idx_t IsConnected(graph_t *graph, idx_t report) {
idx_t ncmps;
ncmps = FindPartitionInducedComponents(graph, NULL, NULL, NULL);
if (ncmps != 1 && report) {
printf("The graph is not connected. It has %"PRIDX" connected components.\n", ncmps);
}
return (ncmps == 1);
}
void RefineKWay(ctrl_t *ctrl, graph_t *orggraph, graph_t *graph)
{
idx_t i, nlevels, contig=ctrl->contig;
graph_t *ptr;
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->UncoarsenTmr));
/* Determine how many levels are there */
for (ptr=graph, nlevels=0; ptr!=orggraph; ptr=ptr->finer, nlevels++);
/* Compute the parameters of the coarsest graph */
ComputeKWayPartitionParams(ctrl, graph);
/* Try to minimize the sub-domain connectivity */
if (ctrl->minconn)
EliminateSubDomainEdges(ctrl, graph);
/* Deal with contiguity constraints at the beginning */
if (contig && FindPartitionInducedComponents(graph, graph->where, NULL, NULL) > ctrl->nparts) {
EliminateComponents(ctrl, graph);
ComputeKWayBoundary(ctrl, graph, BNDTYPE_BALANCE);
Greedy_KWayOptimize(ctrl, graph, 5, 0, OMODE_BALANCE);
ComputeKWayBoundary(ctrl, graph, BNDTYPE_REFINE);
Greedy_KWayOptimize(ctrl, graph, ctrl->niter, 0, OMODE_REFINE);
ctrl->contig = 0;
}
/* Refine each successively finer graph */
for (i=0; ;i++) {
if (ctrl->minconn && i == nlevels/2)
EliminateSubDomainEdges(ctrl, graph);
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->RefTmr));
if (2*i >= nlevels && !IsBalanced(ctrl, graph, .02)) {
ComputeKWayBoundary(ctrl, graph, BNDTYPE_BALANCE);
Greedy_KWayOptimize(ctrl, graph, 1, 0, OMODE_BALANCE);
ComputeKWayBoundary(ctrl, graph, BNDTYPE_REFINE);
}
Greedy_KWayOptimize(ctrl, graph, ctrl->niter, 5.0, OMODE_REFINE);
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->RefTmr));
/* Deal with contiguity constraints in the middle */
if (contig && i == nlevels/2) {
if (FindPartitionInducedComponents(graph, graph->where, NULL, NULL) > ctrl->nparts) {
EliminateComponents(ctrl, graph);
if (!IsBalanced(ctrl, graph, .02)) {
ctrl->contig = 1;
ComputeKWayBoundary(ctrl, graph, BNDTYPE_BALANCE);
Greedy_KWayOptimize(ctrl, graph, 5, 0, OMODE_BALANCE);
ComputeKWayBoundary(ctrl, graph, BNDTYPE_REFINE);
Greedy_KWayOptimize(ctrl, graph, ctrl->niter, 0, OMODE_REFINE);
ctrl->contig = 0;
}
}
}
if (graph == orggraph)
break;
graph = graph->finer;
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->ProjectTmr));
ASSERT(graph->vwgt != NULL);
ProjectKWayPartition(ctrl, graph);
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->ProjectTmr));
}
/* Deal with contiguity requirement at the end */
ctrl->contig = contig;
if (contig && FindPartitionInducedComponents(graph, graph->where, NULL, NULL) > ctrl->nparts)
EliminateComponents(ctrl, graph);
if (!IsBalanced(ctrl, graph, 0.0)) {
ComputeKWayBoundary(ctrl, graph, BNDTYPE_BALANCE);
