/*************************************************************************
* This function computes the balance of the partitioning
**************************************************************************/
void ComputePartitionBalance(GraphType *graph, int nparts, idxtype *where, float *ubvec)
{
int i, j, nvtxs, ncon;
idxtype *kpwgts, *vwgt;
/*float balance;*/
nvtxs = graph->nvtxs;
ncon = graph->ncon;
vwgt = graph->vwgt;
kpwgts = idxsmalloc(nparts, 0, "ComputePartitionInfo: kpwgts");
if (vwgt == NULL) {
for (i=0; i<nvtxs; i++)
kpwgts[where[i]]++;
ubvec[0] = 1.0*nparts*kpwgts[idxamax(nparts, kpwgts)]/(1.0*nvtxs);
}
else {
for (j=0; j<ncon; j++) {
idxset(nparts, 0, kpwgts);
for (i=0; i<graph->nvtxs; i++)
kpwgts[where[i]] += vwgt[i*ncon+j];
ubvec[j] = 1.0*nparts*kpwgts[idxamax(nparts, kpwgts)]/(1.0*idxsum(nparts, kpwgts));
}
}
free(kpwgts);
}
/*************************************************************************
* This function takes a graph and produces a bisection of it
**************************************************************************/
int MlevelRecursiveBisection(CtrlType *ctrl, GraphType *graph, int nparts, idxtype *part, floattype *tpwgts, floattype ubfactor, int fpart)
{
int i, j, nvtxs, cut, tvwgt, tpwgts2[2];
idxtype *label, *where;
GraphType lgraph, rgraph;
floattype wsum;
nvtxs = graph->nvtxs;
if (nvtxs == 0) {
printf("\t***Cannot bisect a graph with 0 vertices!\n\t***You are trying to partition a graph into too many parts!\n");
return 0;
}
/* Determine the weights of the partitions */
tvwgt = idxsum(nvtxs, graph->vwgt);
tpwgts2[0] = tvwgt*ssum(nparts/2, tpwgts);
tpwgts2[1] = tvwgt-tpwgts2[0];
MlevelEdgeBisection(ctrl, graph, tpwgts2, ubfactor);
cut = graph->mincut;
/* printf("%5d %5d %5d [%5d %f]\n", tpwgts2[0], tpwgts2[1], cut, tvwgt, ssum(nparts/2, tpwgts));*/
label = graph->label;
where = graph->where;
for (i=0; i<nvtxs; i++)
part[label[i]] = where[i] + fpart;
if (nparts > 2) {
SplitGraphPart(ctrl, graph, &lgraph, &rgraph);
/* printf("%d %d\n", lgraph.nvtxs, rgraph.nvtxs); */
}
/* Free the memory of the top level graph */
GKfree(&graph->gdata, &graph->rdata, &graph->label, LTERM);
/* Scale the fractions in the tpwgts according to the true weight */
wsum = ssum(nparts/2, tpwgts);
sscale(nparts/2, 1.0/wsum, tpwgts);
sscale(nparts-nparts/2, 1.0/(1.0-wsum), tpwgts+nparts/2);
/*
for (i=0; i<nparts; i++)
printf("%5.3f ", tpwgts[i]);
printf("[%5.3f]\n", wsum);
*/
/* Do the recursive call */
if (nparts > 3) {
cut += MlevelRecursiveBisection(ctrl, &lgraph, nparts/2, part, tpwgts, ubfactor, fpart);
cut += MlevelRecursiveBisection(ctrl, &rgraph, nparts-nparts/2, part, tpwgts+nparts/2, ubfactor, fpart+nparts/2);
}
else if (nparts == 3) {
cut += MlevelRecursiveBisection(ctrl, &rgraph, nparts-nparts/2, part, tpwgts+nparts/2, ubfactor, fpart+nparts/2);
GKfree(&lgraph.gdata, &lgraph.label, LTERM);
}
return cut;
}
/*************************************************************************
* This function takes a graph and produces a bisection of it
**************************************************************************/
void MlevelNestedDissectionCC(CtrlType *ctrl, GraphType *graph, idxtype *order, float ubfactor, int lastvtx)
{
int i, j, nvtxs, nbnd, tvwgt, tpwgts2[2], nsgraphs, ncmps, rnvtxs;
idxtype *label, *bndind;
idxtype *cptr, *cind;
GraphType *sgraphs;
nvtxs = graph->nvtxs;
/* Determine the weights of the partitions */
tvwgt = idxsum(nvtxs, graph->vwgt);
tpwgts2[0] = tvwgt/2;
tpwgts2[1] = tvwgt-tpwgts2[0];
MlevelNodeBisectionMultiple(ctrl, graph, tpwgts2, ubfactor);
IFSET(ctrl->dbglvl, DBG_SEPINFO, printf("Nvtxs: %6d, [%6d %6d %6d]\n", graph->nvtxs, graph->pwgts[0], graph->pwgts[1], graph->pwgts[2]));
/* Order the nodes in the separator */
nbnd = graph->nbnd;
bndind = graph->bndind;
label = graph->label;
for (i=0; i<nbnd; i++)
order[label[bndind[i]]] = --lastvtx;
cptr = idxmalloc(nvtxs, "MlevelNestedDissectionCC: cptr");
cind = idxmalloc(nvtxs, "MlevelNestedDissectionCC: cind");
ncmps = FindComponents(ctrl, graph, cptr, cind);
/*
if (ncmps > 2)
printf("[%5d] has %3d components\n", nvtxs, ncmps);
*/
sgraphs = (GraphType *)GKmalloc(ncmps*sizeof(GraphType), "MlevelNestedDissectionCC: sgraphs");
nsgraphs = SplitGraphOrderCC(ctrl, graph, sgraphs, ncmps, cptr, cind);
/*GKfree(&cptr, &cind, LTERM);*/
GKfree2((void **)&cptr, (void **)&cind);
/* Free the memory of the top level graph */
/*GKfree(&graph->gdata, &graph->rdata, &graph->label, LTERM);*/
GKfree3((void**)&graph->gdata, (void**)&graph->rdata, (void**)&graph->label);
/* Go and process the subgraphs */
for (rnvtxs=i=0; i<nsgraphs; i++) {
if (sgraphs[i].adjwgt == NULL) {
MMDOrder(ctrl, sgraphs+i, order, lastvtx-rnvtxs);
/*GKfree(&sgraphs[i].gdata, &sgraphs[i].label, LTERM);*/
GKfree2((void**)&sgraphs[i].gdata, (void**)&sgraphs[i].label);
}
else {
MlevelNestedDissectionCC(ctrl, sgraphs+i, order, ubfactor, lastvtx-rnvtxs);
}
rnvtxs += sgraphs[i].nvtxs;
}
free(sgraphs);
}
/*************************************************************************
* This function takes a graph and produces a bisection of it
**************************************************************************/
void MlevelNestedDissection(CtrlType *ctrl, GraphType *graph, idxtype *order, float ubfactor, int lastvtx)
{
int i, j, nvtxs, nbnd, tvwgt, tpwgts2[2];
idxtype *label, *bndind;
GraphType lgraph, rgraph;
nvtxs = graph->nvtxs;
/* Determine the weights of the partitions */
tvwgt = idxsum(nvtxs, graph->vwgt);
tpwgts2[0] = tvwgt/2;
tpwgts2[1] = tvwgt-tpwgts2[0];
switch (ctrl->optype) {
case OP_OEMETIS:
MlevelEdgeBisection(ctrl, graph, tpwgts2, ubfactor);
IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->SepTmr));
ConstructMinCoverSeparator(ctrl, graph, ubfactor);
IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->SepTmr));
break;
case OP_ONMETIS:
MlevelNodeBisectionMultiple(ctrl, graph, tpwgts2, ubfactor);
IFSET(ctrl->dbglvl, DBG_SEPINFO, printf("Nvtxs: %6d, [%6d %6d %6d]\n", graph->nvtxs, graph->pwgts[0], graph->pwgts[1], graph->pwgts[2]));
break;
}
/* Order the nodes in the separator */
nbnd = graph->nbnd;
bndind = graph->bndind;
label = graph->label;
for (i=0; i<nbnd; i++)
order[label[bndind[i]]] = --lastvtx;
SplitGraphOrder(ctrl, graph, &lgraph, &rgraph);
/* Free the memory of the top level graph */
/*GKfree(&graph->gdata, &graph->rdata, &graph->label, LTERM);*/
GKfree3((void **)&graph->gdata, (void**)&graph->rdata, (void **)&graph->label);
if (rgraph.nvtxs > MMDSWITCH)
MlevelNestedDissection(ctrl, &rgraph, order, ubfactor, lastvtx);
else {
MMDOrder(ctrl, &rgraph, order, lastvtx);
/*GKfree(&rgraph.gdata, &rgraph.rdata, &rgraph.label, LTERM);*/
GKfree3((void**)&rgraph.gdata, (void**)&rgraph.rdata, (void**)&rgraph.label);
}
if (lgraph.nvtxs > MMDSWITCH)
MlevelNestedDissection(ctrl, &lgraph, order, ubfactor, lastvtx-rgraph.nvtxs);
else {
MMDOrder(ctrl, &lgraph, order, lastvtx-rgraph.nvtxs);
/*GKfree(&lgraph.gdata, &lgraph.rdata, &lgraph.label, LTERM);*/
GKfree3((void**)&lgraph.gdata, (void**)&lgraph.rdata, (void**)&lgraph.label);
}
}
/*************************************************************************
* This function checks if the partition weights are within the balance
* contraints
**************************************************************************/
int IsBalanced(idxtype *pwgts, int nparts, float *tpwgts, float ubfactor)
{
int i, tvwgt;
tvwgt = idxsum(nparts, pwgts);
for (i=0; i<nparts; i++) {
if (pwgts[i] > tpwgts[i]*tvwgt*(ubfactor+0.005))
return 0;
}
return 1;
}
/*************************************************************************
