/*
* Copyright 1997, Regents of the University of Minnesota
*
* mfm2.c
*
* This file contains code that implements the edge-based FM refinement
*
* Started 7/23/97
* George
*
* $Id: mfm2.c,v 1.2 1998/11/30 14:50:44 karypis Exp $
*/
#include <metis.h>
/*************************************************************************
* This function performs an edge-based FM refinement
**************************************************************************/
void MocFM_2WayEdgeRefine2(CtrlType *ctrl, GraphType *graph, float *tpwgts, float *orgubvec,
long npasses)
{
long i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass, me, limit, tmp, cnum;
idxtype *xadj, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind;
idxtype *moved, *swaps, *perm, *qnum;
float *nvwgt, *npwgts, origdiff[MAXNCON], origbal[MAXNCON], minbal[MAXNCON];
PQueueType parts[MAXNCON][2];
long higain, oldgain, mincut, initcut, newcut, mincutorder;
float *maxwgt, *minwgt, ubvec[MAXNCON], tvec[MAXNCON];
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
nvwgt = graph->nvwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
id = graph->id;
ed = graph->ed;
npwgts = graph->npwgts;
bndptr = graph->bndptr;
bndind = graph->bndind;
moved = idxwspacemalloc(ctrl, nvtxs);
swaps = idxwspacemalloc(ctrl, nvtxs);
perm = idxwspacemalloc(ctrl, nvtxs);
qnum = idxwspacemalloc(ctrl, nvtxs);
limit = amin(amax(0.01*nvtxs, 15), 100);
Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, origbal);
for (i=0; i<ncon; i++) {
origdiff[i] = fabs(tpwgts[0]-npwgts[i]);
ubvec[i] = amax(origbal[i], orgubvec[i]);
}
/* Setup the weight intervals of the two subdomains */
minwgt = fwspacemalloc(ctrl, 2*ncon);
maxwgt = fwspacemalloc(ctrl, 2*ncon);
for (i=0; i<2; i++) {
for (j=0; j<ncon; j++) {
maxwgt[i*ncon+j] = tpwgts[i]*ubvec[j];
minwgt[i*ncon+j] = tpwgts[i]*(1.0/ubvec[j]);
}
}
/* Initialize the queues */
for (i=0; i<ncon; i++) {
PQueueInit(ctrl, &parts[i][0], nvtxs, PLUS_GAINSPAN+1);
PQueueInit(ctrl, &parts[i][1], nvtxs, PLUS_GAINSPAN+1);
}
for (i=0; i<nvtxs; i++)
qnum[i] = samax(ncon, nvwgt+i*ncon);
if (ctrl->dbglvl&DBG_REFINE) {
printf("Parts: [");
for (l=0; l<ncon; l++)
printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
printf("] T[%.3f %.3f], Nv-Nb[%5ld, %5ld]. ICut: %6ld, LB: ", tpwgts[0], tpwgts[1],
graph->nvtxs, graph->nbnd, graph->mincut);
for (i=0; i<ncon; i++)
printf("%.3f ", origbal[i]);
printf("\n");
}
idxset(nvtxs, -1, moved);
for (pass=0; pass<npasses; pass++) { /* Do a number of passes */
for (i=0; i<ncon; i++) {
PQueueReset(&parts[i][0]);
PQueueReset(&parts[i][1]);
}
mincutorder = -1;
newcut = mincut = initcut = graph->mincut;
Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, minbal);
ASSERT(ComputeCut(graph, where) == graph->mincut);
ASSERT(CheckBnd(graph));
/* Insert boundary nodes in the priority queues */
nbnd = graph->nbnd;
RandomPermute(nbnd, perm, 1);
for (ii=0; ii<nbnd; ii++) {
i = bndind[perm[ii]];
ASSERT(ed[i] > 0 || id[i] == 0);
ASSERT(bndptr[i] != -1);
PQueueInsert(&parts[qnum[i]][where[i]], i, ed[i]-id[i]);
}
for (nswaps=0; nswaps<nvtxs; nswaps++) {
