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kwayfm.c
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kwayfm.c
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/*!
\file
\brief Routines for k-way refinement
\date Started 7/28/97
\author George
\author Copyright 1997-2009, Regents of the University of Minnesota
\version $Id: kwayfm.c 17513 2014-08-05 16:20:50Z dominique $
*/
#include "metislib.h"
/*************************************************************************/
/* Top-level routine for k-way partitioning refinement. This routine just
calls the appropriate refinement routine based on the objectives and
constraints. */
/*************************************************************************/
void Greedy_KWayOptimize(ctrl_t *ctrl, graph_t *graph, idx_t niter,
real_t ffactor, idx_t omode)
{
switch (ctrl->objtype) {
case METIS_OBJTYPE_CUT:
if (graph->ncon == 1)
Greedy_KWayCutOptimize(ctrl, graph, niter, ffactor, omode);
else
Greedy_McKWayCutOptimize(ctrl, graph, niter, ffactor, omode);
break;
case METIS_OBJTYPE_VOL:
if (graph->ncon == 1)
Greedy_KWayVolOptimize(ctrl, graph, niter, ffactor, omode);
else
Greedy_McKWayVolOptimize(ctrl, graph, niter, ffactor, omode);
break;
default:
gk_errexit(SIGERR, "Unknown objtype of %d\n", ctrl->objtype);
}
}
/*************************************************************************/
/*! K-way partitioning optimization in which the vertices are visited in
decreasing ed/sqrt(nnbrs)-id order. Note this is just an
approximation, as the ed is often split across different subdomains
and the sqrt(nnbrs) is just a crude approximation.
\param graph is the graph that is being refined.
\param niter is the number of refinement iterations.
\param ffactor is the \em fudge-factor for allowing positive gain moves
to violate the max-pwgt constraint.
\param omode is the type of optimization that will performed among
OMODE_REFINE and OMODE_BALANCE
*/
/**************************************************************************/
void Greedy_KWayCutOptimize(ctrl_t *ctrl, graph_t *graph, idx_t niter,
real_t ffactor, idx_t omode)
{
/* Common variables to all types of kway-refinement/balancing routines */
idx_t i, ii, iii, j, k, l, pass, nvtxs, nparts, gain;
idx_t from, me, to, oldcut, vwgt;
idx_t *xadj, *adjncy, *adjwgt;
idx_t *where, *pwgts, *perm, *bndptr, *bndind, *minpwgts, *maxpwgts;
idx_t nmoved, nupd, *vstatus, *updptr, *updind;
idx_t maxndoms, *safetos=NULL, *nads=NULL, *doms=NULL, **adids=NULL, **adwgts=NULL;
idx_t *bfslvl=NULL, *bfsind=NULL, *bfsmrk=NULL;
idx_t bndtype = (omode == OMODE_REFINE ? BNDTYPE_REFINE : BNDTYPE_BALANCE);
real_t *tpwgts, ubfactor;
/* Edgecut-specific/different variables */
idx_t nbnd, oldnnbrs;
rpq_t *queue;
real_t rgain;
ckrinfo_t *myrinfo;
cnbr_t *mynbrs;
ffactor = 0.0;
WCOREPUSH;
/* Link the graph fields */
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bndind = graph->bndind;
bndptr = graph->bndptr;
where = graph->where;
pwgts = graph->pwgts;
nparts = ctrl->nparts;
tpwgts = ctrl->tpwgts;
/* Setup the weight intervals of the various subdomains */
minpwgts = iwspacemalloc(ctrl, nparts);
maxpwgts = iwspacemalloc(ctrl, nparts);
if (omode == OMODE_BALANCE)
ubfactor = ctrl->ubfactors[0];
else
ubfactor = gk_max(ctrl->ubfactors[0], ComputeLoadImbalance(graph, nparts, ctrl->pijbm));
for (i=0; i<nparts; i++) {
maxpwgts[i] = tpwgts[i]*graph->tvwgt[0]*ubfactor;
minpwgts[i] = tpwgts[i]*graph->tvwgt[0]*(1.0/ubfactor);
}
perm = iwspacemalloc(ctrl, nvtxs);
/* This stores the valid target subdomains. It is used when ctrl->minconn to
control the subdomains to which moves are allowed to be made.