* This function is the entry point for OEMETIS
**************************************************************************/
void METIS_EdgeND(int *nvtxs, idxtype *xadj, idxtype *adjncy, int *numflag, int *options,
idxtype *perm, idxtype *iperm)
{
int i, j;
GraphType graph;
CtrlType ctrl;
if (*numflag == 1)
Change2CNumbering(*nvtxs, xadj, adjncy);
SetUpGraph(&graph, OP_OEMETIS, *nvtxs, 1, xadj, adjncy, NULL, NULL, 0);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = OEMETIS_CTYPE;
ctrl.IType = OEMETIS_ITYPE;
ctrl.RType = OEMETIS_RTYPE;
ctrl.dbglvl = OEMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.oflags = 0;
ctrl.pfactor = -1;
ctrl.nseps = 1;
ctrl.optype = OP_OEMETIS;
ctrl.CoarsenTo = 20;
ctrl.maxvwgt = 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);
InitRandom(-1);
AllocateWorkSpace(&ctrl, &graph, 2);
IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));
MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, *nvtxs);
IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));
for (i=0; i<*nvtxs; i++)
perm[iperm[i]] = i;
FreeWorkSpace(&ctrl, &graph);
if (*numflag == 1)
Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);
}
/*************************************************************************
* This function is the entry point for PWMETIS that accepts exact weights
* for the target partitions
**************************************************************************/
void METIS_WPartGraphRecursive(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *adjwgt, int *wgtflag, int *numflag, int *nparts,
floattype *tpwgts, int *options, int *edgecut, idxtype *part)
{
int i, j;
GraphType graph;
CtrlType ctrl;
floattype *mytpwgts;
if (*numflag == 1)
Change2CNumbering(*nvtxs, xadj, adjncy);
SetUpGraph(&graph, OP_PMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, *wgtflag);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = PMETIS_CTYPE;
ctrl.IType = PMETIS_ITYPE;
ctrl.RType = PMETIS_RTYPE;
ctrl.dbglvl = PMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.optype = OP_PMETIS;
ctrl.CoarsenTo = 20;
ctrl.maxvwgt = 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);
mytpwgts = fmalloc(*nparts, "PWMETIS: mytpwgts");
for (i=0; i<*nparts; i++)
mytpwgts[i] = tpwgts[i];
InitRandom(-1);
AllocateWorkSpace(&ctrl, &graph, *nparts);
IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));
*edgecut = MlevelRecursiveBisection(&ctrl, &graph, *nparts, part, mytpwgts, 1.000, 0);
IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));
FreeWorkSpace(&ctrl, &graph);
free(mytpwgts);
if (*numflag == 1)
Change2FNumbering(*nvtxs, xadj, adjncy, part);
}
/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_EdgeComputeSeparator(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *adjwgt, int *options, int *sepsize, idxtype *part)
{
int i, j, tvwgt, tpwgts[2];
GraphType graph;
CtrlType ctrl;
SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
tvwgt = idxsum(*nvtxs, graph.vwgt);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = ONMETIS_CTYPE;
ctrl.IType = ONMETIS_ITYPE;
ctrl.RType = ONMETIS_RTYPE;
ctrl.dbglvl = ONMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.oflags = 0;
ctrl.pfactor = 0;
ctrl.nseps = 5;
ctrl.optype = OP_OEMETIS;
ctrl.CoarsenTo = amin(100, *nvtxs-1);
ctrl.maxvwgt = 1.5*tvwgt/ctrl.CoarsenTo;
InitRandom(options[7]);
AllocateWorkSpace(&ctrl, &graph, 2);
/*============================================================
* Perform the bisection
*============================================================*/
tpwgts[0] = tvwgt/2;
tpwgts[1] = tvwgt-tpwgts[0];
MlevelEdgeBisection(&ctrl, &graph, tpwgts, 1.05);
ConstructMinCoverSeparator(&ctrl, &graph, 1.05);
*sepsize = graph.pwgts[2];
idxcopy(*nvtxs, graph.where, part);
GKfree((void**)&graph.gdata, &graph.rdata, &graph.label, LTERM);
FreeWorkSpace(&ctrl, &graph);
}
/*************************************************************************
* This function computes the initial id/ed
**************************************************************************/
void Compute2WayPartitionParams(CtrlType *ctrl, GraphType *graph)
{
int i, j, k, l, nvtxs, nbnd, mincut;
idxtype *xadj, *vwgt, *adjncy, *adjwgt, *pwgts;
idxtype *id, *ed, *where;
idxtype *bndptr, *bndind;
int me, other;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
pwgts = idxset(2, 0, graph->pwgts);
id = idxset(nvtxs, 0, graph->id);
ed = idxset(nvtxs, 0, graph->ed);
bndptr = idxset(nvtxs, -1, graph->bndptr);
bndind = graph->bndind;
/*------------------------------------------------------------
/ Compute now the id/ed degrees
/------------------------------------------------------------*/
nbnd = mincut = 0;
for (i=0; i<nvtxs; i++) {
ASSERT(where[i] >= 0 && where[i] <= 1);
me = where[i];
pwgts[me] += vwgt[i];
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (me == where[adjncy[j]])
id[i] += adjwgt[j];
else
ed[i] += adjwgt[j];
}
if (ed[i] > 0 || xadj[i] == xadj[i+1]) {
mincut += ed[i];
bndptr[i] = nbnd;
bndind[nbnd++] = i;
}
}
graph->mincut = mincut/2;
graph->nbnd = nbnd;
ASSERT(pwgts[0]+pwgts[1] == idxsum(nvtxs, vwgt));
}
/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_NodeComputeSeparator(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *adjwgt, float *ubfactor, int *options, int *sepsize, idxtype *part)
{
int i, j, tvwgt, tpwgts[2];
GraphType graph;
CtrlType ctrl;
SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
tvwgt = idxsum(*nvtxs, graph.vwgt);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = ONMETIS_CTYPE;
ctrl.IType = ONMETIS_ITYPE;
ctrl.RType = ONMETIS_RTYPE;
ctrl.dbglvl = ONMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.oflags = OFLAG_COMPRESS; /* For by-passing the pre-coarsening for multiple runs */
ctrl.RType = 2; /* Standard 1-sided node refinement code */
ctrl.pfactor = 0;
ctrl.nseps = 5; /* This should match NUM_INIT_MSECTIONS in ParMETISLib/defs.h */
ctrl.optype = OP_ONMETIS;
InitRandom(options[7]);
AllocateWorkSpace(&ctrl, &graph, 2);
/*============================================================
* Perform the bisection
*============================================================*/
tpwgts[0] = tvwgt/2;
tpwgts[1] = tvwgt-tpwgts[0];
MlevelNodeBisectionMultiple(&ctrl, &graph, tpwgts, *ubfactor*.95);
*sepsize = graph.pwgts[2];
idxcopy(*nvtxs, graph.where, part);
GKfree((void **)&graph.gdata, &graph.rdata, &graph.label, LTERM);
FreeWorkSpace(&ctrl, &graph);
}
/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_NodeComputeSeparator(idxtype *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *adjwgt, idxtype *options, idxtype *sepsize, idxtype *part)
{
idxtype i, j, tvwgt, tpwgts[2];
GraphType graph;
CtrlType ctrl;
SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
tvwgt = idxsum(*nvtxs, graph.vwgt, 1);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = ONMETIS_CTYPE;
ctrl.IType = ONMETIS_ITYPE;
ctrl.RType = ONMETIS_RTYPE;
ctrl.dbglvl = ONMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.oflags = 0;
ctrl.pfactor = 0;
ctrl.nseps = 3;
ctrl.optype = OP_ONMETIS;
ctrl.CoarsenTo = amin(100, *nvtxs-1);
ctrl.maxvwgt = 1.5*tvwgt/ctrl.CoarsenTo;
InitRandom(options[7]);
AllocateWorkSpace(&ctrl, &graph, 2);
/*============================================================
* Perform the bisection
*============================================================*/
tpwgts[0] = tvwgt/2;
tpwgts[1] = tvwgt-tpwgts[0];
MlevelNodeBisectionMultiple(&ctrl, &graph, tpwgts, 1.02);
*sepsize = graph.pwgts[2];
idxcopy(*nvtxs, graph.where, part);
FreeGraph(&graph, 0);
FreeWorkSpace(&ctrl, &graph);
}
/*************************************************************************