SelectQueue2(ncon, npwgts, tpwgts, &from, &cnum, parts, maxwgt);
to = (from+1)%2;
if (from == -1 || (higain = PQueueGetMax(&parts[cnum][from])) == -1)
break;
ASSERT(bndptr[higain] != -1);
newcut -= (ed[higain]-id[higain]);
saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1);
Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, tvec);
if ((newcut < mincut && AreAllBelow(ncon, tvec, ubvec)) ||
(newcut == mincut && IsBetter2wayBalance(ncon, tvec, minbal, ubvec))) {
mincut = newcut;
for (i=0; i<ncon; i++)
minbal[i] = tvec[i];
mincutorder = nswaps;
}
else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */
newcut += (ed[higain]-id[higain]);
saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+from*ncon, 1);
saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
break;
}
where[higain] = to;
moved[higain] = nswaps;
swaps[nswaps] = higain;
if (ctrl->dbglvl&DBG_MOVEINFO) {
printf("Moved %6ld from %ld(%ld). Gain: %5ld, Cut: %5ld, NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut);
for (l=0; l<ncon; l++)
printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
printf(", LB: ");
for (i=0; i<ncon; i++)
printf("%.3f ", tvec[i]);
if (mincutorder == nswaps)
printf(" *\n");
else
printf("\n");
}
/**************************************************************
* Update the id[i]/ed[i] values of the affected nodes
***************************************************************/
SWAP(id[higain], ed[higain], tmp);
if (ed[higain] == 0 && xadj[higain] < xadj[higain+1])
BNDDelete(nbnd, bndind, bndptr, higain);
for (j=xadj[higain]; j<xadj[higain+1]; j++) {
k = adjncy[j];
oldgain = ed[k]-id[k];
kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
INC_DEC(id[k], ed[k], kwgt);
/* Update its boundary information and queue position */
if (bndptr[k] != -1) { /* If k was a boundary vertex */
if (ed[k] == 0) { /* Not a boundary vertex any more */
BNDDelete(nbnd, bndind, bndptr, k);
if (moved[k] == -1) /* Remove it if in the queues */
PQueueDelete(&parts[qnum[k]][where[k]], k, oldgain);
}
else { /* If it has not been moved, update its position in the queue */
if (moved[k] == -1)
PQueueUpdate(&parts[qnum[k]][where[k]], k, oldgain, ed[k]-id[k]);
}
}
else {
if (ed[k] > 0) { /* It will now become a boundary vertex */
BNDInsert(nbnd, bndind, bndptr, k);
if (moved[k] == -1)
PQueueInsert(&parts[qnum[k]][where[k]], k, ed[k]-id[k]);
}
}
}
}
/****************************************************************
* Roll back computations
*****************************************************************/
for (i=0; i<nswaps; i++)
moved[swaps[i]] = -1; /* reset moved array */
for (nswaps--; nswaps>mincutorder; nswaps--) {
higain = swaps[nswaps];
to = where[higain] = (where[higain]+1)%2;
SWAP(id[higain], ed[higain], tmp);
if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])
BNDDelete(nbnd, bndind, bndptr, higain);
else if (ed[higain] > 0 && bndptr[higain] == -1)
BNDInsert(nbnd, bndind, bndptr, higain);
saxpy(ncon, 1.0, nvwgt+higain*ncon, 1, npwgts+to*ncon, 1);
saxpy(ncon, -1.0, nvwgt+higain*ncon, 1, npwgts+((to+1)%2)*ncon, 1);
for (j=xadj[higain]; j<xadj[higain+1]; j++) {
k = adjncy[j];
