void METIS_NodeRefine(int nvtxs, idxtype *xadj, idxtype *vwgt, idxtype *adjncy,
idxtype *adjwgt, idxtype *where, idxtype *hmarker, float ubfactor)
{
GraphType *graph;
CtrlType ctrl;
ctrl.dbglvl = ONMETIS_DBGLVL;
ctrl.optype = OP_ONMETIS;
graph = CreateGraph();
SetUpGraph(graph, OP_ONMETIS, nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
AllocateWorkSpace(&ctrl, graph, 2);
Allocate2WayNodePartitionMemory(&ctrl, graph);
idxcopy(nvtxs, where, graph->where);
Compute2WayNodePartitionParams(&ctrl, graph);
FM_2WayNodeRefine_OneSidedP(&ctrl, graph, hmarker, ubfactor, 10);
/* FM_2WayNodeRefine_TwoSidedP(&ctrl, graph, hmarker, ubfactor, 10); */
FreeWorkSpace(&ctrl, graph);
idxcopy(nvtxs, graph->where, where);
FreeGraph(graph);
}
/*************************************************************************
* This function takes a bisection and constructs a minimum weight vertex
* separator out of it. It uses the node-based separator refinement for it.
**************************************************************************/
void ConstructSeparator(CtrlType *ctrl, GraphType *graph, float ubfactor)
{
int i, j, k, nvtxs, nbnd;
idxtype *xadj, *where, *bndind;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
nbnd = graph->nbnd;
bndind = graph->bndind;
where = idxcopy(nvtxs, graph->where, idxwspacemalloc(ctrl, nvtxs));
/* Put the nodes in the boundary into the separator */
for (i=0; i<nbnd; i++) {
j = bndind[i];
if (xadj[j+1]-xadj[j] > 0) /* Ignore islands */
where[j] = 2;
}
GKfree(&graph->rdata, LTERM);
Allocate2WayNodePartitionMemory(ctrl, graph);
idxcopy(nvtxs, where, graph->where);
idxwspacefree(ctrl, nvtxs);
ASSERT(IsSeparable(graph));
Compute2WayNodePartitionParams(ctrl, graph);
ASSERT(CheckNodePartitionParams(graph));
FM_2WayNodeRefine(ctrl, graph, ubfactor, 8);
ASSERT(IsSeparable(graph));
}
void Project2WayNodePartition(ctrl_t *ctrl, graph_t *graph)
{
idx_t i, j, nvtxs;
idx_t *cmap, *where, *cwhere;
graph_t *cgraph;
cgraph = graph->coarser;
cwhere = cgraph->where;
nvtxs = graph->nvtxs;
cmap = graph->cmap;
Allocate2WayNodePartitionMemory(ctrl, graph);
where = graph->where;
/* Project the partition */
for (i=0; i<nvtxs; i++) {
where[i] = cwhere[cmap[i]];
ASSERTP(where[i] >= 0 && where[i] <= 2, ("%"PRIDX" %"PRIDX" %"PRIDX" %"PRIDX"\n",
i, cmap[i], where[i], cwhere[cmap[i]]));
}
FreeGraph(&graph->coarser);
graph->coarser = NULL;
Compute2WayNodePartitionParams(ctrl, graph);
}
/*************************************************************************
* This function performs multilevel bisection. It performs multiple
* bisections and selects the best.
**************************************************************************/
void MlevelNodeBisectionMultiple(CtrlType *ctrl, GraphType *graph, int *tpwgts, float ubfactor)
{
int i, nvtxs, cnvtxs, mincut, tmp;
GraphType *cgraph;
idxtype *bestwhere;
if (ctrl->nseps == 1 || graph->nvtxs < (ctrl->oflags&OFLAG_COMPRESS ? 1000 : 2000)) {
MlevelNodeBisection(ctrl, graph, tpwgts, ubfactor);
return;
}
nvtxs = graph->nvtxs;
if (ctrl->oflags&OFLAG_COMPRESS) { /* Multiple separators at the original graph */
bestwhere = idxmalloc(nvtxs, "MlevelNodeBisection2: bestwhere");
mincut = nvtxs;
for (i=ctrl->nseps; i>0; i--) {
MlevelNodeBisection(ctrl, graph, tpwgts, ubfactor);
/* printf("%5d ", cgraph->mincut); */
if (graph->mincut < mincut) {
mincut = graph->mincut;
idxcopy(nvtxs, graph->where, bestwhere);
}
GKfree(&graph->rdata, LTERM);
if (mincut == 0)
break;
}
/* printf("[%5d]\n", mincut); */
Allocate2WayNodePartitionMemory(ctrl, graph);
idxcopy(nvtxs, bestwhere, graph->where);
free(bestwhere);
Compute2WayNodePartitionParams(ctrl, graph);
}
else { /* Coarsen it a bit */
ctrl->CoarsenTo = nvtxs-1;
cgraph = Coarsen2Way(ctrl, graph);
cnvtxs = cgraph->nvtxs;
bestwhere = idxmalloc(cnvtxs, "MlevelNodeBisection2: bestwhere");
mincut = nvtxs;
for (i=ctrl->nseps; i>0; i--) {
ctrl->CType += 20; /* This is a hack. Look at coarsen.c */
MlevelNodeBisection(ctrl, cgraph, tpwgts, ubfactor);
/* printf("%5d ", cgraph->mincut); */
if (cgraph->mincut < mincut) {
mincut = cgraph->mincut;
idxcopy(cnvtxs, cgraph->where, bestwhere);
}
GKfree(&cgraph->rdata, LTERM);
if (mincut == 0)
break;
}
/* printf("[%5d]\n", mincut); */
Allocate2WayNodePartitionMemory(ctrl, cgraph);
idxcopy(cnvtxs, bestwhere, cgraph->where);
free(bestwhere);
Compute2WayNodePartitionParams(ctrl, cgraph);
Refine2WayNode(ctrl, graph, cgraph, ubfactor);
}
}
/*************************************************************************
* This function takes a bisection and constructs a minimum weight vertex
* separator out of it. It uses an unweighted minimum-cover algorithm
* followed by node-based separator refinement.