* This function is the entry point for KWMETIS
**************************************************************************/
void METIS_WPartGraphVKway(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *vsize, int *wgtflag, int *numflag, int *nparts,
float *tpwgts, int *options, int *volume, idxtype *part)
{
int i, j;
GraphType graph;
CtrlType ctrl;
if (*numflag == 1)
Change2CNumbering(*nvtxs, xadj, adjncy);
VolSetUpGraph(&graph, OP_KVMETIS, *nvtxs, 1, xadj, adjncy, vwgt, vsize, *wgtflag);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = KVMETIS_CTYPE;
ctrl.IType = KVMETIS_ITYPE;
ctrl.RType = KVMETIS_RTYPE;
ctrl.dbglvl = KVMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.optype = OP_KVMETIS;
ctrl.CoarsenTo = amax((*nvtxs)/(40*log2Int(*nparts)), 20*(*nparts));
ctrl.maxvwgt = 1.5*((graph.vwgt ? idxsum(*nvtxs, graph.vwgt) : (*nvtxs))/ctrl.CoarsenTo);
InitRandom(-1);
AllocateWorkSpace(&ctrl, &graph, *nparts);
IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));
*volume = MlevelVolKWayPartitioning(&ctrl, &graph, *nparts, part, tpwgts, 1.03);
IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));
FreeWorkSpace(&ctrl, &graph);
if (*numflag == 1)
Change2FNumbering(*nvtxs, xadj, adjncy, part);
}
/*************************************************************************
* This function is the entry point for KWMETIS with seed specification
* in options[7]
**************************************************************************/
void METIS_WPartGraphKway2(idxtype *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt,
idxtype *adjwgt, idxtype *wgtflag, idxtype *numflag, idxtype *nparts,
float *tpwgts, idxtype *options, idxtype *edgecut, idxtype *part)
{
idxtype i, j;
GraphType graph;
CtrlType ctrl;
if (*numflag == 1)
Change2CNumbering(*nvtxs, xadj, adjncy);
SetUpGraph(&graph, OP_KMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, *wgtflag);
if (options[0] == 0) { /* Use the default parameters */
ctrl.CType = KMETIS_CTYPE;
ctrl.IType = KMETIS_ITYPE;
ctrl.RType = KMETIS_RTYPE;
ctrl.dbglvl = KMETIS_DBGLVL;
}
else {
ctrl.CType = options[OPTION_CTYPE];
ctrl.IType = options[OPTION_ITYPE];
ctrl.RType = options[OPTION_RTYPE];
ctrl.dbglvl = options[OPTION_DBGLVL];
}
ctrl.optype = OP_KMETIS;
ctrl.CoarsenTo = 20*(*nparts);
ctrl.maxvwgt = 1.5*((graph.vwgt ? idxsum(*nvtxs, graph.vwgt, 1) : (*nvtxs))/ctrl.CoarsenTo);
InitRandom(options[7]);
AllocateWorkSpace(&ctrl, &graph, *nparts);
IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
IFSET(ctrl.dbglvl, DBG_TIME, gk_startcputimer(ctrl.TotalTmr));
*edgecut = MlevelKWayPartitioning(&ctrl, &graph, *nparts, part, tpwgts, 1.03);
IFSET(ctrl.dbglvl, DBG_TIME, gk_stopcputimer(ctrl.TotalTmr));
IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));
FreeWorkSpace(&ctrl, &graph);
if (*numflag == 1)
Change2FNumbering(*nvtxs, xadj, adjncy, part);
}
/*************************************************************************
* This function computes the balance of the element partitioning
**************************************************************************/
float ComputeElementBalance(int ne, int nparts, idxtype *where)
{
int i;
idxtype *kpwgts;
float balance;
kpwgts = idxsmalloc(nparts, 0, "ComputeElementBalance: kpwgts");
for (i=0; i<ne; i++)
kpwgts[where[i]]++;
balance = 1.0*nparts*kpwgts[idxamax(nparts, kpwgts)]/(1.0*idxsum(nparts, kpwgts));
free(kpwgts);
return balance;
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void MocGrowBisection(CtrlType *ctrl, GraphType *graph, float *tpwgts, float ubfactor)
{
int i, j, k, nvtxs, ncon, from, bestcut, mincut, nbfs;
idxtype *bestwhere, *where;
nvtxs = graph->nvtxs;
MocAllocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
nbfs = 2*(nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = idxsum(graph->nedges, graph->adjwgt);
for (; nbfs>0; nbfs--) {
idxset(nvtxs, 1, where);
where[RandomInRange(nvtxs)] = 0;
MocCompute2WayPartitionParams(ctrl, graph);
MocInit2WayBalance(ctrl, graph, tpwgts);
MocFM_2WayEdgeRefine(ctrl, graph, tpwgts, 4);
MocBalance2Way(ctrl, graph, tpwgts, 1.02);
MocFM_2WayEdgeRefine(ctrl, graph, tpwgts, 4);
if (bestcut >= graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
/*GKfree(&bestwhere, LTERM);*/
GKfree1((void**)&bestwhere);
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void MocGrowBisection2(CtrlType *ctrl, GraphType *graph, float *tpwgts, float *ubvec)
{
int /*i, j, k,*/ nvtxs, /*ncon, from,*/ bestcut, /*mincut,*/ nbfs;
idxtype *bestwhere, *where;
nvtxs = graph->nvtxs;
MocAllocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
nbfs = 2*(nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = idxsum(graph->nedges, graph->adjwgt);
for (; nbfs>0; nbfs--) {
idxset(nvtxs, 1, where);
where[RandomInRange(nvtxs)] = 0;
MocCompute2WayPartitionParams(ctrl, graph);
MocBalance2Way2(ctrl, graph, tpwgts, ubvec);
MocFM_2WayEdgeRefine2(ctrl, graph, tpwgts, ubvec, 4);
MocBalance2Way2(ctrl, graph, tpwgts, ubvec);
MocFM_2WayEdgeRefine2(ctrl, graph, tpwgts, ubvec, 4);
if (bestcut > graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
GKfree((void**)&bestwhere, LTERM);
}
/*************************************************************************
* This function computes movement statistics for adaptive refinement
* schemes
**************************************************************************/
void Mc_ComputeMoveStatistics(CtrlType *ctrl, GraphType *graph, int *nmoved, int *maxin, int *maxout)
{
int i, nvtxs, nparts, myhome;
idxtype *vwgt, *where;
idxtype *lend, *gend, *lleft, *gleft, *lstart, *gstart;
nvtxs = graph->nvtxs;
vwgt = graph->vwgt;
where = graph->where;
nparts = ctrl->nparts;
lstart = idxsmalloc(nparts, 0, "ComputeMoveStatistics: lstart");
gstart = idxsmalloc(nparts, 0, "ComputeMoveStatistics: gstart");
lleft = idxsmalloc(nparts, 0, "ComputeMoveStatistics: lleft");
gleft = idxsmalloc(nparts, 0, "ComputeMoveStatistics: gleft");
lend = idxsmalloc(nparts, 0, "ComputeMoveStatistics: lend");
gend = idxsmalloc(nparts, 0, "ComputeMoveStatistics: gend");
for (i=0; i<nvtxs; i++) {
myhome = (ctrl->ps_relation == COUPLED) ? ctrl->mype : graph->home[i];
lstart[myhome] += (graph->vsize == NULL) ? 1 : graph->vsize[i];
lend[where[i]] += (graph->vsize == NULL) ? 1 : graph->vsize[i];
if (where[i] != myhome)
lleft[myhome] += (graph->vsize == NULL) ? 1 : graph->vsize[i];
}
/* PrintVector(ctrl, ctrl->npes, 0, lend, "Lend: "); */
MPI_Allreduce((void *)lstart, (void *)gstart, nparts, IDX_DATATYPE, MPI_SUM, ctrl->comm);
MPI_Allreduce((void *)lleft, (void *)gleft, nparts, IDX_DATATYPE, MPI_SUM, ctrl->comm);
MPI_Allreduce((void *)lend, (void *)gend, nparts, IDX_DATATYPE, MPI_SUM, ctrl->comm);
*nmoved = idxsum(nparts, gleft);
*maxout = gleft[idxamax(nparts, gleft)];
for (i=0; i<nparts; i++)
lstart[i] = gend[i]+gleft[i]-gstart[i];
*maxin = lstart[idxamax(nparts, lstart)];
GKfree((void **)&lstart, (void **)&gstart, (void **)&lleft, (void **)&gleft, (void **)&lend, (void **)&gend, LTERM);
}
/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void Random_KWayEdgeRefineMConn(CtrlType *ctrl, GraphType *graph, int nparts, float *tpwgts, float ubfactor, int npasses, int ffactor)
{
int i, ii, iii, j, jj, k, l, pass, nvtxs, nmoves, nbnd, tvwgt, myndegrees;
int from, me, to, oldcut, vwgt, gain;
int maxndoms, nadd;
idxtype *xadj, *adjncy, *adjwgt;
idxtype *where, *pwgts, *perm, *bndptr, *bndind, *minwgt, *maxwgt, *itpwgts;
idxtype *phtable, *pmat, *pmatptr, *ndoms;
EDegreeType *myedegrees;
RInfoType *myrinfo;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bndptr = graph->bndptr;