When ctrl->minconn is false, the default values of 2 allow all moves to
go through and it does not interfere with the zero-gain move selection. */
safetos = iset(nparts, 2, iwspacemalloc(ctrl, nparts));
if (ctrl->minconn) {
ComputeSubDomainGraph(ctrl, graph);
nads = ctrl->nads;
adids = ctrl->adids;
adwgts = ctrl->adwgts;
doms = iset(nparts, 0, ctrl->pvec1);
}
/* Setup updptr, updind like boundary info to keep track of the vertices whose
vstatus's need to be reset at the end of the inner iteration */
vstatus = iset(nvtxs, VPQSTATUS_NOTPRESENT, iwspacemalloc(ctrl, nvtxs));
updptr = iset(nvtxs, -1, iwspacemalloc(ctrl, nvtxs));
updind = iwspacemalloc(ctrl, nvtxs);
if (ctrl->contig) {
/* The arrays that will be used for limited check of articulation points */
bfslvl = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
bfsind = iwspacemalloc(ctrl, nvtxs);
bfsmrk = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
}
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("%s: [%6"PRIDX" %6"PRIDX"]-[%6"PRIDX" %6"PRIDX"], Bal: %5.3"PRREAL","
" Nv-Nb[%6"PRIDX" %6"PRIDX"], Cut: %6"PRIDX,
(omode == OMODE_REFINE ? "GRC" : "GBC"),
pwgts[iargmin(nparts, pwgts,1)], imax(nparts, pwgts,1), minpwgts[0], maxpwgts[0],
ComputeLoadImbalance(graph, nparts, ctrl->pijbm),
graph->nvtxs, graph->nbnd, graph->mincut);
if (ctrl->minconn)
printf(", Doms: [%3"PRIDX" %4"PRIDX"]", imax(nparts, nads,1), isum(nparts, nads,1));
printf("\n");
}
queue = rpqCreate(nvtxs);
/*=====================================================================
* The top-level refinement loop
*======================================================================*/
for (pass=0; pass<niter; pass++) {
ASSERT(ComputeCut(graph, where) == graph->mincut);
if (omode == OMODE_REFINE)
ASSERT(CheckBnd2(graph));
if (omode == OMODE_BALANCE) {
/* Check to see if things are out of balance, given the tolerance */
for (i=0; i<nparts; i++) {
if (pwgts[i] > maxpwgts[i] || pwgts[i] < minpwgts[i])
break;
}
if (i == nparts) /* Things are balanced. Return right away */
break;
}
oldcut = graph->mincut;
nbnd = graph->nbnd;
nupd = 0;
if (ctrl->minconn)
maxndoms = imax(nparts, nads,1);
/* Insert the boundary vertices in the priority queue */
irandArrayPermute(nbnd, perm, nbnd/4, 1);
for (ii=0; ii<nbnd; ii++) {
i = bndind[perm[ii]];
rgain = (graph->ckrinfo[i].nnbrs > 0 ?
1.0*graph->ckrinfo[i].ed/sqrt(graph->ckrinfo[i].nnbrs) : 0.0)
- graph->ckrinfo[i].id;
rpqInsert(queue, i, rgain);
vstatus[i] = VPQSTATUS_PRESENT;
ListInsert(nupd, updind, updptr, i);
}
/* Start extracting vertices from the queue and try to move them */
for (nmoved=0, iii=0;;iii++) {
if ((i = rpqGetTop(queue)) == -1)
break;
vstatus[i] = VPQSTATUS_EXTRACTED;
myrinfo = graph->ckrinfo+i;
mynbrs = ctrl->cnbrpool + myrinfo->inbr;
from = where[i];
vwgt = graph->vwgt[i];
#ifdef XXX
/* Prevent moves that make 'from' domain underbalanced */
if (omode == OMODE_REFINE) {
if (myrinfo->id > 0 && pwgts[from]-vwgt < minpwgts[from])
continue;
}
else { /* OMODE_BALANCE */
if (pwgts[from]-vwgt < minpwgts[from])
continue;
}
#endif
if (ctrl->contig && IsArticulationNode(i, xadj, adjncy, where, bfslvl, bfsind, bfsmrk))
continue;
if (ctrl->minconn)
SelectSafeTargetSubdomains(myrinfo, mynbrs, nads, adids, maxndoms, safetos, doms);
/* Find the most promising subdomain to move to */
if (omode == OMODE_REFINE) {
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
if (((mynbrs[k].ed > myrinfo->id) &&
((pwgts[from]-vwgt >= minpwgts[from]) ||
(tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt))) &&
((pwgts[to]+vwgt <= maxpwgts[to]) ||
(tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt)))
) ||
((mynbrs[k].ed == myrinfo->id) &&
(tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt)))
)
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
if (((mynbrs[j].ed > mynbrs[k].ed) &&
((pwgts[from]-vwgt >= minpwgts[from]) ||
(tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt))) &&
((pwgts[to]+vwgt <= maxpwgts[to]) ||
(tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt)))
) ||
((mynbrs[j].ed == mynbrs[k].ed) &&
(tpwgts[mynbrs[k].pid]*pwgts[to] < tpwgts[to]*pwgts[mynbrs[k].pid]))
)
k = j;
}
to = mynbrs[k].pid;
gain = mynbrs[k].ed-myrinfo->id;
/*
if (!(gain > 0
|| (gain == 0
&& (pwgts[from] >= maxpwgts[from]
|| tpwgts[to]*pwgts[from] > tpwgts[from]*(pwgts[to]+vwgt)
|| (iii%2 == 0 && safetos[to] == 2)
)
)
)
)
continue;
*/
}
else { /* OMODE_BALANCE */
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
/* the correctness of the following test follows from the correctness
of the similar test in the subsequent loop */
if (from >= nparts || tpwgts[from]*pwgts[to] < tpwgts[to]*(pwgts[from]-vwgt))
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
if (tpwgts[mynbrs[k].pid]*pwgts[to] < tpwgts[to]*pwgts[mynbrs[k].pid])
k = j;
}
to = mynbrs[k].pid;
//if (pwgts[from] < maxpwgts[from] && pwgts[to] > minpwgts[to] &&
// mynbrs[k].ed-myrinfo->id < 0)
// continue;
}
/*=====================================================================
* If we got here, we can now move the vertex from 'from' to 'to'
*======================================================================*/
graph->mincut -= mynbrs[k].ed-myrinfo->id;
nmoved++;
IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
printf("\t\tMoving %6"PRIDX" from %3"PRIDX"/%"PRIDX" to %3"PRIDX"/%"PRIDX" [%6"PRIDX" %6"PRIDX"]. Gain: %4"PRIDX". Cut: %6"PRIDX"\n",
i, from, safetos[from], to, safetos[to], pwgts[from], pwgts[to], mynbrs[k].ed-myrinfo->id, graph->mincut));
/* Update the subdomain connectivity information */
if (ctrl->minconn) {
/* take care of i's move itself */
UpdateEdgeSubDomainGraph(ctrl, from, to, myrinfo->id-mynbrs[k].ed, &maxndoms);
/* take care of the adjacent vertices */
for (j=xadj[i]; j<xadj[i+1]; j++) {
me = where[adjncy[j]];
if (me != from && me != to) {
UpdateEdgeSubDomainGraph(ctrl, from, me, -adjwgt[j], &maxndoms);
UpdateEdgeSubDomainGraph(ctrl, to, me, adjwgt[j], &maxndoms);
}
}
}
/* Update ID/ED and BND related information for the moved vertex */
INC_DEC(pwgts[to], pwgts[from], vwgt);
UpdateMovedVertexInfoAndBND(i, from, k, to, myrinfo, mynbrs, where, nbnd,
bndptr, bndind, bndtype);
/* Update the degrees of adjacent vertices */
for (j=xadj[i]; j<xadj[i+1]; j++) {
ii = adjncy[j];
me = where[ii];
myrinfo = graph->ckrinfo+ii;
oldnnbrs = myrinfo->nnbrs;
UpdateAdjacentVertexInfoAndBND(ctrl, ii, xadj[ii+1]-xadj[ii], me,
from, to, myrinfo, adjwgt[j], nbnd, bndptr, bndind, bndtype);
UpdateQueueInfo(queue, vstatus, ii, me, from, to, myrinfo, oldnnbrs,
nupd, updptr, updind, bndtype);
ASSERT(myrinfo->nnbrs <= xadj[ii+1]-xadj[ii]);
}
}
graph->nbnd = nbnd;
/* Reset the vstatus and associated data structures */
for (i=0; i<nupd; i++) {
ASSERT(updptr[updind[i]] != -1);
ASSERT(vstatus[updind[i]] != VPQSTATUS_NOTPRESENT);
vstatus[updind[i]] = VPQSTATUS_NOTPRESENT;
updptr[updind[i]] = -1;
}
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("\t[%6"PRIDX" %6"PRIDX"], Bal: %5.3"PRREAL", Nb: %6"PRIDX"."
