/*************************************************************************
* This function computes the balance of the partitioning
**************************************************************************/
void ComputePartitionBalance(graph_t *graph, idx_t nparts, idx_t *where, real_t *ubvec)
{
idx_t i, j, nvtxs, ncon;
idx_t *kpwgts, *vwgt;
real_t balance;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
vwgt = graph->vwgt;
kpwgts = ismalloc(nparts, 0, "ComputePartitionInfo: kpwgts");
if (vwgt == NULL) {
for (i=0; i<nvtxs; i++)
kpwgts[where[i]]++;
ubvec[0] = 1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*nvtxs);
}
else {
for (j=0; j<ncon; j++) {
iset(nparts, 0, kpwgts);
for (i=0; i<graph->nvtxs; i++)
kpwgts[where[i]] += vwgt[i*ncon+j];
ubvec[j] = 1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1));
}
}
gk_free((void **)&kpwgts, LTERM);
}
void UpdateEdgeSubDomainGraph(ctrl_t *ctrl, idx_t u, idx_t v, idx_t ewgt,
idx_t *r_maxndoms)
{
idx_t i, j, nads;
if (ewgt == 0)
return;
for (i=0; i<2; i++) {
nads = ctrl->nads[u];
/* Find the edge */
for (j=0; j<nads; j++) {
if (ctrl->adids[u][j] == v) {
ctrl->adwgts[u][j] += ewgt;
break;
}
}
if (j == nads) {
/* Deal with the case in which the edge was not found */
ASSERT(ewgt > 0);
if (ctrl->maxnads[u] == nads) {
ctrl->maxnads[u] = 2*(nads+1);
ctrl->adids[u] = irealloc(ctrl->adids[u], ctrl->maxnads[u],
"IncreaseEdgeSubDomainGraph: adids[pid]");
ctrl->adwgts[u] = irealloc(ctrl->adwgts[u], ctrl->maxnads[u],
"IncreaseEdgeSubDomainGraph: adids[pid]");
}
ctrl->adids[u][nads] = v;
ctrl->adwgts[u][nads] = ewgt;
nads++;
if (r_maxndoms != NULL && nads > *r_maxndoms) {
printf("You just increased the maxndoms: %"PRIDX" %"PRIDX"\n",
nads, *r_maxndoms);
*r_maxndoms = nads;
}
}
else {
/* See if the updated edge becomes 0 */
ASSERT(ctrl->adwgts[u][j] >= 0);
if (ctrl->adwgts[u][j] == 0) {
ctrl->adids[u][j] = ctrl->adids[u][nads-1];
ctrl->adwgts[u][j] = ctrl->adwgts[u][nads-1];
nads--;
if (r_maxndoms != NULL && nads+1 == *r_maxndoms)
*r_maxndoms = ctrl->nads[iargmax(ctrl->nparts, ctrl->nads)];
}
}
ctrl->nads[u] = nads;
SWAP(u, v, j);
}
}
void McRandomBisection(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts,
idx_t niparts)
{
idx_t i, ii, j, k, nvtxs, ncon, from, bestcut=0, mincut, inbfs, qnum;
idx_t *bestwhere, *where, *perm, *counts;
idx_t *vwgt;
WCOREPUSH;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
vwgt = graph->vwgt;
Allocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = iwspacemalloc(ctrl, nvtxs);
perm = iwspacemalloc(ctrl, nvtxs);
counts = iwspacemalloc(ctrl, ncon);
for (inbfs=0; inbfs<2*niparts; inbfs++) {
irandArrayPermute(nvtxs, perm, nvtxs/2, 1);
iset(ncon, 0, counts);
/* partition by spliting the queues randomly */
for (ii=0; ii<nvtxs; ii++) {
i = perm[ii];
qnum = iargmax(ncon, vwgt+i*ncon);
where[i] = (counts[qnum]++)%2;
}
Compute2WayPartitionParams(ctrl, graph);
FM_2WayRefine(ctrl, graph, ntpwgts, ctrl->niter);
Balance2Way(ctrl, graph, ntpwgts);
FM_2WayRefine(ctrl, graph, ntpwgts, ctrl->niter);
Balance2Way(ctrl, graph, ntpwgts);
