/*
* Copyright 1997, Regents of the University of Minnesota
*
* subdomains.c
*
* This file contains functions that deal with prunning the number of
* adjacent subdomains in KMETIS
*
* Started 7/15/98
* George
*
* $Id: subdomains.c,v 1.1 1998/11/27 17:59:32 karypis Exp $
*
*/
#include <metis.h>
/*************************************************************************
* This function performs k-way refinement
**************************************************************************/
void Random_KWayEdgeRefineMConn(CtrlType *ctrl, GraphType *graph, long nparts, float *tpwgts, float ubfactor, long npasses, long ffactor)
{
long i, ii, iii, j, jj, k, l, pass, nvtxs, nmoves, nbnd, tvwgt, myndegrees;
long from, me, to, oldcut, vwgt, gain;
long 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: [%6ld %6ld]-[%6ld %6ld], Balance: %5.3f, Nv-Nb[%6ld %6ld]. Cut: %6ld\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 %6ld to %3ld. Gain: %4ld. Cut: %6ld\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: %ld %ld\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: %ld %ld\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[%6ld %6ld], Balance: %5.3f, Nb: %6ld. Nmoves: %5ld, Cut: %5ld, Vol: %5ld, %ld\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 performs k-way refinement
**************************************************************************/
void Greedy_KWayEdgeBalanceMConn(CtrlType *ctrl, GraphType *graph, long nparts, float *tpwgts, float ubfactor, long npasses)
{
long i, ii, iii, j, jj, k, l, pass, nvtxs, nbnd, tvwgt, myndegrees, oldgain, gain, nmoves;
long 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: [%6ld %6ld]-[%6ld %6ld], Balance: %5.3f, Nv-Nb[%6ld %6ld]. Cut: %6ld [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 %6ld to %3ld. Gain: %4ld. Cut: %6ld\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: %ld %ld\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: %ld %ld\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[%6ld %6ld], Balance: %5.3f, Nb: %6ld. Nmoves: %5ld, Cut: %6ld, %ld\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 computes the subdomain graph
**************************************************************************/
void PrintSubDomainGraph(GraphType *graph, long nparts, idxtype *where)
{
long i, j, k, me, nvtxs, total, max;
idxtype *xadj, *adjncy, *adjwgt, *pmat;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
pmat = idxsmalloc(nparts*nparts, 0, "ComputeSubDomainGraph: pmat");
for (i=0; i<nvtxs; i++) {
me = where[i];
for (j=xadj[i]; j<xadj[i+1]; j++) {
k = adjncy[j];
if (where[k] != me)
pmat[me*nparts+where[k]] += adjwgt[j];
}
}
/* printf("Subdomain Info\n"); */
total = max = 0;
for (i=0; i<nparts; i++) {
for (k=0, j=0; j<nparts; j++) {
if (pmat[i*nparts+j] > 0)
k++;
}
total += k;
if (k > max)
max = k;
/*
printf("%2ld -> %2ld ", i, k);
for (j=0; j<nparts; j++) {
if (pmat[i*nparts+j] > 0)
printf("[%2ld %4ld] ", j, pmat[i*nparts+j]);
}
printf("\n");
*/
}
printf("Total adjacent subdomains: %ld, Max: %ld\n", total, max);
free(pmat);
}
/*************************************************************************
* This function computes the subdomain graph
**************************************************************************/
void ComputeSubDomainGraph(GraphType *graph, long nparts, idxtype *pmat, idxtype *ndoms)
{
long i, j, k, me, nvtxs, ndegrees;
idxtype *xadj, *adjncy, *adjwgt, *where;
RInfoType *rinfo;
EDegreeType *edegrees;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
rinfo = graph->rinfo;
idxset(nparts*nparts, 0, pmat);
for (i=0; i<nvtxs; i++) {
if (rinfo[i].ed > 0) {
me = where[i];
ndegrees = rinfo[i].ndegrees;
edegrees = rinfo[i].edegrees;
k = me*nparts;
for (j=0; j<ndegrees; j++)
pmat[k+edegrees[j].pid] += edegrees[j].ed;
}
}
for (i=0; i<nparts; i++) {
ndoms[i] = 0;
for (j=0; j<nparts; j++) {
if (pmat[i*nparts+j] > 0)
ndoms[i]++;
}
}
}
/*************************************************************************
* This function computes the subdomain graph
**************************************************************************/
void EliminateSubDomainEdges(CtrlType *ctrl, GraphType *graph, long nparts, float *tpwgts)
{