" Nmoves: %5"PRIDX", Cut: %6"PRIDX", Vol: %6"PRIDX,
pwgts[iargmin(nparts, pwgts,1)], imax(nparts, pwgts,1),
ComputeLoadImbalance(graph, nparts, ctrl->pijbm),
graph->nbnd, nmoved, graph->mincut, ComputeVolume(graph, where));
if (ctrl->minconn)
printf(", Doms: [%3"PRIDX" %4"PRIDX"]", imax(nparts, nads,1), isum(nparts, nads,1));
printf("\n");
}
if (nmoved == 0 || (omode == OMODE_REFINE && graph->mincut == oldcut))
break;
}
rpqDestroy(queue);
WCOREPOP;
}
/*************************************************************************/
/*! K-way refinement that minimizes the communication volume. This is a
greedy routine and the vertices are visited in decreasing gv order.
\param graph is the graph that is being refined.
\param niter is the number of refinement iterations.
\param ffactor is the \em fudge-factor for allowing positive gain moves
to violate the max-pwgt constraint.
*/
/**************************************************************************/
void Greedy_KWayVolOptimize(ctrl_t *ctrl, graph_t *graph, idx_t niter,
real_t ffactor, idx_t omode)
{
/* Common variables to all types of kway-refinement/balancing routines */
idx_t i, ii, iii, j, k, l, pass, nvtxs, nparts, gain;
idx_t from, me, to, oldcut, vwgt;
idx_t *xadj, *adjncy;
idx_t *where, *pwgts, *perm, *bndptr, *bndind, *minpwgts, *maxpwgts;
idx_t nmoved, nupd, *vstatus, *updptr, *updind;
idx_t maxndoms, *safetos=NULL, *nads=NULL, *doms=NULL, **adids=NULL, **adwgts=NULL;
idx_t *bfslvl=NULL, *bfsind=NULL, *bfsmrk=NULL;
idx_t bndtype = (omode == OMODE_REFINE ? BNDTYPE_REFINE : BNDTYPE_BALANCE);
real_t *tpwgts;
/* Volume-specific/different variables */
ipq_t *queue;
idx_t oldvol, xgain;
idx_t *vmarker, *pmarker, *modind;
vkrinfo_t *myrinfo;
vnbr_t *mynbrs;
WCOREPUSH;
/* Link the graph fields */
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
bndptr = graph->bndptr;
bndind = graph->bndind;
where = graph->where;
pwgts = graph->pwgts;
nparts = ctrl->nparts;
tpwgts = ctrl->tpwgts;
/* Setup the weight intervals of the various subdomains */
minpwgts = iwspacemalloc(ctrl, nparts);
maxpwgts = iwspacemalloc(ctrl, nparts);
for (i=0; i<nparts; i++) {
maxpwgts[i] = ctrl->tpwgts[i]*graph->tvwgt[0]*ctrl->ubfactors[0];
minpwgts[i] = ctrl->tpwgts[i]*graph->tvwgt[0]*(1.0/ctrl->ubfactors[0]);
}
perm = iwspacemalloc(ctrl, nvtxs);
/* This stores the valid target subdomains. It is used when ctrl->minconn to
control the subdomains to which moves are allowed to be made.
When ctrl->minconn is false, the default values of 2 allow all moves to
go through and it does not interfere with the zero-gain move selection. */
safetos = iset(nparts, 2, iwspacemalloc(ctrl, nparts));
if (ctrl->minconn) {
ComputeSubDomainGraph(ctrl, graph);
nads = ctrl->nads;
adids = ctrl->adids;
adwgts = ctrl->adwgts;
doms = iset(nparts, 0, ctrl->pvec1);
}
/* Setup updptr, updind like boundary info to keep track of the vertices whose
vstatus's need to be reset at the end of the inner iteration */
vstatus = iset(nvtxs, VPQSTATUS_NOTPRESENT, iwspacemalloc(ctrl, nvtxs));
updptr = iset(nvtxs, -1, iwspacemalloc(ctrl, nvtxs));
updind = iwspacemalloc(ctrl, nvtxs);
if (ctrl->contig) {
/* The arrays that will be used for limited check of articulation points */
bfslvl = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
bfsind = iwspacemalloc(ctrl, nvtxs);
bfsmrk = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
}
/* Vol-refinement specific working arrays */
modind = iwspacemalloc(ctrl, nvtxs);
vmarker = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
pmarker = iset(nparts, -1, iwspacemalloc(ctrl, nparts));
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("%s: [%6"PRIDX" %6"PRIDX"]-[%6"PRIDX" %6"PRIDX"], Bal: %5.3"PRREAL
", Nv-Nb[%6"PRIDX" %6"PRIDX"], Cut: %5"PRIDX", Vol: %5"PRIDX,