FM_2WayRefine(ctrl, graph, ntpwgts, ctrl->niter);
if (inbfs == 0 || bestcut >= graph->mincut) {
bestcut = graph->mincut;
icopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
icopy(nvtxs, bestwhere, where);
WCOREPOP;
}
/*************************************************************************
* This function computes the balance of the element partitioning
**************************************************************************/
real_t ComputeElementBalance(idx_t ne, idx_t nparts, idx_t *where)
{
idx_t i;
idx_t *kpwgts;
real_t balance;
kpwgts = ismalloc(nparts, 0, "ComputeElementBalance: kpwgts");
for (i=0; i<ne; i++)
kpwgts[where[i]]++;
balance = 1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1));
gk_free((void **)&kpwgts, LTERM);
return balance;
}
void InduceRowPartFromColumnPart(idx_t nrows, idx_t *rowptr, idx_t *rowind,
idx_t *rpart, idx_t *cpart, idx_t nparts, real_t *tpwgts)
{
idx_t i, j, k, me;
idx_t nnbrs, *pwgts, *nbrdom, *nbrwgt, *nbrmrk;
idx_t *itpwgts;
pwgts = ismalloc(nparts, 0, "InduceRowPartFromColumnPart: pwgts");
nbrdom = ismalloc(nparts, 0, "InduceRowPartFromColumnPart: nbrdom");
nbrwgt = ismalloc(nparts, 0, "InduceRowPartFromColumnPart: nbrwgt");
nbrmrk = ismalloc(nparts, -1, "InduceRowPartFromColumnPart: nbrmrk");
iset(nrows, -1, rpart);
/* setup the integer target partition weights */
itpwgts = imalloc(nparts, "InduceRowPartFromColumnPart: itpwgts");
if (tpwgts == NULL) {
iset(nparts, 1+nrows/nparts, itpwgts);
}
else {
for (i=0; i<nparts; i++)
itpwgts[i] = 1+nrows*tpwgts[i];
}
/* first assign the rows consisting only of columns that belong to
a single partition. Assign rows that are empty to -2 (un-assigned) */
for (i=0; i<nrows; i++) {
if (rowptr[i+1]-rowptr[i] == 0) {
rpart[i] = -2;
continue;
}
me = cpart[rowind[rowptr[i]]];
for (j=rowptr[i]+1; j<rowptr[i+1]; j++) {
if (cpart[rowind[j]] != me)
break;
}
if (j == rowptr[i+1]) {
rpart[i] = me;
pwgts[me]++;
}
}
/* next assign the rows consisting of columns belonging to multiple
partitions in a balanced way */
for (i=0; i<nrows; i++) {
if (rpart[i] == -1) {
for (nnbrs=0, j=rowptr[i]; j<rowptr[i+1]; j++) {
me = cpart[rowind[j]];
if (nbrmrk[me] == -1) {
nbrdom[nnbrs] = me;
nbrwgt[nnbrs] = 1;
nbrmrk[me] = nnbrs++;
}
else {
nbrwgt[nbrmrk[me]]++;
}
}
ASSERT(nnbrs > 0);
/* assign it first to the domain with most things in common */
rpart[i] = nbrdom[iargmax(nnbrs, nbrwgt)];
/* if overweight, assign it to the light domain */
if (pwgts[rpart[i]] > itpwgts[rpart[i]]) {
for (j=0; j<nnbrs; j++) {
if (pwgts[nbrdom[j]] < itpwgts[nbrdom[j]] ||
pwgts[nbrdom[j]]-itpwgts[nbrdom[j]] < pwgts[rpart[i]]-itpwgts[rpart[i]]) {
rpart[i] = nbrdom[j];
break;
}
}
}
pwgts[rpart[i]]++;
/* reset nbrmrk array */
for (j=0; j<nnbrs; j++)
nbrmrk[nbrdom[j]] = -1;
}
}
gk_free((void **)&pwgts, &nbrdom, &nbrwgt, &nbrmrk, &itpwgts, LTERM);
}
/*************************************************************************
* This function performs a k-way directed diffusion