**************************************************************************/
void ConstructMinCoverSeparator(CtrlType *ctrl, GraphType *graph, float ubfactor)
{
int i, ii, j, jj, k, l, nvtxs, nbnd, bnvtxs[3], bnedges[2], csize;
idxtype *xadj, *adjncy, *bxadj, *badjncy;
idxtype *where, *bndind, *bndptr, *vmap, *ivmap, *cover;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
nbnd = graph->nbnd;
bndind = graph->bndind;
bndptr = graph->bndptr;
where = graph->where;
vmap = idxwspacemalloc(ctrl, nvtxs);
ivmap = idxwspacemalloc(ctrl, nbnd);
cover = idxwspacemalloc(ctrl, nbnd);
if (nbnd > 0) {
/* Go through the boundary and determine the sizes of the bipartite graph */
bnvtxs[0] = bnvtxs[1] = bnedges[0] = bnedges[1] = 0;
for (i=0; i<nbnd; i++) {
j = bndind[i];
k = where[j];
if (xadj[j+1]-xadj[j] > 0) {
bnvtxs[k]++;
bnedges[k] += xadj[j+1]-xadj[j];
}
}
bnvtxs[2] = bnvtxs[0]+bnvtxs[1];
bnvtxs[1] = bnvtxs[0];
bnvtxs[0] = 0;
bxadj = idxmalloc(bnvtxs[2]+1, "ConstructMinCoverSeparator: bxadj");
badjncy = idxmalloc(bnedges[0]+bnedges[1]+1, "ConstructMinCoverSeparator: badjncy");
/* Construct the ivmap and vmap */
ASSERT(idxset(nvtxs, -1, vmap) == vmap);
for (i=0; i<nbnd; i++) {
j = bndind[i];
k = where[j];
if (xadj[j+1]-xadj[j] > 0) {
vmap[j] = bnvtxs[k];
ivmap[bnvtxs[k]++] = j;
}
}
/* OK, go through and put the vertices of each part starting from 0 */
bnvtxs[1] = bnvtxs[0];
bnvtxs[0] = 0;
bxadj[0] = l = 0;
for (k=0; k<2; k++) {
for (ii=0; ii<nbnd; ii++) {
i = bndind[ii];
if (where[i] == k && xadj[i] < xadj[i+1]) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
jj = adjncy[j];
if (where[jj] != k) {
ASSERT(bndptr[jj] != -1);
ASSERTP(vmap[jj] != -1, ("%d %d %d\n", jj, vmap[jj], graph->bndptr[jj]));
badjncy[l++] = vmap[jj];
}
}
bxadj[++bnvtxs[k]] = l;
}
}
}
ASSERT(l <= bnedges[0]+bnedges[1]);
MinCover(bxadj, badjncy, bnvtxs[0], bnvtxs[1], cover, &csize);
IFSET(ctrl->dbglvl, DBG_SEPINFO,
printf("Nvtxs: %6d, [%5d %5d], Cut: %6d, SS: [%6d %6d], Cover: %6d\n", nvtxs, graph->pwgts[0], graph->pwgts[1], graph->mincut, bnvtxs[0], bnvtxs[1]-bnvtxs[0], csize));
for (i=0; i<csize; i++) {
j = ivmap[cover[i]];
where[j] = 2;
}
GKfree(&bxadj, &badjncy, LTERM);
}
else {
IFSET(ctrl->dbglvl, DBG_SEPINFO,
printf("Nvtxs: %6d, [%5d %5d], Cut: %6d, SS: [%6d %6d], Cover: %6d\n", nvtxs, graph->pwgts[0], graph->pwgts[1], graph->mincut, 0, 0, 0));
}
/* Prepare to refine the vertex separator */
idxcopy(nvtxs, graph->where, vmap);
GKfree(&graph->rdata, LTERM);
Allocate2WayNodePartitionMemory(ctrl, graph);
idxcopy(nvtxs, vmap, graph->where);
idxwspacefree(ctrl, nvtxs+2*graph->nbnd);
Compute2WayNodePartitionParams(ctrl, graph);
ASSERT(CheckNodePartitionParams(graph));
FM_2WayNodeRefine_OneSided(ctrl, graph, ubfactor, 6);
ASSERT(IsSeparable(graph));
}