(omode == OMODE_REFINE ? "GRV" : "GBV"),
pwgts[iargmin(nparts, pwgts,1)], imax(nparts, pwgts,1), minpwgts[0], maxpwgts[0],
ComputeLoadImbalance(graph, nparts, ctrl->pijbm),
graph->nvtxs, graph->nbnd, graph->mincut, graph->minvol);
if (ctrl->minconn)
printf(", Doms: [%3"PRIDX" %4"PRIDX"]", imax(nparts, nads,1), isum(nparts, nads,1));
printf("\n");
}
queue = ipqCreate(nvtxs);
/*=====================================================================
* The top-level refinement loop
*======================================================================*/
for (pass=0; pass<niter; pass++) {
ASSERT(ComputeVolume(graph, where) == graph->minvol);
if (omode == OMODE_BALANCE) {
/* Check to see if things are out of balance, given the tolerance */
for (i=0; i<nparts; i++) {
if (pwgts[i] > maxpwgts[i])
break;
}
if (i == nparts) /* Things are balanced. Return right away */
break;
}
oldcut = graph->mincut;
oldvol = graph->minvol;
nupd = 0;
if (ctrl->minconn)
maxndoms = imax(nparts, nads,1);
/* Insert the boundary vertices in the priority queue */
irandArrayPermute(graph->nbnd, perm, graph->nbnd/4, 1);
for (ii=0; ii<graph->nbnd; ii++) {
i = bndind[perm[ii]];
ipqInsert(queue, i, graph->vkrinfo[i].gv);
vstatus[i] = VPQSTATUS_PRESENT;
ListInsert(nupd, updind, updptr, i);
}
/* Start extracting vertices from the queue and try to move them */
for (nmoved=0, iii=0;;iii++) {
if ((i = ipqGetTop(queue)) == -1)
break;
vstatus[i] = VPQSTATUS_EXTRACTED;
myrinfo = graph->vkrinfo+i;
mynbrs = ctrl->vnbrpool + myrinfo->inbr;
from = where[i];
vwgt = graph->vwgt[i];
/* Prevent moves that make 'from' domain underbalanced */
if (omode == OMODE_REFINE) {
if (myrinfo->nid > 0 && pwgts[from]-vwgt < minpwgts[from])
continue;
}
else { /* OMODE_BALANCE */
if (pwgts[from]-vwgt < minpwgts[from])
continue;
}
if (ctrl->contig && IsArticulationNode(i, xadj, adjncy, where, bfslvl, bfsind, bfsmrk))
continue;
if (ctrl->minconn)
SelectSafeTargetSubdomains(myrinfo, mynbrs, nads, adids, maxndoms, safetos, doms);
xgain = (myrinfo->nid == 0 && myrinfo->ned > 0 ? graph->vsize[i] : 0);
/* Find the most promising subdomain to move to */
if (omode == OMODE_REFINE) {
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
gain = mynbrs[k].gv + xgain;
if (gain >= 0 && pwgts[to]+vwgt <= maxpwgts[to]+ffactor*gain)
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
gain = mynbrs[j].gv + xgain;
if ((mynbrs[j].gv > mynbrs[k].gv &&
pwgts[to]+vwgt <= maxpwgts[to]+ffactor*gain)
||
(mynbrs[j].gv == mynbrs[k].gv &&
mynbrs[j].ned > mynbrs[k].ned &&
pwgts[to]+vwgt <= maxpwgts[to])
||
(mynbrs[j].gv == mynbrs[k].gv &&
mynbrs[j].ned == mynbrs[k].ned &&
tpwgts[mynbrs[k].pid]*pwgts[to] < tpwgts[to]*pwgts[mynbrs[k].pid])
)
k = j;
}
to = mynbrs[k].pid;
ASSERT(xgain+mynbrs[k].gv >= 0);
j = 0;
if (xgain+mynbrs[k].gv > 0 || mynbrs[k].ned-myrinfo->nid > 0)
j = 1;
else if (mynbrs[k].ned-myrinfo->nid == 0) {
if ((iii%2 == 0 && safetos[to] == 2) ||
pwgts[from] >= maxpwgts[from] ||
tpwgts[from]*(pwgts[to]+vwgt) < tpwgts[to]*pwgts[from])
j = 1;
}
if (j == 0)
continue;
}
else { /* OMODE_BALANCE */
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
if (pwgts[to]+vwgt <= maxpwgts[to] ||
tpwgts[from]*(pwgts[to]+vwgt) <= tpwgts[to]*pwgts[from])
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
if (tpwgts[mynbrs[k].pid]*pwgts[to] < tpwgts[to]*pwgts[mynbrs[k].pid])
k = j;
}
to = mynbrs[k].pid;
if (pwgts[from] < maxpwgts[from] && pwgts[to] > minpwgts[to] &&
(xgain+mynbrs[k].gv < 0 ||
(xgain+mynbrs[k].gv == 0 && mynbrs[k].ned-myrinfo->nid < 0))
)
continue;
}
/*=====================================================================
* If we got here, we can now move the vertex from 'from' to 'to'
*======================================================================*/
INC_DEC(pwgts[to], pwgts[from], vwgt);