**************************************************************************/
real_t WavefrontDiffusion(ctrl_t *ctrl, graph_t *graph, idx_t *home)
{
idx_t ii, i, j, k, l, nvtxs, nedges, nparts;
idx_t from, to, edge, done, nswaps, noswaps, totalv, wsize;
idx_t npasses, first, second, third, mind, maxd;
idx_t *xadj, *adjncy, *adjwgt, *where, *perm;
idx_t *rowptr, *colind, *ed, *psize;
real_t *transfer, *tmpvec;
real_t balance = -1.0, *load, *solution, *workspace;
real_t *nvwgt, *npwgts, flowFactor, cost, ubfactor;
matrix_t matrix;
ikv_t *cand;
idx_t ndirty, nclean, dptr, clean;
nvtxs = graph->nvtxs;
nedges = graph->nedges;
xadj = graph->xadj;
nvwgt = graph->nvwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
nparts = ctrl->nparts;
ubfactor = ctrl->ubvec[0];
matrix.nrows = nparts;
flowFactor = 0.35;
flowFactor = (ctrl->mype == 2) ? 0.50 : flowFactor;
flowFactor = (ctrl->mype == 3) ? 0.75 : flowFactor;
flowFactor = (ctrl->mype == 4) ? 1.00 : flowFactor;
/* allocate memory */
solution = rmalloc(4*nparts+2*nedges, "WavefrontDiffusion: solution");
tmpvec = solution + nparts;
npwgts = solution + 2*nparts;
load = solution + 3*nparts;
matrix.values = solution + 4*nparts;
transfer = matrix.transfer = solution + 4*nparts + nedges;
perm = imalloc(2*nvtxs+2*nparts+nedges+1, "WavefrontDiffusion: perm");
ed = perm + nvtxs;
psize = perm + 2*nvtxs;
rowptr = matrix.rowptr = perm + 2*nvtxs + nparts;
colind = matrix.colind = perm + 2*nvtxs + 2*nparts + 1;
/*GKTODO - Potential problem with this malloc */
wsize = gk_max(sizeof(real_t)*nparts*6, sizeof(idx_t)*(nvtxs+nparts*2+1));
workspace = (real_t *)gk_malloc(wsize, "WavefrontDiffusion: workspace");
cand = ikvmalloc(nvtxs, "WavefrontDiffusion: cand");
/*****************************/
/* Populate empty subdomains */
/*****************************/
iset(nparts, 0, psize);
for (i=0; i<nvtxs; i++)
psize[where[i]]++;
mind = iargmin(nparts, psize);
maxd = iargmax(nparts, psize);
if (psize[mind] == 0) {
for (i=0; i<nvtxs; i++) {
k = (RandomInRange(nvtxs)+i)%nvtxs;
if (where[k] == maxd) {
where[k] = mind;
psize[mind]++;
psize[maxd]--;
break;
}
}
}
iset(nvtxs, 0, ed);
rset(nparts, 0.0, npwgts);
for (i=0; i<nvtxs; i++) {
npwgts[where[i]] += nvwgt[i];
for (j=xadj[i]; j<xadj[i+1]; j++)
ed[i] += (where[i] != where[adjncy[j]] ? adjwgt[j] : 0);
}
ComputeLoad(graph, nparts, load, ctrl->tpwgts, 0);
done = 0;
/* zero out the tmpvec array */
rset(nparts, 0.0, tmpvec);
npasses = gk_min(nparts/2, NGD_PASSES);
for (l=0; l<npasses; l++) {
/* Set-up and solve the diffusion equation */
nswaps = 0;
/************************/
/* Solve flow equations */
/************************/
SetUpConnectGraph(graph, &matrix, (idx_t *)workspace);
/* check for disconnected subdomains */
for(i=0; i<matrix.nrows; i++) {
if (matrix.rowptr[i]+1 == matrix.rowptr[i+1]) {
cost = (real_t)(ctrl->mype);
goto CleanUpAndExit;
}
}
ConjGrad2(&matrix, load, solution, 0.001, workspace);
ComputeTransferVector(1, &matrix, solution, transfer, 0);
GetThreeMax(nparts, load, &first, &second, &third);
if (l%3 == 0) {
FastRandomPermute(nvtxs, perm, 1);
}
else {
/*****************************/
