Cloned library METIS with extra build files for internal package management.
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/*!
\file
\brief Functions for the edge-based balancing
\date Started 7/23/97
\author George
\author Copyright 1997-2011, Regents of the University of Minnesota
\version\verbatim $Id: balance.c 10187 2011-06-13 13:46:57Z karypis $ \endverbatim
*/
#include "metislib.h"
/*************************************************************************
* This function is the entry poidx_t of the bisection balancing algorithms.
**************************************************************************/
void Balance2Way(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
{
if (ComputeLoadImbalanceDiff(graph, 2, ctrl->pijbm, ctrl->ubfactors) <= 0)
return;
if (graph->ncon == 1) {
/* return right away if the balance is OK */
if (rabs(ntpwgts[0]*graph->tvwgt[0]-graph->pwgts[0]) < 3*graph->tvwgt[0]/graph->nvtxs)
return;
if (graph->nbnd > 0)
Bnd2WayBalance(ctrl, graph, ntpwgts);
else
General2WayBalance(ctrl, graph, ntpwgts);
}
else {
McGeneral2WayBalance(ctrl, graph, ntpwgts);
}
}
/*************************************************************************
* This function balances two partitions by moving boundary nodes
* from the domain that is overweight to the one that is underweight.
**************************************************************************/
void Bnd2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
{
idx_t i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, tmp;
idx_t *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
idx_t *moved, *perm;
rpq_t *queue;
idx_t higain, mincut, mindiff;
idx_t tpwgts[2];
WCOREPUSH;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
id = graph->id;
ed = graph->ed;
pwgts = graph->pwgts;
bndptr = graph->bndptr;
bndind = graph->bndind;
moved = iwspacemalloc(ctrl, nvtxs);
perm = iwspacemalloc(ctrl, nvtxs);
/* Determine from which domain you will be moving data */
tpwgts[0] = graph->tvwgt[0]*ntpwgts[0];
tpwgts[1] = graph->tvwgt[0] - tpwgts[0];
mindiff = iabs(tpwgts[0]-pwgts[0]);
from = (pwgts[0] < tpwgts[0] ? 1 : 0);
to = (from+1)%2;
IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
printf("Partitions: [%6"PRIDX" %6"PRIDX"] T[%6"PRIDX" %6"PRIDX"], Nv-Nb[%6"PRIDX" %6"PRIDX"]. ICut: %6"PRIDX" [B]\n",
pwgts[0], pwgts[1], tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd,
graph->mincut));
queue = rpqCreate(nvtxs);
iset(nvtxs, -1, moved);
ASSERT(ComputeCut(graph, where) == graph->mincut);
ASSERT(CheckBnd(graph));
/* Insert the boundary nodes of the proper partition whose size is OK in the priority queue */
nbnd = graph->nbnd;
irandArrayPermute(nbnd, perm, nbnd/5, 1);
for (ii=0; ii<nbnd; ii++) {
i = perm[ii];
ASSERT(ed[bndind[i]] > 0 || id[bndind[i]] == 0);
ASSERT(bndptr[bndind[i]] != -1);
if (where[bndind[i]] == from && vwgt[bndind[i]] <= mindiff)
rpqInsert(queue, bndind[i], ed[bndind[i]]-id[bndind[i]]);
}
mincut = graph->mincut;
for (nswaps=0; nswaps<nvtxs; nswaps++) {
if ((higain = rpqGetTop(queue)) == -1)
break;
ASSERT(bndptr[higain] != -1);
if (pwgts[to]+vwgt[higain] > tpwgts[to])
break;
mincut -= (ed[higain]-id[higain]);
INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);
where[higain] = to;
moved[higain] = nswaps;
IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
printf("Moved %6"PRIDX" from %"PRIDX". [%3"PRIDX" %3"PRIDX"] %5"PRIDX" [%4"PRIDX" %4"PRIDX"]\n", higain, from, ed[higain]-id[higain], vwgt[higain], mincut, pwgts[0], pwgts[1]));
/**************************************************************
* 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];
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 && where[k] == from && vwgt[k] <= mindiff) /* Remove it if in the queues */
rpqDelete(queue, k);
}
else { /* If it has not been moved, update its position in the queue */
if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
rpqUpdate(queue, k, 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 && where[k] == from && vwgt[k] <= mindiff)
rpqInsert(queue, k, ed[k]-id[k]);
}
}
}
}
IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
printf("\tMinimum cut: %6"PRIDX", PWGTS: [%6"PRIDX" %6"PRIDX"], NBND: %6"PRIDX"\n", mincut, pwgts[0], pwgts[1], nbnd));
graph->mincut = mincut;
graph->nbnd = nbnd;
rpqDestroy(queue);
WCOREPOP;
}
/*************************************************************************
* This function balances two partitions by moving the highest gain
* (including negative gain) vertices to the other domain.