graph->mincut -= mynbrs[k].ned-myrinfo->nid;
graph->minvol -= (xgain+mynbrs[k].gv);
where[i] = to;
nmoved++;
IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
printf("\t\tMoving %6"PRIDX" from %3"PRIDX" to %3"PRIDX". "
"Gain: [%4"PRIDX" %4"PRIDX"]. Cut: %6"PRIDX", Vol: %6"PRIDX"\n",
i, from, to, xgain+mynbrs[k].gv, mynbrs[k].ned-myrinfo->nid,
graph->mincut, graph->minvol));
/* Update the subdomain connectivity information */
if (ctrl->minconn) {
/* take care of i's move itself */
UpdateEdgeSubDomainGraph(ctrl, from, to, myrinfo->nid-mynbrs[k].ned, &maxndoms);
/* take care of the adjacent vertices */
for (j=xadj[i]; j<xadj[i+1]; j++) {
me = where[adjncy[j]];
if (me != from && me != to) {
UpdateEdgeSubDomainGraph(ctrl, from, me, -1, &maxndoms);
UpdateEdgeSubDomainGraph(ctrl, to, me, 1, &maxndoms);
}
}
}
/* Update the id/ed/gains/bnd/queue of potentially affected nodes */
KWayVolUpdate(ctrl, graph, i, from, to, queue, vstatus, &nupd, updptr,
updind, bndtype, vmarker, pmarker, modind);
/*CheckKWayVolPartitionParams(ctrl, graph); */
}
/* Reset the vstatus and associated data structures */
for (i=0; i<nupd; i++) {
ASSERT(updptr[updind[i]] != -1);
ASSERT(vstatus[updind[i]] != VPQSTATUS_NOTPRESENT);
vstatus[updind[i]] = VPQSTATUS_NOTPRESENT;
updptr[updind[i]] = -1;
}
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("\t[%6"PRIDX" %6"PRIDX"], Bal: %5.3"PRREAL", Nb: %6"PRIDX"."
" Nmoves: %5"PRIDX", Cut: %6"PRIDX", Vol: %6"PRIDX,
pwgts[iargmin(nparts, pwgts,1)], imax(nparts, pwgts,1),
ComputeLoadImbalance(graph, nparts, ctrl->pijbm),
graph->nbnd, nmoved, graph->mincut, graph->minvol);
if (ctrl->minconn)
printf(", Doms: [%3"PRIDX" %4"PRIDX"]", imax(nparts, nads,1), isum(nparts, nads,1));
printf("\n");
}
if (nmoved == 0 ||
(omode == OMODE_REFINE && graph->minvol == oldvol && graph->mincut == oldcut))
break;
}
ipqDestroy(queue);
WCOREPOP;
}
/*************************************************************************/
/*! K-way partitioning optimization in which the vertices are visited in
decreasing ed/sqrt(nnbrs)-id order. Note this is just an
approximation, as the ed is often split across different subdomains
and the sqrt(nnbrs) is just a crude approximation.
\param graph is the graph that is being refined.
\param niter is the number of refinement iterations.
\param ffactor is the \em fudge-factor for allowing positive gain moves
to violate the max-pwgt constraint.
\param omode is the type of optimization that will performed among
OMODE_REFINE and OMODE_BALANCE
*/
/**************************************************************************/
void Greedy_McKWayCutOptimize(ctrl_t *ctrl, graph_t *graph, idx_t niter,
real_t ffactor, idx_t omode)
{
/* Common variables to all types of kway-refinement/balancing routines */
idx_t i, ii, iii, j, k, l, pass, nvtxs, ncon, nparts, gain;
idx_t from, me, to, cto, oldcut;
idx_t *xadj, *vwgt, *adjncy, *adjwgt;
idx_t *where, *pwgts, *perm, *bndptr, *bndind, *minpwgts, *maxpwgts;
idx_t nmoved, nupd, *vstatus, *updptr, *updind;
idx_t maxndoms, *safetos=NULL, *nads=NULL, *doms=NULL, **adids=NULL, **adwgts=NULL;
idx_t *bfslvl=NULL, *bfsind=NULL, *bfsmrk=NULL;
idx_t bndtype = (omode == OMODE_REFINE ? BNDTYPE_REFINE : BNDTYPE_BALANCE);
real_t *ubfactors, *pijbm;
real_t origbal;
/* Edgecut-specific/different variables */
idx_t nbnd, oldnnbrs;
rpq_t *queue;
real_t rgain;
ckrinfo_t *myrinfo;
cnbr_t *mynbrs;
WCOREPUSH;
/* Link the graph fields */
nvtxs = graph->nvtxs;
ncon = graph->ncon;
xadj = graph->xadj;
vwgt = graph->vwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
bndind = graph->bndind;
bndptr = graph->bndptr;
where = graph->where;
pwgts = graph->pwgts;
nparts = ctrl->nparts;
pijbm = ctrl->pijbm;
/* Determine the ubfactors. The method used is different based on omode.