/* move dirty vertices first */
/*****************************/
ndirty = 0;
for (i=0; i<nvtxs; i++) {
if (where[i] != home[i])
ndirty++;
}
dptr = 0;
for (i=0; i<nvtxs; i++) {
if (where[i] != home[i])
perm[dptr++] = i;
else
perm[ndirty++] = i;
}
PASSERT(ctrl, ndirty == nvtxs);
ndirty = dptr;
nclean = nvtxs-dptr;
FastRandomPermute(ndirty, perm, 0);
FastRandomPermute(nclean, perm+ndirty, 0);
}
if (ctrl->mype == 0) {
for (j=nvtxs, k=0, ii=0; ii<nvtxs; ii++) {
i = perm[ii];
if (ed[i] != 0) {
cand[k].key = -ed[i];
cand[k++].val = i;
}
else {
cand[--j].key = 0;
cand[j].val = i;
}
}
ikvsorti(k, cand);
}
for (ii=0; ii<nvtxs/3; ii++) {
i = (ctrl->mype == 0) ? cand[ii].val : perm[ii];
from = where[i];
/* don't move out the last vertex in a subdomain */
if (psize[from] == 1)
continue;
clean = (from == home[i]) ? 1 : 0;
/* only move from top three or dirty vertices */
if (from != first && from != second && from != third && clean)
continue;
/* Scatter the sparse transfer row into the dense tmpvec row */
for (j=rowptr[from]+1; j<rowptr[from+1]; j++)
tmpvec[colind[j]] = transfer[j];
for (j=xadj[i]; j<xadj[i+1]; j++) {
to = where[adjncy[j]];
if (from != to) {
if (tmpvec[to] > (flowFactor * nvwgt[i])) {
tmpvec[to] -= nvwgt[i];
INC_DEC(psize[to], psize[from], 1);
INC_DEC(npwgts[to], npwgts[from], nvwgt[i]);
INC_DEC(load[to], load[from], nvwgt[i]);
where[i] = to;
nswaps++;
/* Update external degrees */
ed[i] = 0;
for (k=xadj[i]; k<xadj[i+1]; k++) {
edge = adjncy[k];
ed[i] += (to != where[edge] ? adjwgt[k] : 0);
if (where[edge] == from)
ed[edge] += adjwgt[k];
if (where[edge] == to)
ed[edge] -= adjwgt[k];
}
break;
}
}
}
/* Gather the dense tmpvec row into the sparse transfer row */
for (j=rowptr[from]+1; j<rowptr[from+1]; j++) {
transfer[j] = tmpvec[colind[j]];
tmpvec[colind[j]] = 0.0;
}
ASSERT(fabs(rsum(nparts, tmpvec, 1)) < .0001)
}
if (l % 2 == 1) {
balance = rmax(nparts, npwgts)*nparts;
if (balance < ubfactor + 0.035)
done = 1;
if (GlobalSESum(ctrl, done) > 0)
break;
noswaps = (nswaps > 0) ? 0 : 1;
if (GlobalSESum(ctrl, noswaps) > ctrl->npes/2)
break;
}
}
graph->mincut = ComputeSerialEdgeCut(graph);
totalv = Mc_ComputeSerialTotalV(graph, home);
cost = ctrl->ipc_factor * (real_t)graph->mincut + ctrl->redist_factor * (real_t)totalv;
CleanUpAndExit:
gk_free((void **)&solution, (void **)&perm, (void **)&workspace, (void **)&cand, LTERM);
return cost;
}
/*************************************************************************
* This function computes cuts and balance information
**************************************************************************/
void ComputePartitionInfoBipartite(graph_t *graph, idx_t nparts, idx_t *where)
{
idx_t i, j, k, nvtxs, ncon, mustfree=0;
idx_t *xadj, *adjncy, *vwgt, *vsize, *adjwgt, *kpwgts, *tmpptr;
idx_t *padjncy, *padjwgt, *padjcut;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
adjncy = graph->adjncy;
vwgt = graph->vwgt;
vsize = graph->vsize;
adjwgt = graph->adjwgt;
if (vwgt == NULL) {
vwgt = graph->vwgt = ismalloc(nvtxs, 1, "vwgt");
mustfree = 1;
}