Greedy_KWayOptimize(ctrl, graph, 10, 0, OMODE_BALANCE);
ComputeKWayBoundary(ctrl, graph, BNDTYPE_REFINE);
Greedy_KWayOptimize(ctrl, graph, ctrl->niter, 0, OMODE_REFINE);
}
if (ctrl->contig)
ASSERT(FindPartitionInducedComponents(graph, graph->where, NULL, NULL) == ctrl->nparts);
IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopcputimer(ctrl->UncoarsenTmr));
}
void EliminateComponents(ctrl_t *ctrl, graph_t *graph) {
idx_t i, ii, j, jj, k, me, nparts, nvtxs, ncon, ncmps, other,
ncand, target;
idx_t *xadj, *adjncy, *vwgt, *adjwgt, *where, *pwgts;
idx_t *cptr, *cind, *cpvec, *pcptr, *pcind, *cwhere;
idx_t cid, bestcid, *cwgt, *bestcwgt;
idx_t ntodo, oldntodo, *todo;
rkv_t *cand;
real_t *tpwgts;
idx_t *vmarker = NULL, *pmarker = NULL, *modind = NULL; /* volume specific work arrays */
WCOREPUSH;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
adjncy = graph->adjncy;
vwgt = graph->vwgt;
adjwgt = (ctrl->objtype == METIS_OBJTYPE_VOL ? NULL : graph->adjwgt);
where = graph->where;
pwgts = graph->pwgts;
nparts = ctrl->nparts;
tpwgts = ctrl->tpwgts;
cptr = iwspacemalloc(ctrl, nvtxs + 1);
cind = iwspacemalloc(ctrl, nvtxs);
ncmps = FindPartitionInducedComponents(graph, where, cptr, cind);
IFSET(ctrl->dbglvl, METIS_DBG_CONTIGINFO,
printf("I found %"PRIDX" components, for this %"PRIDX"-way partition\n",
ncmps, nparts));
/* There are more components than partitions */
if (ncmps > nparts) {
cwgt = iwspacemalloc(ctrl, ncon);
bestcwgt = iwspacemalloc(ctrl, ncon);
cpvec = iwspacemalloc(ctrl, nparts);
pcptr = iset(nparts + 1, 0, iwspacemalloc(ctrl, nparts + 1));
pcind = iwspacemalloc(ctrl, ncmps);
cwhere = iset(nvtxs, -1, iwspacemalloc(ctrl, nvtxs));
todo = iwspacemalloc(ctrl, ncmps);
cand = (rkv_t *) wspacemalloc(ctrl, nparts * sizeof(rkv_t));
if (ctrl->objtype == METIS_OBJTYPE_VOL) {
/* Vol-refinement specific working arrays */
modind = iwspacemalloc(ctrl, nvtxs);
vmarker = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
pmarker = iset(nparts, -1, iwspacemalloc(ctrl, nparts));
}
/* Get a CSR representation of the components-2-partitions mapping */
for (i = 0; i < ncmps; i++) {
pcptr[where[cind[cptr[i]]]]++;
}
MAKECSR(i, nparts, pcptr);
for (i = 0; i < ncmps; i++) {
pcind[pcptr[where[cind[cptr[i]]]]++] = i;
}
SHIFTCSR(i, nparts, pcptr);
/* Assign the heaviest component of each partition to its original partition */
for (ntodo = 0, i = 0; i < nparts; i++) {
if (pcptr[i + 1] - pcptr[i] == 1) {
bestcid = pcind[pcptr[i]];
} else {
for (bestcid = -1, j = pcptr[i]; j < pcptr[i + 1]; j++) {
cid = pcind[j];
iset(ncon, 0, cwgt);
for (ii = cptr[cid]; ii < cptr[cid + 1]; ii++) {
iaxpy(ncon, 1, vwgt + cind[ii] * ncon, 1, cwgt, 1);
}
if (bestcid == -1 || isum(ncon, bestcwgt, 1) < isum(ncon, cwgt, 1)) {
bestcid = cid;