bndind = graph->bndind;
where = graph->where;
pwgts = graph->pwgts;
pmat = ctrl->wspace.pmat;
phtable = idxwspacemalloc(ctrl, nparts);
ndoms = idxwspacemalloc(ctrl, nparts);
ComputeSubDomainGraph(graph, nparts, pmat, ndoms);
/* Setup the weight intervals of the various subdomains */
minwgt = idxwspacemalloc(ctrl, nparts);
maxwgt = idxwspacemalloc(ctrl, nparts);
itpwgts = idxwspacemalloc(ctrl, nparts);
tvwgt = idxsum(nparts, pwgts);
ASSERT(tvwgt == idxsum(nvtxs, graph->vwgt));
for (i=0; i<nparts; i++) {
itpwgts[i] = tpwgts[i]*tvwgt;
maxwgt[i] = tpwgts[i]*tvwgt*ubfactor;
minwgt[i] = tpwgts[i]*tvwgt*(1.0/ubfactor);
}
perm = idxwspacemalloc(ctrl, nvtxs);
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("Partitions: [%6d %6d]-[%6d %6d], Balance: %5.3f, Nv-Nb[%6d %6d]. Cut: %6d\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)], minwgt[0], maxwgt[0],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nvtxs, graph->nbnd,
graph->mincut));
for (pass=0; pass<npasses; pass++) {
ASSERT(ComputeCut(graph, where) == graph->mincut);
maxndoms = ndoms[idxamax(nparts, ndoms)];
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];
vwgt = graph->vwgt[i];
if (myrinfo->id > 0 && pwgts[from]-vwgt < minwgt[from])
continue; /* This cannot be moved! */
myedegrees = myrinfo->edegrees;
myndegrees = myrinfo->ndegrees;
/* Determine the valid domains */
for (j=0; j<myndegrees; j++) {
to = myedegrees[j].pid;
phtable[to] = 1;
pmatptr = pmat + to*nparts;
for (nadd=0, k=0; k<myndegrees; k++) {
if (k == j)
continue;
l = myedegrees[k].pid;
if (pmatptr[l] == 0) {
if (ndoms[l] > maxndoms-1) {
phtable[to] = 0;
nadd = maxndoms;
break;
}
nadd++;
}
}
if (ndoms[to]+nadd > maxndoms)
phtable[to] = 0;
if (nadd == 0)
phtable[to] = 2;
}
/* Find the first valid move */
j = myrinfo->id;
for (k=0; k<myndegrees; k++) {
to = myedegrees[k].pid;
if (!phtable[to])
continue;
gain = myedegrees[k].ed-j; /* j = myrinfo->id. Allow good nodes to move */
if (pwgts[to]+vwgt <= maxwgt[to]+ffactor*gain && gain >= 0)
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 (!phtable[to])
continue;
if ((myedegrees[j].ed > myedegrees[k].ed && pwgts[to]+vwgt <= maxwgt[to]) ||
(myedegrees[j].ed == myedegrees[k].ed &&
itpwgts[myedegrees[k].pid]*pwgts[to] < itpwgts[to]*pwgts[myedegrees[k].pid]))
k = j;
}
to = myedegrees[k].pid;
j = 0;
if (myedegrees[k].ed-myrinfo->id > 0)
j = 1;
else if (myedegrees[k].ed-myrinfo->id == 0) {
if (/*(iii&7) == 0 ||*/ phtable[myedegrees[k].pid] == 2 || pwgts[from] >= maxwgt[from] || itpwgts[from]*(pwgts[to]+vwgt) < itpwgts[to]*pwgts[from])
j = 1;
}
if (j == 0)
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 pmat to reflect the move of 'i' */
pmat[from*nparts+to] += (myrinfo->id-myedegrees[k].ed);
pmat[to*nparts+from] += (myrinfo->id-myedegrees[k].ed);
if (pmat[from*nparts+to] == 0) {
ndoms[from]--;
if (ndoms[from]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[to*nparts+from] == 0) {
ndoms[to]--;
if (ndoms[to]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
/* Update where, weight, and ID/ED information of the vertex you moved */
where[i] = to;
INC_DEC(pwgts[to], pwgts[from], vwgt);
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];
}
}
/* Update pmat to reflect the move of 'i' for domains other than 'from' and 'to' */
if (me != from && me != to) {
pmat[me*nparts+from] -= adjwgt[j];
pmat[from*nparts+me] -= adjwgt[j];
if (pmat[me*nparts+from] == 0) {
ndoms[me]--;
if (ndoms[me]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[from*nparts+me] == 0) {
ndoms[from]--;
if (ndoms[from]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[me*nparts+to] == 0) {
ndoms[me]++;
if (ndoms[me] > maxndoms) {
printf("You just increased the maxndoms: %d %d\n", ndoms[me], maxndoms);
maxndoms = ndoms[me];
}
}
if (pmat[to*nparts+me] == 0) {
ndoms[to]++;
if (ndoms[to] > maxndoms) {
printf("You just increased the maxndoms: %d %d\n", ndoms[to], maxndoms);
maxndoms = ndoms[to];
}
}
pmat[me*nparts+to] += adjwgt[j];
pmat[to*nparts+me] += adjwgt[j];
}
ASSERT(myrinfo->ndegrees <= xadj[ii+1]-xadj[ii]);
ASSERT(CheckRInfo(myrinfo));
}
nmoves++;
}
}
graph->nbnd = nbnd;
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("\t[%6d %6d], Balance: %5.3f, Nb: %6d. Nmoves: %5d, Cut: %5d, Vol: %5d, %d\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nbnd, nmoves,
graph->mincut, ComputeVolume(graph, where), idxsum(nparts, ndoms)));
if (graph->mincut == oldcut)
break;
}
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nvtxs);
}
/*************************************************************************
* This function finds all the connected components induced by the
* partitioning vector in wgraph->where and tries to push them around to
* remove some of them
**************************************************************************/
void EliminateComponents(CtrlType *ctrl, GraphType *graph, int nparts, float *tpwgts, float ubfactor)
{
int i, ii, j, jj, k, me, nvtxs, tvwgt, first, last, nleft, ncmps, cwgt, other, target, deltawgt;
idxtype *xadj, *adjncy, *vwgt, *adjwgt, *where, *pwgts, *maxpwgt;
idxtype *cpvec, *touched, *perm, *todo, *cind, *cptr, *npcmps;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
vwgt = graph->vwgt;
adjwgt = graph->adjwgt;
where = graph->where;
pwgts = graph->pwgts;
touched = idxset(nvtxs, 0, idxwspacemalloc(ctrl, nvtxs));
cptr = idxwspacemalloc(ctrl, nvtxs);
cind = idxwspacemalloc(ctrl, nvtxs);
perm = idxwspacemalloc(ctrl, nvtxs);
todo = idxwspacemalloc(ctrl, nvtxs);
maxpwgt = idxwspacemalloc(ctrl, nparts);
cpvec = idxwspacemalloc(ctrl, nparts);
npcmps = idxset(nparts, 0, idxwspacemalloc(ctrl, nparts));
for (i=0; i<nvtxs; i++)
perm[i] = todo[i] = i;
/* Find the connected componends induced by the partition */
ncmps = -1;
first = last = 0;
nleft = nvtxs;
while (nleft > 0) {
if (first == last) { /* Find another starting vertex */
cptr[++ncmps] = first;
ASSERT(touched[todo[0]] == 0);
i = todo[0];
cind[last++] = i;
touched[i] = 1;
me = where[i];
npcmps[me]++;
}
i = cind[first++];
k = perm[i];
j = todo[k] = todo[--nleft];
perm[j] = k;
for (j=xadj[i]; j<xadj[i+1]; j++) {
k = adjncy[j];
if (where[k] == me && !touched[k]) {
cind[last++] = k;
touched[k] = 1;
}
}
}
cptr[++ncmps] = first;
/* printf("I found %d components, for this %d-way partition\n", ncmps, nparts); */
if (ncmps > nparts) { /* There are more components than processors */
/* First determine the max allowed load imbalance */
tvwgt = idxsum(nparts, pwgts);
for (i=0; i<nparts; i++)
maxpwgt[i] = ubfactor*tpwgts[i]*tvwgt;
deltawgt = 5;
for (i=0; i<ncmps; i++) {
me = where[cind[cptr[i]]]; /* Get the domain of this component */
if (npcmps[me] == 1)
continue; /* Skip it because it is contigous */
/*printf("Trying to move %d from %d\n", i, me); */
/* Determine the weight of the block to be moved and abort if too high */
for (cwgt=0, j=cptr[i]; j<cptr[i+1]; j++)
cwgt += vwgt[cind[j]];
if (cwgt > .30*pwgts[me])
continue; /* Skip the component if it is over 30% of the weight */
/* Determine the connectivity */
idxset(nparts, 0, cpvec);
for (j=cptr[i]; j<cptr[i+1]; j++) {
ii = cind[j];
for (jj=xadj[ii]; jj<xadj[ii+1]; jj++)
cpvec[where[adjncy[jj]]] += adjwgt[jj];
}
cpvec[me] = 0;
target = -1;
for (j=0; j<nparts; j++) {
if (cpvec[j] > 0 && (cwgt < deltawgt || pwgts[j] + cwgt < maxpwgt[j])) {
if (target == -1 || cpvec[target] < cpvec[j])
target = j;
}
}
/* printf("\tMoving it to %d [%d]\n", target, cpvec[target]);*/
if (target != -1) {
/* Assign all the vertices of 'me' to 'target' and update data structures */
INC_DEC(pwgts[target], pwgts[me], cwgt);
npcmps[me]--;