* It is used only when the unbalance is due to non contiguous
* subdomains. That is, the are no boundary vertices.
* It moves vertices from the domain that is overweight to the one that
* is underweight.
**************************************************************************/
void General2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
{
idx_t i, ii, j, k, kwgt, nvtxs, nbnd, nswaps, from, to, pass, me, tmp;
idx_t *xadj, *vwgt, *adjncy, *adjwgt, *where, *id, *ed, *bndptr, *bndind, *pwgts;
idx_t *moved, *perm;
rpq_t *queue;
idx_t higain, mincut, mindiff;
idx_t tpwgts[2];
WCOREPUSH;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
id = graph->id;
ed = graph->ed;
pwgts = graph->pwgts;
bndptr = graph->bndptr;
bndind = graph->bndind;
moved = iwspacemalloc(ctrl, nvtxs);
perm = iwspacemalloc(ctrl, nvtxs);
/* Determine from which domain you will be moving data */
tpwgts[0] = graph->tvwgt[0]*ntpwgts[0];
tpwgts[1] = graph->tvwgt[0] - tpwgts[0];
mindiff = iabs(tpwgts[0]-pwgts[0]);
from = (pwgts[0] < tpwgts[0] ? 1 : 0);
to = (from+1)%2;
IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
printf("Partitions: [%6"PRIDX" %6"PRIDX"] T[%6"PRIDX" %6"PRIDX"], Nv-Nb[%6"PRIDX" %6"PRIDX"]. ICut: %6"PRIDX" [B]\n",
pwgts[0], pwgts[1], tpwgts[0], tpwgts[1], graph->nvtxs, graph->nbnd, graph->mincut));
queue = rpqCreate(nvtxs);
iset(nvtxs, -1, moved);
ASSERT(ComputeCut(graph, where) == graph->mincut);
ASSERT(CheckBnd(graph));
/* Insert the nodes of the proper partition whose size is OK in the priority queue */
irandArrayPermute(nvtxs, perm, nvtxs/5, 1);
for (ii=0; ii<nvtxs; ii++) {
i = perm[ii];
if (where[i] == from && vwgt[i] <= mindiff)
rpqInsert(queue, i, ed[i]-id[i]);
}
mincut = graph->mincut;
nbnd = graph->nbnd;
for (nswaps=0; nswaps<nvtxs; nswaps++) {
if ((higain = rpqGetTop(queue)) == -1)
break;
if (pwgts[to]+vwgt[higain] > tpwgts[to])
break;
mincut -= (ed[higain]-id[higain]);
INC_DEC(pwgts[to], pwgts[from], vwgt[higain]);
where[higain] = to;
moved[higain] = nswaps;
IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
printf("Moved %6"PRIDX" from %"PRIDX". [%3"PRIDX" %3"PRIDX"] %5"PRIDX" [%4"PRIDX" %4"PRIDX"]\n", higain, from, ed[higain]-id[higain], vwgt[higain], mincut, pwgts[0], pwgts[1]));
/**************************************************************
* Update the id[i]/ed[i] values of the affected nodes
***************************************************************/
SWAP(id[higain], ed[higain], tmp);
if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])
BNDDelete(nbnd, bndind, bndptr, higain);
if (ed[higain] > 0 && bndptr[higain] == -1)
BNDInsert(nbnd, bndind, bndptr, higain);
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);
/* Update the queue position */
if (moved[k] == -1 && where[k] == from && vwgt[k] <= mindiff)
rpqUpdate(queue, k, ed[k]-id[k]);
/* Update its boundary information */
if (ed[k] == 0 && bndptr[k] != -1)
BNDDelete(nbnd, bndind, bndptr, k);