icopy(ncon, cwgt, bestcwgt);
}
}
/* Keep track of those that need to be dealt with */
for (j = pcptr[i]; j < pcptr[i + 1]; j++) {
if (pcind[j] != bestcid) {
todo[ntodo++] = pcind[j];
}
}
}
for (j = cptr[bestcid]; j < cptr[bestcid + 1]; j++) {
ASSERT(where[cind[j]] == i);
cwhere[cind[j]] = i;
}
}
while (ntodo > 0) {
oldntodo = ntodo;
for (i = 0; i < ntodo; i++) {
cid = todo[i];
me = where[cind[cptr[cid]]]; /* Get the domain of this component */
/* Determine the weight of the block to be moved */
iset(ncon, 0, cwgt);
for (j = cptr[cid]; j < cptr[cid + 1]; j++) {
iaxpy(ncon, 1, vwgt + cind[j] * ncon, 1, cwgt, 1);
}
IFSET(ctrl->dbglvl, METIS_DBG_CONTIGINFO,
printf("Trying to move %"PRIDX" [%"PRIDX"] from %"PRIDX"\n",
cid, isum(ncon, cwgt, 1), me));
/* Determine the connectivity */
iset(nparts, 0, cpvec);
for (j = cptr[cid]; j < cptr[cid + 1]; j++) {
ii = cind[j];
for (jj = xadj[ii]; jj < xadj[ii + 1]; jj++) {
if (cwhere[adjncy[jj]] != -1) {
cpvec[cwhere[adjncy[jj]]] += (adjwgt ? adjwgt[jj] : 1);
}
}
}
/* Put the neighbors into a cand[] array for sorting */
for (ncand = 0, j = 0; j < nparts; j++) {
if (cpvec[j] > 0) {
cand[ncand].key = cpvec[j];
cand[ncand++].val = j;
}
}
if (ncand == 0) {
continue;
}
rkvsortd(ncand, cand);
/* Limit the moves to only the top candidates, which are defined as
those with connectivity at least 50% of the best.
This applies only when ncon=1, as for multi-constraint, balancing
will be hard. */
if (ncon == 1) {
for (j = 1; j < ncand; j++) {
if (cand[j].key < .5 * cand[0].key) {
break;
}
}
ncand = j;
}
/* Now among those, select the one with the best balance */
target = cand[0].val;
for (j = 1; j < ncand; j++) {
if (BetterBalanceKWay(ncon, cwgt, ctrl->ubfactors,
1, pwgts + target * ncon, ctrl->pijbm + target * ncon,
1, pwgts + cand[j].val * ncon, ctrl->pijbm + cand[j].val * ncon)) {
target = cand[j].val;
}
}
IFSET(ctrl->dbglvl, METIS_DBG_CONTIGINFO,
printf("\tMoving it to %"PRIDX" [%"PRIDX"] [%"PRIDX"]\n", target, cpvec[target], ncand));
/* Note that as a result of a previous movement, a connected component may
now will like to stay to its original partition */
if (target != me) {
switch (ctrl->objtype) {
case METIS_OBJTYPE_CUT:MoveGroupContigForCut(ctrl, graph, target, cid, cptr, cind);
break;
case METIS_OBJTYPE_VOL:
MoveGroupContigForVol(ctrl, graph, target, cid, cptr, cind,
vmarker, pmarker, modind);
break;
default:gk_errexit(SIGERR, "Unknown objtype %d\n", ctrl->objtype);
}
}
/* Update the cwhere vector */
for (j = cptr[cid]; j < cptr[cid + 1]; j++) {
cwhere[cind[j]] = target;
}
todo[i] = todo[--ntodo];
}
if (oldntodo == ntodo) {
IFSET(ctrl->dbglvl, METIS_DBG_CONTIGINFO, printf("Stopped at ntodo: %"PRIDX"\n", ntodo));
break;
}
}
for (i = 0; i < nvtxs; i++) {
ASSERT(where[i] == cwhere[i]);
}
}
WCOREPOP;
}