MoveGroup(ctrl, graph, nparts, target, i, cptr, cind);
}
}
}
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
}
/*************************************************************************
* This function creates the coarser graph
**************************************************************************/
void CreateCoarseGraph_NVW(CtrlType *ctrl, GraphType *graph, int cnvtxs, idxtype *match, idxtype *perm)
{
int i, j, jj, k, kk, l, m, istart, iend, nvtxs, nedges, ncon, cnedges, v, u, mask;
idxtype *xadj, *adjncy, *adjwgtsum, *auxadj;
idxtype *cmap, *htable;
idxtype *cxadj, *cvwgt, *cadjncy, *cadjwgt, *cadjwgtsum;
float *nvwgt, *cnvwgt;
GraphType *cgraph;
IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->ContractTmr));
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
nvwgt = graph->nvwgt;
adjncy = graph->adjncy;
adjwgtsum = graph->adjwgtsum;
cmap = graph->cmap;
/* Initialize the coarser graph */
cgraph = SetUpCoarseGraph(graph, cnvtxs, 0);
cxadj = cgraph->xadj;
cvwgt = cgraph->vwgt;
cnvwgt = cgraph->nvwgt;
cadjwgtsum = cgraph->adjwgtsum;
cadjncy = cgraph->adjncy;
cadjwgt = cgraph->adjwgt;
iend = xadj[nvtxs];
auxadj = ctrl->wspace.auxcore;
memcpy(auxadj, adjncy, iend*sizeof(idxtype));
for (i=0; i<iend; i++)
auxadj[i] = cmap[auxadj[i]];
mask = HTLENGTH;
htable = idxset(mask+1, -1, idxwspacemalloc(ctrl, mask+1));
cxadj[0] = cnvtxs = cnedges = 0;
for (i=0; i<nvtxs; i++) {
v = perm[i];
if (cmap[v] != cnvtxs)
continue;
u = match[v];
cvwgt[cnvtxs] = 1;
cadjwgtsum[cnvtxs] = adjwgtsum[v];
nedges = 0;
istart = xadj[v];
iend = xadj[v+1];
for (j=istart; j<iend; j++) {
k = auxadj[j];
kk = k&mask;
if ((m = htable[kk]) == -1) {
cadjncy[nedges] = k;
cadjwgt[nedges] = 1;
htable[kk] = nedges++;
}
else if (cadjncy[m] == k) {
cadjwgt[m]++;
}
else {
for (jj=0; jj<nedges; jj++) {
if (cadjncy[jj] == k) {
cadjwgt[jj]++;
break;
}
}
if (jj == nedges) {
cadjncy[nedges] = k;
cadjwgt[nedges++] = 1;
}
}
}
if (v != u) {
cvwgt[cnvtxs]++;
cadjwgtsum[cnvtxs] += adjwgtsum[u];
istart = xadj[u];
iend = xadj[u+1];
for (j=istart; j<iend; j++) {
k = auxadj[j];
kk = k&mask;
if ((m = htable[kk]) == -1) {
cadjncy[nedges] = k;
cadjwgt[nedges] = 1;
htable[kk] = nedges++;
}
else if (cadjncy[m] == k) {
cadjwgt[m]++;
}
else {
for (jj=0; jj<nedges; jj++) {
if (cadjncy[jj] == k) {
cadjwgt[jj]++;
break;
}
}
if (jj == nedges) {
cadjncy[nedges] = k;
cadjwgt[nedges++] = 1;
}
}
}
/* Remove the contracted adjacency weight */
jj = htable[cnvtxs&mask];
if (jj >= 0 && cadjncy[jj] != cnvtxs) {
for (jj=0; jj<nedges; jj++) {
if (cadjncy[jj] == cnvtxs)
break;
}
}
if (jj >= 0 && cadjncy[jj] == cnvtxs) { /* This 2nd check is needed for non-adjacent matchings */
cadjwgtsum[cnvtxs] -= cadjwgt[jj];
cadjncy[jj] = cadjncy[--nedges];
cadjwgt[jj] = cadjwgt[nedges];
}
}
ASSERTP(cadjwgtsum[cnvtxs] == idxsum(nedges, cadjwgt), ("%d %d %d %d %d\n", cnvtxs, cadjwgtsum[cnvtxs], idxsum(nedges, cadjwgt), adjwgtsum[u], adjwgtsum[v]));
for (j=0; j<nedges; j++)
htable[cadjncy[j]&mask] = -1; /* Zero out the htable */
htable[cnvtxs&mask] = -1;
cnedges += nedges;
cxadj[++cnvtxs] = cnedges;
cadjncy += nedges;
cadjwgt += nedges;
}
cgraph->nedges = cnedges;
ReAdjustMemory(graph, cgraph, 0);
IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->ContractTmr));
idxwspacefree(ctrl, mask+1);
}
/*************************************************************************
* This function creates the coarser graph
**************************************************************************/
void CreateCoarseGraphNoMask(CtrlType *ctrl, GraphType *graph, int cnvtxs, idxtype *match, idxtype *perm)
{
int i, j, k, m, istart, iend, nvtxs, nedges, ncon, cnedges, v, u, dovsize;
idxtype *xadj, *vwgt, *vsize, *adjncy, *adjwgt, *adjwgtsum, *auxadj;
idxtype *cmap, *htable;
idxtype *cxadj, *cvwgt, *cvsize, *cadjncy, *cadjwgt, *cadjwgtsum;
float *nvwgt, *cnvwgt;
GraphType *cgraph;
dovsize = (ctrl->optype == OP_KVMETIS ? 1 : 0);
IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->ContractTmr));
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
vwgt = graph->vwgt;
vsize = graph->vsize;
nvwgt = graph->nvwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
adjwgtsum = graph->adjwgtsum;
cmap = graph->cmap;
/* Initialize the coarser graph */
cgraph = SetUpCoarseGraph(graph, cnvtxs, dovsize);
cxadj = cgraph->xadj;
cvwgt = cgraph->vwgt;
cvsize = cgraph->vsize;
cnvwgt = cgraph->nvwgt;
cadjwgtsum = cgraph->adjwgtsum;
cadjncy = cgraph->adjncy;
cadjwgt = cgraph->adjwgt;
htable = idxset(cnvtxs, -1, idxwspacemalloc(ctrl, cnvtxs));
iend = xadj[nvtxs];
auxadj = ctrl->wspace.auxcore;
memcpy(auxadj, adjncy, iend*sizeof(idxtype));
for (i=0; i<iend; i++)
auxadj[i] = cmap[auxadj[i]];
cxadj[0] = cnvtxs = cnedges = 0;
for (i=0; i<nvtxs; i++) {
v = perm[i];
if (cmap[v] != cnvtxs)
continue;
u = match[v];
if (ncon == 1)
cvwgt[cnvtxs] = vwgt[v];
else
scopy(ncon, nvwgt+v*ncon, cnvwgt+cnvtxs*ncon);
if (dovsize)
cvsize[cnvtxs] = vsize[v];
cadjwgtsum[cnvtxs] = adjwgtsum[v];
nedges = 0;
istart = xadj[v];
iend = xadj[v+1];
for (j=istart; j<iend; j++) {
k = auxadj[j];
if ((m = htable[k]) == -1) {
cadjncy[nedges] = k;
cadjwgt[nedges] = adjwgt[j];
htable[k] = nedges++;
}
else {
cadjwgt[m] += adjwgt[j];
}
}
if (v != u) {
if (ncon == 1)
cvwgt[cnvtxs] += vwgt[u];
else
saxpy(ncon, 1.0, nvwgt+u*ncon, 1, cnvwgt+cnvtxs*ncon, 1);
if (dovsize)
cvsize[cnvtxs] += vsize[u];
cadjwgtsum[cnvtxs] += adjwgtsum[u];
istart = xadj[u];
iend = xadj[u+1];
for (j=istart; j<iend; j++) {
k = auxadj[j];
if ((m = htable[k]) == -1) {
cadjncy[nedges] = k;
cadjwgt[nedges] = adjwgt[j];
htable[k] = nedges++;
}
else {
cadjwgt[m] += adjwgt[j];
}
}
/* Remove the contracted adjacency weight */
if ((j = htable[cnvtxs]) != -1) {
ASSERT(cadjncy[j] == cnvtxs);
cadjwgtsum[cnvtxs] -= cadjwgt[j];
cadjncy[j] = cadjncy[--nedges];
cadjwgt[j] = cadjwgt[nedges];
htable[cnvtxs] = -1;
}
}
ASSERTP(cadjwgtsum[cnvtxs] == idxsum(nedges, cadjwgt), ("%d %d\n", cadjwgtsum[cnvtxs], idxsum(nedges, cadjwgt)));
for (j=0; j<nedges; j++)
htable[cadjncy[j]] = -1; /* Zero out the htable */
cnedges += nedges;
cxadj[++cnvtxs] = cnedges;
cadjncy += nedges;
cadjwgt += nedges;
}
cgraph->nedges = cnedges;
ReAdjustMemory(graph, cgraph, dovsize);
IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->ContractTmr));
idxwspacefree(ctrl, cnvtxs);
}
/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void Greedy_KWayEdgeBalanceMConn(CtrlType *ctrl, GraphType *graph, int nparts, float *tpwgts, float ubfactor, int npasses)
{
int i, ii, iii, j, jj, k, l, pass, nvtxs, nbnd, tvwgt, myndegrees, oldgain, gain, nmoves;
int from, me, to, oldcut, vwgt, maxndoms, nadd;
idxtype *xadj, *adjncy, *adjwgt;
idxtype *where, *pwgts, *perm, *bndptr, *bndind, *minwgt, *maxwgt, *moved, *itpwgts;
idxtype *phtable, *pmat, *pmatptr, *ndoms;
EDegreeType *myedegrees;
RInfoType *myrinfo;
PQueueType queue;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bndind = graph->bndind;
bndptr = graph->bndptr;
where = graph->where;
pwgts = graph->pwgts;
pmat = ctrl->wspace.pmat;
phtable = idxwspacemalloc(ctrl, nparts);
ndoms = idxwspacemalloc(ctrl, nparts);
ComputeSubDomainGraph(graph, nparts, pmat, ndoms);
/* Setup the weight intervals of the various subdomains */
minwgt = idxwspacemalloc(ctrl, nparts);
maxwgt = idxwspacemalloc(ctrl, nparts);
itpwgts = idxwspacemalloc(ctrl, nparts);
tvwgt = idxsum(nparts, pwgts);
ASSERT(tvwgt == idxsum(nvtxs, graph->vwgt));
for (i=0; i<nparts; i++) {
itpwgts[i] = tpwgts[i]*tvwgt;
maxwgt[i] = tpwgts[i]*tvwgt*ubfactor;
minwgt[i] = tpwgts[i]*tvwgt*(1.0/ubfactor);
}
perm = idxwspacemalloc(ctrl, nvtxs);
moved = idxwspacemalloc(ctrl, nvtxs);