kwgt = (to == where[k] ? adjwgt[j] : -adjwgt[j]);
INC_DEC(id[k], ed[k], kwgt);
if (bndptr[k] != -1 && ed[k] == 0)
BNDDelete(nbnd, bndind, bndptr, k);
if (bndptr[k] == -1 && ed[k] > 0)
BNDInsert(nbnd, bndind, bndptr, k);
}
}
if (ctrl->dbglvl&DBG_REFINE) {
printf("\tMincut: %6ld at %5ld, NBND: %6ld, NPwgts: [", mincut, mincutorder, nbnd);
for (l=0; l<ncon; l++)
printf("(%.3f, %.3f) ", npwgts[l], npwgts[ncon+l]);
printf("], LB: ");
Compute2WayHLoadImbalanceVec(ncon, npwgts, tpwgts, tvec);
for (i=0; i<ncon; i++)
printf("%.3f ", tvec[i]);
printf("\n");
}
graph->mincut = mincut;
graph->nbnd = nbnd;
if (mincutorder == -1 || mincut == initcut)
break;
}
for (i=0; i<ncon; i++) {
PQueueFree(ctrl, &parts[i][0]);
PQueueFree(ctrl, &parts[i][1]);
}
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
idxwspacefree(ctrl, nvtxs);
fwspacefree(ctrl, 2*ncon);
fwspacefree(ctrl, 2*ncon);
}
/*************************************************************************
* This function selects the partition number and the queue from which
* we will move vertices out
**************************************************************************/
void SelectQueue2(long ncon, float *npwgts, float *tpwgts, long *from, long *cnum,
PQueueType queues[MAXNCON][2], float *maxwgt)
{
long i, j, maxgain=0;
float diff, max, maxdiff=0.0;
*from = -1;
*cnum = -1;
/* First determine the side and the queue, irrespective of the presence of nodes */
for (j=0; j<2; j++) {
for (i=0; i<ncon; i++) {
diff = npwgts[j*ncon+i]-maxwgt[j*ncon+i];
if (diff >= maxdiff) {
maxdiff = diff;
*from = j;
*cnum = i;
}
}
}
if (*from != -1 && PQueueGetSize(&queues[*cnum][*from]) == 0) {
/* The desired queue is empty, select a node from that side anyway */
for (i=0; i<ncon; i++) {
if (PQueueGetSize(&queues[i][*from]) > 0) {
max = (npwgts[(*from)*ncon+i] - maxwgt[(*from)*ncon+i]);
*cnum = i;
break;
}
}
for (i++; i<ncon; i++) {
diff = npwgts[(*from)*ncon+i] - maxwgt[(*from)*ncon+i];
if (diff > max && PQueueGetSize(&queues[i][*from]) > 0) {
max = diff;
*cnum = i;
}
}
}
/* Check to see if you can focus on the cut */
if (maxdiff <= 0.0 || *from == -1) {
maxgain = -100000;
for (j=0; j<2; j++) {
for (i=0; i<ncon; i++) {
if (PQueueGetSize(&queues[i][j]) > 0 && PQueueGetKey(&queues[i][j]) > maxgain) {
maxgain = PQueueGetKey(&queues[i][j]);
*from = j;
*cnum = i;
}
}
}
/* printf("(%2ld %2ld) %3ld\n", *from, *cnum, maxgain); */
}
}
/*************************************************************************
* This function checks if the newbal is better than oldbal given the
* ubvector ubvec
**************************************************************************/
long IsBetter2wayBalance(long ncon, float *newbal, float *oldbal, float *ubvec)
{
long i, j;
float max1=0.0, max2=0.0, sum1=0.0, sum2=0.0, tmp;
for (i=0; i<ncon; i++) {
tmp = (newbal[i]-1)/(ubvec[i]-1);
max1 = (max1 < tmp ? tmp : max1);
sum1 += tmp;
tmp = (oldbal[i]-1)/(ubvec[i]-1);
max2 = (max2 < tmp ? tmp : max2);
sum2 += tmp;
}
if (max1 < max2)
return 1;
else if (max1 > max2)
return 0;
else
return sum1 <= sum2;
}
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