else if (ed[k] > 0 && bndptr[k] == -1)
BNDInsert(nbnd, bndind, bndptr, k);
}
}
IFSET(ctrl->dbglvl, METIS_DBG_REFINE,
printf("\tMinimum cut: %6"PRIDX", PWGTS: [%6"PRIDX" %6"PRIDX"], NBND: %6"PRIDX"\n", mincut, pwgts[0], pwgts[1], nbnd));
graph->mincut = mincut;
graph->nbnd = nbnd;
rpqDestroy(queue);
WCOREPOP;
}
/*************************************************************************
* This function performs an edge-based FM refinement
**************************************************************************/
void McGeneral2WayBalance(ctrl_t *ctrl, graph_t *graph, real_t *ntpwgts)
{
idx_t i, ii, j, k, l, kwgt, nvtxs, ncon, nbnd, nswaps, from, to, pass,
me, limit, tmp, cnum;
idx_t *xadj, *adjncy, *vwgt, *adjwgt, *where, *pwgts, *id, *ed, *bndptr, *bndind;
idx_t *moved, *swaps, *perm, *qnum, *qsizes;
idx_t higain, mincut, newcut, mincutorder;
real_t *invtvwgt, *minbalv, *newbalv, minbal, newbal;
rpq_t **queues;
WCOREPUSH;
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
invtvwgt = graph->invtvwgt;
where = graph->where;
id = graph->id;
ed = graph->ed;
pwgts = graph->pwgts;
bndptr = graph->bndptr;
bndind = graph->bndind;
moved = iwspacemalloc(ctrl, nvtxs);
swaps = iwspacemalloc(ctrl, nvtxs);
perm = iwspacemalloc(ctrl, nvtxs);
qnum = iwspacemalloc(ctrl, nvtxs);
newbalv = rwspacemalloc(ctrl, ncon);
minbalv = rwspacemalloc(ctrl, ncon);
qsizes = iwspacemalloc(ctrl, 2*ncon);
limit = gk_min(gk_max(0.01*nvtxs, 15), 100);
/* Initialize the queues */
queues = (rpq_t **)wspacemalloc(ctrl, 2*ncon*sizeof(rpq_t *));
for (i=0; i<2*ncon; i++) {
queues[i] = rpqCreate(nvtxs);
qsizes[i] = 0;
}
for (i=0; i<nvtxs; i++) {
qnum[i] = iargmax_nrm(ncon, vwgt+i*ncon, invtvwgt);
qsizes[2*qnum[i]+where[i]]++;
}
/* for the empty queues, move into them vertices from other queues */
for (from=0; from<2; from++) {
for (j=0; j<ncon; j++) {
if (qsizes[2*j+from] == 0) {
for (i=0; i<nvtxs; i++) {
if (where[i] != from)
continue;
k = iargmax2_nrm(ncon, vwgt+i*ncon, invtvwgt);
if (k == j &&
qsizes[2*qnum[i]+from] > qsizes[2*j+from] &&
vwgt[i*ncon+qnum[i]]*invtvwgt[qnum[i]] < 1.3*vwgt[i*ncon+j]*invtvwgt[j]) {
qsizes[2*qnum[i]+from]--;
qsizes[2*j+from]++;
qnum[i] = j;
}
}
}
}
}
minbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ctrl->ubfactors, minbalv);
ASSERT(minbal > 0.0);
newcut = mincut = graph->mincut;
mincutorder = -1;
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("Parts: [");
for (l=0; l<ncon; l++)
printf("(%6"PRIDX" %6"PRIDX" %.3"PRREAL" %.3"PRREAL") ",
pwgts[l], pwgts[ncon+l], ntpwgts[l], ntpwgts[ncon+l]);
printf("] Nv-Nb[%5"PRIDX", %5"PRIDX"]. ICut: %6"PRIDX", LB: %+.3"PRREAL" [B]\n",
graph->nvtxs, graph->nbnd, graph->mincut, minbal);
}
iset(nvtxs, -1, moved);
ASSERT(ComputeCut(graph, where) == graph->mincut);
ASSERT(CheckBnd(graph));
/* Insert all nodes in the priority queues */
nbnd = graph->nbnd;
irandArrayPermute(nvtxs, perm, nvtxs/10, 1);