PQueueInit(ctrl, &queue, nvtxs, graph->adjwgtsum[idxamax(nvtxs, graph->adjwgtsum)]);
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("Partitions: [%6d %6d]-[%6d %6d], Balance: %5.3f, Nv-Nb[%6d %6d]. Cut: %6d [B]\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)], minwgt[0], maxwgt[0],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nvtxs, graph->nbnd,
graph->mincut));
for (pass=0; pass<npasses; pass++) {
ASSERT(ComputeCut(graph, where) == graph->mincut);
/* Check to see if things are out of balance, given the tolerance */
for (i=0; i<nparts; i++) {
if (pwgts[i] > maxwgt[i])
break;
}
if (i == nparts) /* Things are balanced. Return right away */
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;
}
maxndoms = ndoms[idxamax(nparts, ndoms)];
for (nmoves=0;;) {
if ((i = PQueueGetMax(&queue)) == -1)
break;
moved[i] = 1;
myrinfo = graph->rinfo+i;
from = where[i];
vwgt = graph->vwgt[i];
if (pwgts[from]-vwgt < minwgt[from])
continue; /* This cannot be moved! */
myedegrees = myrinfo->edegrees;
myndegrees = myrinfo->ndegrees;
/* Determine the valid domains */
for (j=0; j<myndegrees; j++) {
to = myedegrees[j].pid;
phtable[to] = 1;
pmatptr = pmat + to*nparts;
for (nadd=0, k=0; k<myndegrees; k++) {
if (k == j)
continue;
l = myedegrees[k].pid;
if (pmatptr[l] == 0) {
if (ndoms[l] > maxndoms-1) {
phtable[to] = 0;
nadd = maxndoms;
break;
}
nadd++;
}
}
if (ndoms[to]+nadd > maxndoms)
phtable[to] = 0;
}
for (k=0; k<myndegrees; k++) {
to = myedegrees[k].pid;
if (!phtable[to])
continue;
if (pwgts[to]+vwgt <= maxwgt[to] || itpwgts[from]*(pwgts[to]+vwgt) <= itpwgts[to]*pwgts[from])
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 (!phtable[to])
continue;
if (itpwgts[myedegrees[k].pid]*pwgts[to] < itpwgts[to]*pwgts[myedegrees[k].pid])
k = j;
}
to = myedegrees[k].pid;
if (pwgts[from] < maxwgt[from] && pwgts[to] > minwgt[to] && myedegrees[k].ed-myrinfo->id < 0)
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 pmat to reflect the move of 'i' */
pmat[from*nparts+to] += (myrinfo->id-myedegrees[k].ed);
pmat[to*nparts+from] += (myrinfo->id-myedegrees[k].ed);
if (pmat[from*nparts+to] == 0) {
ndoms[from]--;
if (ndoms[from]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[to*nparts+from] == 0) {
ndoms[to]--;
if (ndoms[to]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
/* Update where, weight, and ID/ED information of the vertex you moved */
where[i] = to;
INC_DEC(pwgts[to], pwgts[from], vwgt);
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 pmat to reflect the move of 'i' for domains other than 'from' and 'to' */
if (me != from && me != to) {
pmat[me*nparts+from] -= adjwgt[j];
pmat[from*nparts+me] -= adjwgt[j];
if (pmat[me*nparts+from] == 0) {
ndoms[me]--;
if (ndoms[me]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[from*nparts+me] == 0) {
ndoms[from]--;
if (ndoms[from]+1 == maxndoms)
maxndoms = ndoms[idxamax(nparts, ndoms)];
}
if (pmat[me*nparts+to] == 0) {
ndoms[me]++;
if (ndoms[me] > maxndoms) {
printf("You just increased the maxndoms: %d %d\n", ndoms[me], maxndoms);
maxndoms = ndoms[me];
}
}
if (pmat[to*nparts+me] == 0) {
ndoms[to]++;
if (ndoms[to] > maxndoms) {
printf("You just increased the maxndoms: %d %d\n", ndoms[to], maxndoms);
maxndoms = ndoms[to];
}
}
pmat[me*nparts+to] += adjwgt[j];
pmat[to*nparts+me] += 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;
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("\t[%6d %6d], Balance: %5.3f, Nb: %6d. Nmoves: %5d, Cut: %6d, %d\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nbnd, nmoves, graph->mincut,idxsum(nparts, ndoms)));
}
PQueueFree(ctrl, &queue);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void MocRandomBisection(CtrlType *ctrl, GraphType *graph, float *tpwgts, float ubfactor)
{
int i, ii, j, k, nvtxs, ncon, from, bestcut, mincut, nbfs, qnum;
idxtype *bestwhere, *where, *perm;
int counts[MAXNCON];
float *nvwgt;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
nvwgt = graph->nvwgt;
MocAllocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
nbfs = 2*(nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = idxsum(graph->nedges, graph->adjwgt);
perm = idxmalloc(nvtxs, "BisectGraph: perm");
for (; nbfs>0; nbfs--) {
for (i=0; i<ncon; i++)
counts[i] = 0;
RandomPermute(nvtxs, perm, 1);
/* Partition by spliting the queues randomly */
for (ii=0; ii<nvtxs; ii++) {
i = perm[ii];
qnum = samax(ncon, nvwgt+i*ncon);
where[i] = counts[qnum];
counts[qnum] = (counts[qnum]+1)%2;
}
MocCompute2WayPartitionParams(ctrl, graph);
MocFM_2WayEdgeRefine(ctrl, graph, tpwgts, 6);
MocBalance2Way(ctrl, graph, tpwgts, 1.02);
MocFM_2WayEdgeRefine(ctrl, graph, tpwgts, 6);
MocBalance2Way(ctrl, graph, tpwgts, 1.02);
MocFM_2WayEdgeRefine(ctrl, graph, tpwgts, 6);
/*
printf("Edgecut: %6d, NPwgts: [", graph->mincut);
for (i=0; i<graph->ncon; i++)
printf("(%.3f %.3f) ", graph->npwgts[i], graph->npwgts[graph->ncon+i]);
printf("]\n");
*/
if (bestcut > graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
GKfree((void**)&bestwhere, &perm, LTERM);
}
/*************************************************************************
* This function takes a graph and creates a sequence of coarser graphs
**************************************************************************/
GraphType *Coarsen2Way(CtrlType *ctrl, GraphType *graph)
{
int clevel;
GraphType *cgraph;
IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->CoarsenTmr));
cgraph = graph;
/* The following is ahack to allow the multiple bisections to go through with correct
coarsening */
if (ctrl->CType > 20) {
clevel = 1;
ctrl->CType -= 20;
}
else
clevel = 0;
do {
IFSET(ctrl->dbglvl, DBG_COARSEN, printf("%6d %7d [%d] [%d %d]\n",
cgraph->nvtxs, cgraph->nedges, ctrl->CoarsenTo, ctrl->maxvwgt,
(cgraph->vwgt ? idxsum(cgraph->nvtxs, cgraph->vwgt) : cgraph->nvtxs)));
if (cgraph->adjwgt) {
switch (ctrl->CType) {
case MATCH_RM:
Match_RM(ctrl, cgraph);
break;
case MATCH_HEM:
if (clevel < 1)
Match_RM(ctrl, cgraph);
else
Match_HEM(ctrl, cgraph);
break;
case MATCH_SHEM:
if (clevel < 1)
Match_RM(ctrl, cgraph);
else
Match_SHEM(ctrl, cgraph);
break;
case MATCH_SHEMKWAY:
Match_SHEM(ctrl, cgraph);
break;
default:
errexit("Unknown CType: %d\n", ctrl->CType);
}
}
else {
Match_RM_NVW(ctrl, cgraph);
}
cgraph = cgraph->coarser;
clevel++;
} while (cgraph->nvtxs > ctrl->CoarsenTo && cgraph->nvtxs < COARSEN_FRACTION2*cgraph->finer->nvtxs && cgraph->nedges > cgraph->nvtxs/2);
IFSET(ctrl->dbglvl, DBG_COARSEN, printf("%6d %7d [%d] [%d %d]\n",
cgraph->nvtxs, cgraph->nedges, ctrl->CoarsenTo, ctrl->maxvwgt,
(cgraph->vwgt ? idxsum(cgraph->nvtxs, cgraph->vwgt) : cgraph->nvtxs)));
IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->CoarsenTmr));
return cgraph;
}
/*************************************************************************
* 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);
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void GrowBisection(CtrlType *ctrl, GraphType *graph, int *tpwgts, float ubfactor)
{
int i, j, k, nvtxs, drain, nleft, first, last, pwgts[2], minpwgt[2], maxpwgt[2], from, bestcut, icut, mincut, me, pass, nbfs;
idxtype *xadj, *vwgt, *adjncy, *adjwgt, *where;
idxtype *queue, *touched, *gain, *bestwhere;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
Allocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
queue = idxmalloc(nvtxs, "BisectGraph: queue");
touched = idxmalloc(nvtxs, "BisectGraph: touched");
ASSERTP(tpwgts[0]+tpwgts[1] == idxsum(nvtxs, vwgt), ("%d %d\n", tpwgts[0]+tpwgts[1], idxsum(nvtxs, vwgt)));
maxpwgt[0] = ubfactor*tpwgts[0];
maxpwgt[1] = ubfactor*tpwgts[1];