if (adjwgt == NULL) {
adjwgt = graph->adjwgt = ismalloc(xadj[nvtxs], 1, "adjwgt");
mustfree += 2;
}
printf("%"PRIDX"-way Cut: %5"PRIDX", Vol: %5"PRIDX", ", nparts, ComputeCut(graph, where), ComputeVolume(graph, where));
/* Compute balance information */
kpwgts = ismalloc(ncon*nparts, 0, "ComputePartitionInfo: kpwgts");
for (i=0; i<nvtxs; i++) {
for (j=0; j<ncon; j++)
kpwgts[where[i]*ncon+j] += vwgt[i*ncon+j];
}
if (ncon == 1) {
printf("\tBalance: %5.3"PRREAL" out of %5.3"PRREAL"\n",
1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1)),
1.0*nparts*vwgt[iargmax(nvtxs, vwgt)]/(1.0*isum(nparts, kpwgts, 1)));
}
else {
printf("\tBalance:");
for (j=0; j<ncon; j++)
printf(" (%5.3"PRREAL" out of %5.3"PRREAL")",
1.0*nparts*kpwgts[ncon*iargmax_strd(nparts, kpwgts+j, ncon)+j]/(1.0*isum(nparts, kpwgts+j, ncon)),
1.0*nparts*vwgt[ncon*iargmax_strd(nvtxs, vwgt+j, ncon)+j]/(1.0*isum(nparts, kpwgts+j, ncon)));
printf("\n");
}
/* Compute p-adjncy information */
padjncy = ismalloc(nparts*nparts, 0, "ComputePartitionInfo: padjncy");
padjwgt = ismalloc(nparts*nparts, 0, "ComputePartitionInfo: padjwgt");
padjcut = ismalloc(nparts*nparts, 0, "ComputePartitionInfo: padjwgt");
iset(nparts, 0, kpwgts);
for (i=0; i<nvtxs; i++) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (where[i] != where[adjncy[j]]) {
padjncy[where[i]*nparts+where[adjncy[j]]] = 1;
padjcut[where[i]*nparts+where[adjncy[j]]] += adjwgt[j];
if (kpwgts[where[adjncy[j]]] == 0) {
padjwgt[where[i]*nparts+where[adjncy[j]]] += vsize[i];
kpwgts[where[adjncy[j]]] = 1;
}
}
}
for (j=xadj[i]; j<xadj[i+1]; j++)
kpwgts[where[adjncy[j]]] = 0;
}
for (i=0; i<nparts; i++)
kpwgts[i] = isum(nparts, padjncy+i*nparts, 1);
printf("Min/Max/Avg/Bal # of adjacent subdomains: %5"PRIDX" %5"PRIDX" %5"PRIDX" %7.3"PRREAL"\n",
kpwgts[iargmin(nparts, kpwgts)], kpwgts[iargmax(nparts, kpwgts)], isum(nparts, kpwgts, 1)/nparts,
1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1)));
for (i=0; i<nparts; i++)
kpwgts[i] = isum(nparts, padjcut+i*nparts, 1);
printf("Min/Max/Avg/Bal # of adjacent subdomain cuts: %5"PRIDX" %5"PRIDX" %5"PRIDX" %7.3"PRREAL"\n",
kpwgts[iargmin(nparts, kpwgts)], kpwgts[iargmax(nparts, kpwgts)], isum(nparts, kpwgts, 1)/nparts,
1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1)));
for (i=0; i<nparts; i++)
kpwgts[i] = isum(nparts, padjwgt+i*nparts, 1);
printf("Min/Max/Avg/Bal/Frac # of interface nodes: %5"PRIDX" %5"PRIDX" %5"PRIDX" %7.3"PRREAL" %7.3"PRREAL"\n",
kpwgts[iargmin(nparts, kpwgts)], kpwgts[iargmax(nparts, kpwgts)], isum(nparts, kpwgts, 1)/nparts,
1.0*nparts*kpwgts[iargmax(nparts, kpwgts)]/(1.0*isum(nparts, kpwgts, 1)), 1.0*isum(nparts, kpwgts, 1)/(1.0*nvtxs));
if (mustfree == 1 || mustfree == 3) {
gk_free((void **)&vwgt, LTERM);
graph->vwgt = NULL;
}
if (mustfree == 2 || mustfree == 3) {
gk_free((void **)&adjwgt, LTERM);
graph->adjwgt = NULL;
}
gk_free((void **)&kpwgts, &padjncy, &padjwgt, &padjcut, LTERM);
}
void EliminateSubDomainEdges(ctrl_t *ctrl, graph_t *graph)
{
idx_t i, ii, j, k, ncon, nparts, scheme, pid_from, pid_to, me, other, nvtxs,