When OMODE_BALANCE, the ubfactors are those supplied by the user.
When OMODE_REFINE, the ubfactors are the max of the current partition
and the user-specified ones. */
ubfactors = rwspacemalloc(ctrl, ncon);
ComputeLoadImbalanceVec(graph, nparts, pijbm, ubfactors);
origbal = rvecmaxdiff(ncon, ubfactors, ctrl->ubfactors);
if (omode == OMODE_BALANCE) {
rcopy(ncon, ctrl->ubfactors, ubfactors);
}
else {
for (i=0; i<ncon; i++)
ubfactors[i] = (ubfactors[i] > ctrl->ubfactors[i] ? ubfactors[i] : ctrl->ubfactors[i]);
}
/* Setup the weight intervals of the various subdomains */
minpwgts = iwspacemalloc(ctrl, nparts*ncon);
maxpwgts = iwspacemalloc(ctrl, nparts*ncon);
for (i=0; i<nparts; i++) {
for (j=0; j<ncon; j++) {
maxpwgts[i*ncon+j] = ctrl->tpwgts[i*ncon+j]*graph->tvwgt[j]*ubfactors[j];
/*minpwgts[i*ncon+j] = ctrl->tpwgts[i*ncon+j]*graph->tvwgt[j]*(.9/ubfactors[j]);*/
minpwgts[i*ncon+j] = ctrl->tpwgts[i*ncon+j]*graph->tvwgt[j]*.2;
}
}
perm = iwspacemalloc(ctrl, nvtxs);
/* This stores the valid target subdomains. It is used when ctrl->minconn to
control the subdomains to which moves are allowed to be made.
When ctrl->minconn is false, the default values of 2 allow all moves to
go through and it does not interfere with the zero-gain move selection. */
safetos = iset(nparts, 2, iwspacemalloc(ctrl, nparts));
if (ctrl->minconn) {
ComputeSubDomainGraph(ctrl, graph);
nads = ctrl->nads;
adids = ctrl->adids;
adwgts = ctrl->adwgts;
doms = iset(nparts, 0, ctrl->pvec1);
}
/* Setup updptr, updind like boundary info to keep track of the vertices whose
vstatus's need to be reset at the end of the inner iteration */
vstatus = iset(nvtxs, VPQSTATUS_NOTPRESENT, iwspacemalloc(ctrl, nvtxs));
updptr = iset(nvtxs, -1, iwspacemalloc(ctrl, nvtxs));
updind = iwspacemalloc(ctrl, nvtxs);
if (ctrl->contig) {
/* The arrays that will be used for limited check of articulation points */
bfslvl = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
bfsind = iwspacemalloc(ctrl, nvtxs);
bfsmrk = iset(nvtxs, 0, iwspacemalloc(ctrl, nvtxs));
}
if (ctrl->dbglvl&METIS_DBG_REFINE) {
printf("%s: [%6"PRIDX" %6"PRIDX" %6"PRIDX"], Bal: %5.3"PRREAL"(%.3"PRREAL"),"
" Nv-Nb[%6"PRIDX" %6"PRIDX"], Cut: %6"PRIDX", (%"PRIDX")",
(omode == OMODE_REFINE ? "GRC" : "GBC"),
imin(nparts*ncon, pwgts,1), imax(nparts*ncon, pwgts,1), imax(nparts*ncon, maxpwgts,1),
ComputeLoadImbalance(graph, nparts, pijbm), origbal,
graph->nvtxs, graph->nbnd, graph->mincut, niter);
if (ctrl->minconn)
printf(", Doms: [%3"PRIDX" %4"PRIDX"]", imax(nparts, nads,1), isum(nparts, nads,1));
printf("\n");
}
queue = rpqCreate(nvtxs);
/*=====================================================================
* The top-level refinement loop
*======================================================================*/
for (pass=0; pass<niter; pass++) {
ASSERT(ComputeCut(graph, where) == graph->mincut);
if (omode == OMODE_REFINE)
ASSERT(CheckBnd2(graph));
/* In balancing mode, exit as soon as balance is reached */
if (omode == OMODE_BALANCE && IsBalanced(ctrl, graph, 0))
break;
oldcut = graph->mincut;
nbnd = graph->nbnd;
nupd = 0;
if (ctrl->minconn)
maxndoms = imax(nparts, nads,1);
/* Insert the boundary vertices in the priority queue */
irandArrayPermute(nbnd, perm, nbnd/4, 1);
for (ii=0; ii<nbnd; ii++) {
i = bndind[perm[ii]];
rgain = (graph->ckrinfo[i].nnbrs > 0 ?