minpwgt[0] = (1.0/ubfactor)*tpwgts[0];
minpwgt[1] = (1.0/ubfactor)*tpwgts[1];
nbfs = (nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = idxsum(nvtxs, graph->adjwgtsum)+1; /* The +1 is for the 0 edges case */
for (; nbfs>0; nbfs--) {
idxset(nvtxs, 0, touched);
pwgts[1] = tpwgts[0]+tpwgts[1];
pwgts[0] = 0;
idxset(nvtxs, 1, where);
queue[0] = RandomInRange(nvtxs);
touched[queue[0]] = 1;
first = 0; last = 1;
nleft = nvtxs-1;
drain = 0;
/* Start the BFS from queue to get a partition */
for (;;) {
if (first == last) { /* Empty. Disconnected graph! */
if (nleft == 0 || drain)
break;
k = RandomInRange(nleft);
for (i=0; i<nvtxs; i++) {
if (touched[i] == 0) {
if (k == 0)
break;
else
k--;
}
}
queue[0] = i;
touched[i] = 1;
first = 0; last = 1;;
nleft--;
}
i = queue[first++];
if (pwgts[0] > 0 && pwgts[1]-vwgt[i] < minpwgt[1]) {
drain = 1;
continue;
}
where[i] = 0;
INC_DEC(pwgts[0], pwgts[1], vwgt[i]);
if (pwgts[1] <= maxpwgt[1])
break;
drain = 0;
for (j=xadj[i]; j<xadj[i+1]; j++) {
k = adjncy[j];
if (touched[k] == 0) {
queue[last++] = k;
touched[k] = 1;
nleft--;
}
}
}
/* Check to see if we hit any bad limiting cases */
if (pwgts[1] == 0) {
i = RandomInRange(nvtxs);
where[i] = 1;
INC_DEC(pwgts[1], pwgts[0], vwgt[i]);
}
/*************************************************************
* Do some partition refinement
**************************************************************/
Compute2WayPartitionParams(ctrl, graph);
/*printf("IPART: %3d [%5d %5d] [%5d %5d] %5d\n", graph->nvtxs, pwgts[0], pwgts[1], graph->pwgts[0], graph->pwgts[1], graph->mincut); */
Balance2Way(ctrl, graph, tpwgts, ubfactor);
/*printf("BPART: [%5d %5d] %5d\n", graph->pwgts[0], graph->pwgts[1], graph->mincut);*/
FM_2WayEdgeRefine(ctrl, graph, tpwgts, 4);
/*printf("RPART: [%5d %5d] %5d\n", graph->pwgts[0], graph->pwgts[1], graph->mincut);*/
if (bestcut > graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
GKfree(&bestwhere, &queue, &touched, LTERM);
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void RandomBisection(CtrlType *ctrl, GraphType *graph, int *tpwgts, float ubfactor)
{
int i, ii, j, k, nvtxs, pwgts[2], minpwgt[2], maxpwgt[2], from, bestcut, icut, mincut, me, pass, nbfs;
idxtype *xadj, *vwgt, *adjncy, *adjwgt, *where;
idxtype *perm, *bestwhere;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
Allocate2WayPartitionMemory(ctrl, graph);
where = graph->where;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
perm = idxmalloc(nvtxs, "BisectGraph: queue");
ASSERTP(tpwgts[0]+tpwgts[1] == idxsum(nvtxs, vwgt), ("%d %d\n", tpwgts[0]+tpwgts[1], idxsum(nvtxs, vwgt)));
maxpwgt[0] = ubfactor*tpwgts[0];
maxpwgt[1] = ubfactor*tpwgts[1];
minpwgt[0] = (1.0/ubfactor)*tpwgts[0];
minpwgt[1] = (1.0/ubfactor)*tpwgts[1];
nbfs = (nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = idxsum(nvtxs, graph->adjwgtsum)+1; /* The +1 is for the 0 edges case */
for (; nbfs>0; nbfs--) {
RandomPermute(nvtxs, perm, 1);
idxset(nvtxs, 1, where);
pwgts[1] = tpwgts[0]+tpwgts[1];
pwgts[0] = 0;
if (nbfs != 1) {
for (ii=0; ii<nvtxs; ii++) {
i = perm[ii];
if (pwgts[0]+vwgt[i] < maxpwgt[0]) {
where[i] = 0;
pwgts[0] += vwgt[i];
pwgts[1] -= vwgt[i];
if (pwgts[0] > minpwgt[0])
break;
}
}
}
/*************************************************************
* Do some partition refinement
**************************************************************/
Compute2WayPartitionParams(ctrl, graph);
/* printf("IPART: %3d [%5d %5d] [%5d %5d] %5d\n", graph->nvtxs, pwgts[0], pwgts[1], graph->pwgts[0], graph->pwgts[1], graph->mincut); */
Balance2Way(ctrl, graph, tpwgts, ubfactor);
/* printf("BPART: [%5d %5d] %5d\n", graph->pwgts[0], graph->pwgts[1], graph->mincut); */
FM_2WayEdgeRefine(ctrl, graph, tpwgts, 4);
/* printf("RPART: [%5d %5d] %5d\n", graph->pwgts[0], graph->pwgts[1], graph->mincut); */
if (bestcut > graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
if (bestcut == 0)
break;
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
GKfree(&bestwhere, &perm, LTERM);
}
/*************************************************************************
* This function takes a graph and produces a bisection by using a region
* growing algorithm. The resulting partition is returned in
* graph->where
**************************************************************************/
void GrowBisectionNode(CtrlType *ctrl, GraphType *graph, float ubfactor)
{
int i, j, k, nvtxs, drain, nleft, first, last, pwgts[2], tpwgts[2], minpwgt[2], maxpwgt[2], from, bestcut, icut, mincut, me, pass, nbfs;
idxtype *xadj, *vwgt, *adjncy, *adjwgt, *where, *bndind;
idxtype *queue, *touched, *gain, *bestwhere;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bestwhere = idxmalloc(nvtxs, "BisectGraph: bestwhere");
queue = idxmalloc(nvtxs, "BisectGraph: queue");
touched = idxmalloc(nvtxs, "BisectGraph: touched");
tpwgts[0] = idxsum(nvtxs, vwgt);
tpwgts[1] = tpwgts[0]/2;
tpwgts[0] -= tpwgts[1];
maxpwgt[0] = ubfactor*tpwgts[0];
maxpwgt[1] = ubfactor*tpwgts[1];
minpwgt[0] = (1.0/ubfactor)*tpwgts[0];
minpwgt[1] = (1.0/ubfactor)*tpwgts[1];
/* Allocate memory for graph->rdata. Allocate sufficient memory for both edge and node */
graph->rdata = idxmalloc(5*nvtxs+3, "GrowBisectionNode: graph->rdata");
graph->pwgts = graph->rdata;
graph->where = graph->rdata + 3;
graph->bndptr = graph->rdata + nvtxs + 3;
graph->bndind = graph->rdata + 2*nvtxs + 3;
graph->nrinfo = (NRInfoType *)(graph->rdata + 3*nvtxs + 3);
graph->id = graph->rdata + 3*nvtxs + 3;
graph->ed = graph->rdata + 4*nvtxs + 3;
where = graph->where;
bndind = graph->bndind;
nbfs = (nvtxs <= ctrl->CoarsenTo ? SMALLNIPARTS : LARGENIPARTS);
bestcut = tpwgts[0]+tpwgts[1];
for (nbfs++; nbfs>0; nbfs--) {
idxset(nvtxs, 0, touched);
pwgts[1] = tpwgts[0]+tpwgts[1];
pwgts[0] = 0;
idxset(nvtxs, 1, where);
queue[0] = RandomInRange(nvtxs);
touched[queue[0]] = 1;
first = 0; last = 1;
nleft = nvtxs-1;
drain = 0;
/* Start the BFS from queue to get a partition */
if (nbfs >= 1) {
for (;;) {
if (first == last) { /* Empty. Disconnected graph! */
if (nleft == 0 || drain)
break;
k = RandomInRange(nleft);
for (i=0; i<nvtxs; i++) {
if (touched[i] == 0) {
if (k == 0)
break;
else
k--;
}
}
queue[0] = i;
touched[i] = 1;
first = 0; last = 1;;
nleft--;
}
i = queue[first++];
if (pwgts[1]-vwgt[i] < minpwgt[1]) {
drain = 1;
continue;
}
where[i] = 0;
INC_DEC(pwgts[0], pwgts[1], vwgt[i]);
if (pwgts[1] <= maxpwgt[1])
break;
drain = 0;
for (j=xadj[i]; j<xadj[i+1]; j++) {
k = adjncy[j];
if (touched[k] == 0) {
queue[last++] = k;
touched[k] = 1;
nleft--;
}
}
}
}
/*************************************************************
* Do some partition refinement
**************************************************************/
Compute2WayPartitionParams(ctrl, graph);
Balance2Way(ctrl, graph, tpwgts, ubfactor);
FM_2WayEdgeRefine(ctrl, graph, tpwgts, 4);
/* Construct and refine the vertex separator */
for (i=0; i<graph->nbnd; i++)
where[bndind[i]] = 2;
Compute2WayNodePartitionParams(ctrl, graph);
FM_2WayNodeRefine(ctrl, graph, ubfactor, 6);
/* printf("ISep: [%d %d %d] %d\n", graph->pwgts[0], graph->pwgts[1], graph->pwgts[2], bestcut); */
if (bestcut > graph->mincut) {
bestcut = graph->mincut;
idxcopy(nvtxs, where, bestwhere);
}
}
graph->mincut = bestcut;
idxcopy(nvtxs, bestwhere, where);
Compute2WayNodePartitionParams(ctrl, graph);
GKfree(&bestwhere, &queue, &touched, LTERM);
}
/*************************************************************************
* This function computes the subdomain graph
**************************************************************************/
void EliminateSubDomainEdges(CtrlType *ctrl, GraphType *graph, int nparts, float *tpwgts)