total, max, avg, totalout, nind=0, ncand=0, ncand2, target, target2,
nadd, bestnadd=0;
idx_t min, move, *cpwgt;
idx_t *xadj, *adjncy, *vwgt, *adjwgt, *pwgts, *where, *maxpwgt,
*mypmat, *otherpmat, *kpmat, *ind;
idx_t *nads, **adids, **adwgts;
ikv_t *cand, *cand2;
ipq_t queue;
real_t *tpwgts, badfactor=1.4;
idx_t *pptr, *pind;
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; /* We assume that this is properly initialized */
nparts = ctrl->nparts;
tpwgts = ctrl->tpwgts;
cpwgt = iwspacemalloc(ctrl, ncon);
maxpwgt = iwspacemalloc(ctrl, nparts*ncon);
ind = iwspacemalloc(ctrl, nvtxs);
otherpmat = iset(nparts, 0, iwspacemalloc(ctrl, nparts));
cand = ikvwspacemalloc(ctrl, nparts);
cand2 = ikvwspacemalloc(ctrl, nparts);
pptr = iwspacemalloc(ctrl, nparts+1);
pind = iwspacemalloc(ctrl, nvtxs);
iarray2csr(nvtxs, nparts, where, pptr, pind);
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));
}
/* Compute the pmat matrix and ndoms */
ComputeSubDomainGraph(ctrl, graph);
nads = ctrl->nads;
adids = ctrl->adids;
adwgts = ctrl->adwgts;
mypmat = iset(nparts, 0, ctrl->pvec1);
kpmat = iset(nparts, 0, ctrl->pvec2);
/* Compute the maximum allowed weight for each domain */
for (i=0; i<nparts; i++) {
for (j=0; j<ncon; j++)
maxpwgt[i*ncon+j] =
(ncon == 1 ? 1.25 : 1.025)*tpwgts[i]*graph->tvwgt[j]*ctrl->ubfactors[j];
}
ipqInit(&queue, nparts);
/* Get into the loop eliminating subdomain connections */
while (1) {
total = isum(nparts, nads, 1);
avg = total/nparts;
max = nads[iargmax(nparts, nads)];
IFSET(ctrl->dbglvl, METIS_DBG_CONNINFO,
printf("Adjacent Subdomain Stats: Total: %3"PRIDX", "
"Max: %3"PRIDX"[%zu], Avg: %3"PRIDX"\n",
total, max, iargmax(nparts, nads), avg));
if (max < badfactor*avg)
break;
/* Add the subdomains that you will try to reduce their connectivity */
ipqReset(&queue);
for (i=0; i<nparts; i++) {
if (nads[i] >= avg + (max-avg)/2)
ipqInsert(&queue, i, nads[i]);
}
move = 0;
while ((me = ipqGetTop(&queue)) != -1) {
totalout = isum(nads[me], adwgts[me], 1);
for (ncand2=0, i=0; i<nads[me]; i++) {
mypmat[adids[me][i]] = adwgts[me][i];
/* keep track of the weakly connected adjacent subdomains */
if (2*nads[me]*adwgts[me][i] < totalout) {
cand2[ncand2].val = adids[me][i];
cand2[ncand2++].key = adwgts[me][i];
}
}
IFSET(ctrl->dbglvl, METIS_DBG_CONNINFO,
printf("Me: %"PRIDX", Degree: %4"PRIDX", TotalOut: %"PRIDX",\n",
me, nads[me], totalout));
/* Sort the connections according to their cut */
ikvsorti(ncand2, cand2);
/* Two schemes are used for eliminating subdomain edges.
The first, tries to eliminate subdomain edges by moving remote groups
of vertices to subdomains that 'me' is already connected to.
The second, tries to eliminate subdomain edges by moving entire sets of
my vertices that connect to the 'other' subdomain to a subdomain that
I'm already connected to.
These two schemes are applied in sequence. */
target = target2 = -1;
for (scheme=0; scheme<2; scheme++) {
for (min=0; min<ncand2; min++) {
other = cand2[min].val;
/* pid_from is the subdomain from where the vertices will be removed.