long i, ii, j, k, me, other, nvtxs, total, max, avg, totalout, nind, ncand, ncand2, target, target2, nadd;
long 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: %3ld, Max: %3ld, Avg: %3ld [%5ld]\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: %ld, TotalOut: %ld,\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: %ld to %ld\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=%ld, nadd=%ld, %ld\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 %ld\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 moves a collection of vertices and updates their rinfo
**************************************************************************/
void MoveGroupMConn(CtrlType *ctrl, GraphType *graph, idxtype *ndoms, idxtype *pmat,
long nparts, long to, long nind, idxtype *ind)
{
long i, ii, iii, j, jj, k, l, nvtxs, nbnd, myndegrees;
long from, me;
idxtype *xadj, *adjncy, *adjwgt;
idxtype *where, *bndptr, *bndind;
EDegreeType *myedegrees;
RInfoType *myrinfo;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
bndptr = graph->bndptr;
bndind = graph->bndind;
nbnd = graph->nbnd;
for (iii=0; iii<nind; iii++) {
i = ind[iii];
from = where[i];
myrinfo = graph->rinfo+i;
if (myrinfo->edegrees == NULL) {
myrinfo->edegrees = ctrl->wspace.edegrees+ctrl->wspace.cdegree;
ctrl->wspace.cdegree += xadj[i+1]-xadj[i];
myrinfo->ndegrees = 0;
}
myedegrees = myrinfo->edegrees;
/* find the location of 'to' in myrinfo or create it if it is not there */
for (k=0; k<myrinfo->ndegrees; k++) {
if (myedegrees[k].pid == to)
break;
}
if (k == myrinfo->ndegrees) {
myedegrees[k].pid = to;
myedegrees[k].ed = 0;
myrinfo->ndegrees++;
}
graph->mincut -= myedegrees[k].ed-myrinfo->id;
/* 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 (pmat[to*nparts+from] == 0)
ndoms[to]--;
/* Update where, weight, and ID/ED information of the vertex you moved */
where[i] = to;
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 && bndptr[i] != -1)
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 (pmat[from*nparts+me] == 0)
ndoms[from]--;
if (pmat[me*nparts+to] == 0)
ndoms[me]++;
if (pmat[to*nparts+me] == 0)
ndoms[to]++;
pmat[me*nparts+to] += adjwgt[j];
pmat[to*nparts+me] += adjwgt[j];
}
ASSERT(CheckRInfo(myrinfo));
}
ASSERT(CheckRInfo(graph->rinfo+i));
}
graph->nbnd = nbnd;
}
/*************************************************************************
* 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, long nparts, float *tpwgts, float ubfactor)
{
long 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 %ld components, for this %ld-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 %ld from %ld\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 %ld [%ld]\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 moves a collection of vertices and updates their rinfo
**************************************************************************/
void MoveGroup(CtrlType *ctrl, GraphType *graph, long nparts, long to, long gid, idxtype *ptr, idxtype *ind)
{
long i, ii, iii, j, jj, k, l, nvtxs, nbnd, myndegrees;
long from, me;
idxtype *xadj, *adjncy, *adjwgt;
idxtype *where, *bndptr, *bndind;
EDegreeType *myedegrees;
RInfoType *myrinfo;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
bndptr = graph->bndptr;
bndind = graph->bndind;
nbnd = graph->nbnd;
for (iii=ptr[gid]; iii<ptr[gid+1]; iii++) {
i = ind[iii];
from = where[i];
myrinfo = graph->rinfo+i;
if (myrinfo->edegrees == NULL) {
myrinfo->edegrees = ctrl->wspace.edegrees+ctrl->wspace.cdegree;
ctrl->wspace.cdegree += xadj[i+1]-xadj[i];
myrinfo->ndegrees = 0;
}
myedegrees = myrinfo->edegrees;
/* find the location of 'to' in myrinfo or create it if it is not there */
for (k=0; k<myrinfo->ndegrees; k++) {
if (myedegrees[k].pid == to)
break;
}
if (k == myrinfo->ndegrees) {
myedegrees[k].pid = to;
myedegrees[k].ed = 0;
myrinfo->ndegrees++;
}
graph->mincut -= myedegrees[k].ed-myrinfo->id;
/* Update where, weight, and ID/ED information of the vertex you moved */
where[i] = to;
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 && bndptr[i] != -1)
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];
}
}
ASSERT(CheckRInfo(myrinfo));
}
ASSERT(CheckRInfo(graph->rinfo+i));
}
graph->nbnd = nbnd;
}
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