{
int i, ii, j, k, me, other, nvtxs, total, max, avg, totalout, nind, ncand, ncand2, target, target2, nadd;
int min, move, cpwgt, tvwgt;
idxtype *xadj, *adjncy, *vwgt, *adjwgt, *pwgts, *where, *maxpwgt, *pmat, *ndoms, *mypmat, *otherpmat, *ind;
KeyValueType *cand, *cand2;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
vwgt = graph->vwgt;
adjwgt = graph->adjwgt;
where = graph->where;
pwgts = graph->pwgts; /* We assume that this is properly initialized */
maxpwgt = idxwspacemalloc(ctrl, nparts);
ndoms = idxwspacemalloc(ctrl, nparts);
otherpmat = idxwspacemalloc(ctrl, nparts);
ind = idxwspacemalloc(ctrl, nvtxs);
pmat = ctrl->wspace.pmat;
cand = (KeyValueType *)GKmalloc(nparts*sizeof(KeyValueType), "EliminateSubDomainEdges: cand");
cand2 = (KeyValueType *)GKmalloc(nparts*sizeof(KeyValueType), "EliminateSubDomainEdges: cand");
/* Compute the pmat matrix and ndoms */
ComputeSubDomainGraph(graph, nparts, pmat, ndoms);
/* Compute the maximum allowed weight for each domain */
tvwgt = idxsum(nparts, pwgts);
for (i=0; i<nparts; i++)
maxpwgt[i] = 1.25*tpwgts[i]*tvwgt;
/* Get into the loop eliminating subdomain connections */
for (;;) {
total = idxsum(nparts, ndoms);
avg = total/nparts;
max = ndoms[idxamax(nparts, ndoms)];
/* printf("Adjacent Subdomain Stats: Total: %3d, Max: %3d, Avg: %3d [%5d]\n", total, max, avg, idxsum(nparts*nparts, pmat)); */
if (max < 1.4*avg)
break;
me = idxamax(nparts, ndoms);
mypmat = pmat + me*nparts;
totalout = idxsum(nparts, mypmat);
/*printf("Me: %d, TotalOut: %d,\n", me, totalout);*/
/* Sort the connections according to their cut */
for (ncand2=0, i=0; i<nparts; i++) {
if (mypmat[i] > 0) {
cand2[ncand2].key = mypmat[i];
cand2[ncand2++].val = i;
}
}
ikeysort(ncand2, cand2);
move = 0;
for (min=0; min<ncand2; min++) {
if (cand2[min].key > totalout/(2*ndoms[me]))
break;
other = cand2[min].val;
/*printf("\tMinOut: %d to %d\n", mypmat[other], other);*/
idxset(nparts, 0, otherpmat);
/* Go and find the vertices in 'other' that are connected in 'me' */
for (nind=0, i=0; i<nvtxs; i++) {
if (where[i] == other) {
for (j=xadj[i]; j<xadj[i+1]; j++) {
if (where[adjncy[j]] == me) {
ind[nind++] = i;
break;
}
}
}
}
/* Go and construct the otherpmat to see where these nind vertices are connected to */
for (cpwgt=0, ii=0; ii<nind; ii++) {
i = ind[ii];
cpwgt += vwgt[i];
for (j=xadj[i]; j<xadj[i+1]; j++)
otherpmat[where[adjncy[j]]] += adjwgt[j];
}
otherpmat[other] = 0;
for (ncand=0, i=0; i<nparts; i++) {
if (otherpmat[i] > 0) {
cand[ncand].key = -otherpmat[i];
cand[ncand++].val = i;
}
}
ikeysort(ncand, cand);
/*
* Go through and the select the first domain that is common with 'me', and
* does not increase the ndoms[target] higher than my ndoms, subject to the
* maxpwgt constraint. Traversal is done from the mostly connected to the least.
*/
target = target2 = -1;
for (i=0; i<ncand; i++) {
k = cand[i].val;
if (mypmat[k] > 0) {
if (pwgts[k] + cpwgt > maxpwgt[k]) /* Check if balance will go off */
continue;
for (j=0; j<nparts; j++) {
if (otherpmat[j] > 0 && ndoms[j] >= ndoms[me]-1 && pmat[nparts*j+k] == 0)
break;
}
if (j == nparts) { /* No bad second level effects */
for (nadd=0, j=0; j<nparts; j++) {
if (otherpmat[j] > 0 && pmat[nparts*k+j] == 0)
nadd++;
}
/*printf("\t\tto=%d, nadd=%d, %d\n", k, nadd, ndoms[k]);*/
if (target2 == -1 && ndoms[k]+nadd < ndoms[me]) {
target2 = k;
}
if (nadd == 0) {
target = k;
break;
}
}
}
}
if (target == -1 && target2 != -1)
target = target2;
if (target == -1) {
/* printf("\t\tCould not make the move\n");*/
continue;
}
/*printf("\t\tMoving to %d\n", target);*/
/* Update the partition weights */
INC_DEC(pwgts[target], pwgts[other], cpwgt);
MoveGroupMConn(ctrl, graph, ndoms, pmat, nparts, target, nind, ind);
move = 1;
break;
}
if (move == 0)
break;
}
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nvtxs);
GKfree(&cand, &cand2, LTERM);
}
/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void Greedy_KWayEdgeRefine(CtrlType *ctrl, GraphType *graph, int nparts, float *tpwgts, float ubfactor, int npasses)
{
int i, ii, iii, j, jj, k, l, pass, nvtxs, nbnd, tvwgt, myndegrees, oldgain, gain;
int from, me, to, oldcut, vwgt;
idxtype *xadj, *adjncy, *adjwgt;
idxtype *where, *pwgts, *perm, *bndptr, *bndind, *minwgt, *maxwgt, *moved, *itpwgts;
EDegreeType *myedegrees;
RInfoType *myrinfo;
PQueueType queue;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bndind = graph->bndind;
bndptr = graph->bndptr;
where = graph->where;
pwgts = graph->pwgts;
/* Setup the weight intervals of the various subdomains */
minwgt = idxwspacemalloc(ctrl, nparts);
maxwgt = idxwspacemalloc(ctrl, nparts);
itpwgts = idxwspacemalloc(ctrl, nparts);
tvwgt = idxsum(nparts, pwgts);
ASSERT(tvwgt == idxsum(nvtxs, graph->vwgt));
for (i=0; i<nparts; i++) {
itpwgts[i] = tpwgts[i]*tvwgt;
maxwgt[i] = tpwgts[i]*tvwgt*ubfactor;
minwgt[i] = tpwgts[i]*tvwgt*(1.0/ubfactor);
}
perm = idxwspacemalloc(ctrl, nvtxs);
moved = idxwspacemalloc(ctrl, nvtxs);
PQueueInit(ctrl, &queue, nvtxs, graph->adjwgtsum[idxamax(nvtxs, graph->adjwgtsum)]);
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("Partitions: [%6d %6d]-[%6d %6d], Balance: %5.3f, Nv-Nb[%6d %6d]. Cut: %6d\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)], minwgt[0], maxwgt[0],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nvtxs, graph->nbnd,
graph->mincut));
for (pass=0; pass<npasses; pass++) {
ASSERT(ComputeCut(graph, where) == graph->mincut);
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;
}
for (iii=0;; iii++) {
if ((i = PQueueGetMax(&queue)) == -1)
break;
moved[i] = 1;
myrinfo = graph->rinfo+i;
from = where[i];
vwgt = graph->vwgt[i];
if (pwgts[from]-vwgt < minwgt[from])
continue; /* This cannot be moved! */
myedegrees = myrinfo->edegrees;
myndegrees = myrinfo->ndegrees;
j = myrinfo->id;
for (k=0; k<myndegrees; k++) {
to = myedegrees[k].pid;
gain = myedegrees[k].ed-j; /* j = myrinfo->id. Allow good nodes to move */
if (pwgts[to]+vwgt <= maxwgt[to]+gain && gain >= 0)
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 && pwgts[to]+vwgt <= maxwgt[to]) ||
(myedegrees[j].ed == myedegrees[k].ed &&
itpwgts[myedegrees[k].pid]*pwgts[to] < itpwgts[to]*pwgts[myedegrees[k].pid]))
k = j;
}
to = myedegrees[k].pid;
j = 0;
if (myedegrees[k].ed-myrinfo->id > 0)
j = 1;
else if (myedegrees[k].ed-myrinfo->id == 0) {
if ((iii&7) == 0 || pwgts[from] >= maxwgt[from] || itpwgts[from]*(pwgts[to]+vwgt) < itpwgts[to]*pwgts[from])
j = 1;
}
if (j == 0)
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 */
where[i] = to;
INC_DEC(pwgts[to], pwgts[from], vwgt);
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)
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-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];
}
}
/* Update the queue */
if (me == to || me == from) {
gain = myrinfo->ed-myrinfo->id;
if (moved[ii] == 2) {
if (gain >= 0)
PQueueUpdate(&queue, ii, oldgain, gain);
else {
PQueueDelete(&queue, ii, oldgain);
moved[ii] = -1;
}
}
else if (moved[ii] == -1 && gain >= 0) {
PQueueInsert(&queue, ii, gain);
moved[ii] = 2;
}
}
ASSERT(myrinfo->ndegrees <= xadj[ii+1]-xadj[ii]);
ASSERT(CheckRInfo(myrinfo));
}
}
graph->nbnd = nbnd;
IFSET(ctrl->dbglvl, DBG_REFINE,
printf("\t[%6d %6d], Balance: %5.3f, Nb: %6d. Cut: %6d\n",
pwgts[idxamin(nparts, pwgts)], pwgts[idxamax(nparts, pwgts)],
1.0*nparts*pwgts[idxamax(nparts, pwgts)]/tvwgt, graph->nbnd, graph->mincut));
if (graph->mincut == oldcut)
break;
}
PQueueFree(ctrl, &queue);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nparts);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
}