pid_to is the adjacent subdomain to pid_from that defines the
(me, other) subdomain edge that needs to be removed */
if (scheme == 0) {
pid_from = other;
pid_to = me;
}
else {
pid_from = me;
pid_to = other;
}
/* Go and find the vertices in 'other' that are connected in 'me' */
for (nind=0, ii=pptr[pid_from]; ii<pptr[pid_from+1]; ii++) {
i = pind[ii];
ASSERT(where[i] == pid_from);
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (where[adjncy[j]] == pid_to) {
ind[nind++] = i;
break;
}
}
}
/* Go and construct the otherpmat to see where these nind vertices are
connected to */
iset(ncon, 0, cpwgt);
for (ncand=0, ii=0; ii<nind; ii++) {
i = ind[ii];
iaxpy(ncon, 1, vwgt+i*ncon, 1, cpwgt, 1);
for (j=xadj[i]; j<xadj[i+1]; j++) {
if ((k = where[adjncy[j]]) == pid_from)
continue;
if (otherpmat[k] == 0)
cand[ncand++].val = k;
otherpmat[k] += (adjwgt ? adjwgt[j] : 1);
}
}
for (i=0; i<ncand; i++) {
cand[i].key = otherpmat[cand[i].val];
ASSERT(cand[i].key > 0);
}
ikvsortd(ncand, cand);
IFSET(ctrl->dbglvl, METIS_DBG_CONNINFO,
printf("\tMinOut: %4"PRIDX", to: %3"PRIDX", TtlWgt: %5"PRIDX"[#:%"PRIDX"]\n",
mypmat[other], other, isum(ncon, cpwgt, 1), nind));
/* Go through and select the first domain that is common with 'me', and does
not increase the nads[target] higher than nads[me], subject to the maxpwgt
constraint. Traversal is done from the mostly connected to the least. */
for (i=0; i<ncand; i++) {
k = cand[i].val;
if (mypmat[k] > 0) {
/* Check if balance will go off */
if (!ivecaxpylez(ncon, 1, cpwgt, pwgts+k*ncon, maxpwgt+k*ncon))
continue;
/* get a dense vector out of k's connectivity */
for (j=0; j<nads[k]; j++)
kpmat[adids[k][j]] = adwgts[k][j];
/* Check if the move to domain k will increase the nads of another
subdomain j that the set of vertices being moved are connected
to but domain k is not connected to. */
for (j=0; j<nparts; j++) {
if (otherpmat[j] > 0 && kpmat[j] == 0 && nads[j]+1 >= nads[me])
break;
}
/* There were no bad second level effects. See if you can find a
subdomain to move to. */
if (j == nparts) {
for (nadd=0, j=0; j<nparts; j++) {
if (otherpmat[j] > 0 && kpmat[j] == 0)
nadd++;
}
IFSET(ctrl->dbglvl, METIS_DBG_CONNINFO,
printf("\t\tto=%"PRIDX", nadd=%"PRIDX", %"PRIDX"\n", k, nadd, nads[k]));
if (nads[k]+nadd < nads[me]) {
if (target2 == -1 || nads[target2]+bestnadd > nads[k]+nadd ||
(nads[target2]+bestnadd == nads[k]+nadd && bestnadd > nadd)) {
target2 = k;
bestnadd = nadd;
}
}
if (nadd == 0)
target = k;
}
/* reset kpmat for the next iteration */
for (j=0; j<nads[k]; j++)
kpmat[adids[k][j]] = 0;
}
if (target != -1)
break;
}
/* reset the otherpmat for the next iteration */
for (i=0; i<ncand; i++)
otherpmat[cand[i].val] = 0;
if (target == -1 && target2 != -1)
target = target2;
if (target != -1) {
IFSET(ctrl->dbglvl, METIS_DBG_CONNINFO,
printf("\t\tScheme: %"PRIDX". Moving to %"PRIDX"\n", scheme, target));
move = 1;
break;
}
}
if (target != -1)
break; /* A move was found. No need to try the other scheme */
}
/* reset the mypmat for next iteration */
for (i=0; i<nads[me]; i++)
mypmat[adids[me][i]] = 0;
/* Note that once a target is found the above loops exit right away. So the
following variables are valid */
if (target != -1) {
switch (ctrl->objtype) {
case METIS_OBJTYPE_CUT:
MoveGroupMinConnForCut(ctrl, graph, target, nind, ind);
break;
case METIS_OBJTYPE_VOL:
MoveGroupMinConnForVol(ctrl, graph, target, nind, ind, vmarker,
pmarker, modind);
break;
default:
gk_errexit(SIGERR, "Unknown objtype of %d\n", ctrl->objtype);
}
/* Update the csr representation of the partitioning vector */
iarray2csr(nvtxs, nparts, where, pptr, pind);
}
}
if (move == 0)
break;
}
ipqFree(&queue);
WCOREPOP;
}