for (ii=0; ii<nvtxs; ii++) {
i = perm[ii];
rpqInsert(queues[2*qnum[i]+where[i]], i, ed[i]-id[i]);
}
for (nswaps=0; nswaps<nvtxs; nswaps++) {
if (minbal <= 0.0)
break;
SelectQueue(graph, ctrl->pijbm, ctrl->ubfactors, queues, &from, &cnum);
to = (from+1)%2;
if (from == -1 || (higain = rpqGetTop(queues[2*cnum+from])) == -1)
break;
newcut -= (ed[higain]-id[higain]);
iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+from*ncon, 1);
newbal = ComputeLoadImbalanceDiffVec(graph, 2, ctrl->pijbm, ctrl->ubfactors, newbalv);
if (newbal < minbal || (newbal == minbal &&
(newcut < mincut ||
(newcut == mincut && BetterBalance2Way(ncon, minbalv, newbalv))))) {
mincut = newcut;
minbal = newbal;
mincutorder = nswaps;
rcopy(ncon, newbalv, minbalv);
}
else if (nswaps-mincutorder > limit) { /* We hit the limit, undo last move */
newcut += (ed[higain]-id[higain]);
iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+from*ncon, 1);
iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
break;
}
where[higain] = to;
moved[higain] = nswaps;
swaps[nswaps] = higain;
if (ctrl->dbglvl&METIS_DBG_MOVEINFO) {
printf("Moved %6"PRIDX" from %"PRIDX"(%"PRIDX"). Gain: %5"PRIDX", "
"Cut: %5"PRIDX", NPwgts: ", higain, from, cnum, ed[higain]-id[higain], newcut);
for (l=0; l<ncon; l++)
printf("(%6"PRIDX", %6"PRIDX") ", pwgts[l], pwgts[ncon+l]);
printf(", %+.3"PRREAL" LB: %+.3"PRREAL"\n", minbal, newbal);
}
/**************************************************************
* Update the id[i]/ed[i] values of the affected nodes
***************************************************************/
SWAP(id[higain], ed[higain], tmp);
if (ed[higain] == 0 && bndptr[higain] != -1 && xadj[higain] < xadj[higain+1])
BNDDelete(nbnd, bndind, bndptr, higain);
if (ed[higain] > 0 && bndptr[higain] == -1)
BNDInsert(nbnd, bndind, bndptr, higain);
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);
/* Update the queue position */
if (moved[k] == -1)
rpqUpdate(queues[2*qnum[k]+where[k]], k, ed[k]-id[k]);
/* Update its boundary information */
if (ed[k] == 0 && bndptr[k] != -1)
BNDDelete(nbnd, bndind, bndptr, k);
else if (ed[k] > 0 && bndptr[k] == -1)
BNDInsert(nbnd, bndind, bndptr, k);
}
}
/****************************************************************
* Roll back computations
*****************************************************************/
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);
iaxpy(ncon, 1, vwgt+higain*ncon, 1, pwgts+to*ncon, 1);
iaxpy(ncon, -1, vwgt+higain*ncon, 1, pwgts+((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&METIS_DBG_REFINE) {
printf("\tMincut: %6"PRIDX" at %5"PRIDX", NBND: %6"PRIDX", NPwgts: [",
mincut, mincutorder, nbnd);
for (l=0; l<ncon; l++)
printf("(%6"PRIDX", %6"PRIDX") ", pwgts[l], pwgts[ncon+l]);
printf("], LB: %.3"PRREAL"\n", ComputeLoadImbalance(graph, 2, ctrl->pijbm));
}
graph->mincut = mincut;
graph->nbnd = nbnd;
for (i=0; i<2*ncon; i++)
rpqDestroy(queues[i]);
WCOREPOP;
}