[to] > pwgts[other]) break; } IFSET(ctrl->dbglvl, DBG_REFINE, mprintf("\tBalanced sep: %6D at %4D, PWGTS: [%6D %6D], NBND: %6D\n", pwgts[2], nswaps, pwgts[0], pwgts[1], nbnd)); graph->mincut = pwgts[2]; graph->nbnd = nbnd; PQueueFree(ctrl, &parts); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }
void FM_2WayNodeRefine_OneSidedP(CtrlType *ctrl, GraphType *graph, idxtype *hmarker, float ubfactor, int npasses) { int i, ii, j, k, jj, kk, nvtxs, nbnd, nswaps, nmind, nbad, qsize; idxtype *xadj, *vwgt, *adjncy, *where, *pwgts, *edegrees, *bndind, *bndptr; idxtype *mptr, *mind, *swaps, *perm, *inqueue; PQueueType parts; NRInfoType *rinfo; int higain, oldgain, mincut, initcut, mincutorder; int pass, from, to, limit; int badmaxpwgt, mindiff, newdiff; ASSERT(graph->mincut == graph->pwgts[2]); nvtxs = graph->nvtxs; xadj = graph->xadj; adjncy = graph->adjncy; vwgt = graph->vwgt; bndind = graph->bndind; bndptr = graph->bndptr; where = graph->where; pwgts = graph->pwgts; rinfo = graph->nrinfo; PQueueInit(ctrl, &parts, nvtxs, ComputeMaxNodeGain(nvtxs, xadj, adjncy, vwgt)); perm = idxwspacemalloc(ctrl, nvtxs); swaps = idxwspacemalloc(ctrl, nvtxs); mptr = idxwspacemalloc(ctrl, nvtxs+1); mind = idxwspacemalloc(ctrl, nvtxs); inqueue = idxwspacemalloc(ctrl, nvtxs); idxset(nvtxs, -1, inqueue); badmaxpwgt = (int)(ubfactor*amax(pwgts[0], pwgts[1])); IFSET(ctrl->dbglvl, DBG_REFINE, printf("Partitions-N1: [%6d %6d] Nv-Nb[%6d %6d] MaxPwgt[%6d]. ISep: %6d\n", pwgts[0], pwgts[1], graph->nvtxs, graph->nbnd, badmaxpwgt, graph->mincut)); to = (pwgts[0] < pwgts[1] ? 1 : 0); for (pass=0; pass<npasses; pass++) { from = to; to = (from+1)%2; PQueueReset(&parts); mincutorder = -1; initcut = mincut = graph->mincut; nbnd = graph->nbnd; RandomPermute(nbnd, perm, 1); for (ii=0; ii<nbnd; ii++) { i = bndind[perm[ii]]; ASSERT(where[i] == 2); if (hmarker[i] == -1 || hmarker[i] == to) { PQueueInsert(&parts, i, vwgt[i]-rinfo[i].edegrees[from]); inqueue[i] = pass; } } qsize = parts.nnodes; ASSERT(CheckNodeBnd(graph, nbnd)); ASSERT(CheckNodePartitionParams(graph)); limit = nbnd; /****************************************************** * Get into the FM loop *******************************************************/ mptr[0] = nmind = nbad = 0; mindiff = abs(pwgts[0]-pwgts[1]); for (nswaps=0; nswaps<nvtxs; nswaps++) { if ((higain = PQueueGetMax(&parts)) == -1) break; inqueue[higain] = -1; ASSERT(bndptr[higain] != -1); if (pwgts[to]+vwgt[higain] > badmaxpwgt) { /* Skip this vertex */ if (nbad++ > limit) break; else { nswaps--; continue; } } pwgts[2] -= (vwgt[higain]-rinfo[higain].edegrees[from]); newdiff = abs(pwgts[to]+vwgt[higain] - (pwgts[from]-rinfo[higain].edegrees[from])); if (pwgts[2] < mincut || (pwgts[2] == mincut && newdiff < mindiff)) { mincut = pwgts[2]; mincutorder = nswaps; mindiff = newdiff; nbad = 0; } else { if (nbad++ > limit) { pwgts[2] += (vwgt[higain]-rinfo[higain].edegrees[from]); break; /* No further improvement, break out */ } } BNDDelete(nbnd, bndind, bndptr, higain); pwgts[to] += vwgt[higain]; where[higain] = to; swaps[nswaps] = higain; /********************************************************** * Update the degrees of the affected nodes ***********************************************************/ for (j=xadj[higain]; j<xadj[higain+1]; j++) { k = adjncy[j]; if (where[k] == 2) { /* For the in-separator vertices modify their edegree[to] */ rinfo[k].edegrees[to] += vwgt[higain]; } else if (where[k] == from) { /* This vertex is pulled into the separator */ ASSERTP(bndptr[k] == -1, ("%d %d %d\n", k, bndptr[k], where[k])); BNDInsert(nbnd, bndind, bndptr, k); mind[nmind++] = k; /* Keep track for rollback */ where[k] = 2; pwgts[from] -= vwgt[k]; edegrees = rinfo[k].edegrees; edegrees[0] = edegrees[1] = 0; for (jj=xadj[k]; jj<xadj[k+1]; jj++) { kk = adjncy[jj]; if (where[kk] != 2) edegrees[where[kk]] += vwgt[kk]; else { oldgain = vwgt[kk]-rinfo[kk].edegrees[from]; rinfo[kk].edegrees[from] -= vwgt[k]; /* Update the gain of this node if it was skipped */ if (inqueue[kk] == pass) PQueueUpdateUp(&parts, kk, oldgain, oldgain+vwgt[k]); } } /* Insert the new vertex into the priority queue. Safe due to one-sided moves */ if (hmarker[k] == -1 || hmarker[k] == to) { PQueueInsert(&parts, k, vwgt[k]-edegrees[from]); inqueue[k] = pass; } } } mptr[nswaps+1] = nmind; IFSET(ctrl->dbglvl, DBG_MOVEINFO, printf("Moved %6d to %3d, Gain: %5d [%5d] \t[%5d %5d %5d] [%3d %2d]\n", higain, to, (vwgt[higain]-rinfo[higain].edegrees[from]), vwgt[higain], pwgts[0], pwgts[1], pwgts[2], nswaps, limit)); } /**************************************************************** * Roll back computation *****************************************************************/ for (nswaps--; nswaps>mincutorder; nswaps--) { higain = swaps[nswaps]; ASSERT(CheckNodePartitionParams(graph)); ASSERT(where[higain] == to); INC_DEC(pwgts[2], pwgts[to], vwgt[higain]); where[higain] = 2; BNDInsert(nbnd, bndind, bndptr, higain); edegrees = rinfo[higain].edegrees; edegrees[0] = edegrees[1] = 0; for (j=xadj[higain]; j<xadj[higain+1]; j++) { k = adjncy[j]; if (where[k] == 2) rinfo[k].edegrees[to] -= vwgt[higain]; else edegrees[where[k]] += vwgt[k]; } /* Push nodes out of the separator */ for (j=mptr[nswaps]; j<mptr[nswaps+1]; j++) { k = mind[j]; ASSERT(where[k] == 2); where[k] = from; INC_DEC(pwgts[from], pwgts[2], vwgt[k]); BNDDelete(nbnd, bndind, bndptr, k); for (jj=xadj[k]; jj<xadj[k+1]; jj++) { kk = adjncy[jj]; if (where[kk] == 2) rinfo[kk].edegrees[from] += vwgt[k]; } } } ASSERT(mincut == pwgts[2]); IFSET(ctrl->dbglvl, DBG_REFINE, printf("\tMinimum sep: %6d at %5d, PWGTS: [%6d %6d], NBND: %6d, QSIZE: %6d\n", mincut, mincutorder, pwgts[0], pwgts[1], nbnd, qsize)); graph->mincut = mincut; graph->nbnd = nbnd; if (pass%2 == 1 && (mincutorder == -1 || mincut >= initcut)) break; } PQueueFree(ctrl, &parts); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs+1); idxwspacefree(ctrl, nvtxs); idxwspacefree(ctrl, nvtxs); }