1.0*graph->ckrinfo[i].ed/sqrt(graph->ckrinfo[i].nnbrs) : 0.0)
- graph->ckrinfo[i].id;
rpqInsert(queue, i, rgain);
vstatus[i] = VPQSTATUS_PRESENT;
ListInsert(nupd, updind, updptr, i);
}
/* Start extracting vertices from the queue and try to move them */
for (nmoved=0, iii=0;;iii++) {
if ((i = rpqGetTop(queue)) == -1)
break;
vstatus[i] = VPQSTATUS_EXTRACTED;
myrinfo = graph->ckrinfo+i;
mynbrs = ctrl->cnbrpool + myrinfo->inbr;
from = where[i];
/* Prevent moves that make 'from' domain underbalanced */
if (omode == OMODE_REFINE) {
if (myrinfo->id > 0 &&
!ivecaxpygez(ncon, -1, vwgt+i*ncon, pwgts+from*ncon, minpwgts+from*ncon))
continue;
}
else { /* OMODE_BALANCE */
if (!ivecaxpygez(ncon, -1, vwgt+i*ncon, pwgts+from*ncon, minpwgts+from*ncon))
continue;
}
if (ctrl->contig && IsArticulationNode(i, xadj, adjncy, where, bfslvl, bfsind, bfsmrk))
continue;
if (ctrl->minconn)
SelectSafeTargetSubdomains(myrinfo, mynbrs, nads, adids, maxndoms, safetos, doms);
/* Find the most promising subdomain to move to */
if (omode == OMODE_REFINE) {
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
gain = mynbrs[k].ed-myrinfo->id;
if (gain >= 0 && ivecaxpylez(ncon, 1, vwgt+i*ncon, pwgts+to*ncon, maxpwgts+to*ncon))
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
cto = to;
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
if ((mynbrs[j].ed > mynbrs[k].ed &&
ivecaxpylez(ncon, 1, vwgt+i*ncon, pwgts+to*ncon, maxpwgts+to*ncon))
||
(mynbrs[j].ed == mynbrs[k].ed &&
BetterBalanceKWay(ncon, vwgt+i*ncon, ubfactors,
1, pwgts+cto*ncon, pijbm+cto*ncon,
1, pwgts+to*ncon, pijbm+to*ncon))) {
k = j;
cto = to;
}
}
to = cto;
gain = mynbrs[k].ed-myrinfo->id;
if (!(gain > 0
|| (gain == 0
&& (BetterBalanceKWay(ncon, vwgt+i*ncon, ubfactors,
-1, pwgts+from*ncon, pijbm+from*ncon,
+1, pwgts+to*ncon, pijbm+to*ncon)
|| (iii%2 == 0 && safetos[to] == 2)
)
)
)
)
continue;
}
else { /* OMODE_BALANCE */
for (k=myrinfo->nnbrs-1; k>=0; k--) {
if (!safetos[to=mynbrs[k].pid])
continue;
if (ivecaxpylez(ncon, 1, vwgt+i*ncon, pwgts+to*ncon, maxpwgts+to*ncon) ||
BetterBalanceKWay(ncon, vwgt+i*ncon, ubfactors,
-1, pwgts+from*ncon, pijbm+from*ncon,
+1, pwgts+to*ncon, pijbm+to*ncon))
break;
}
if (k < 0)
continue; /* break out if you did not find a candidate */
cto = to;
for (j=k-1; j>=0; j--) {
if (!safetos[to=mynbrs[j].pid])
continue;
if (BetterBalanceKWay(ncon, vwgt+i*ncon, ubfactors,
1, pwgts+cto*ncon, pijbm+cto*ncon,
1, pwgts+to*ncon, pijbm+to*ncon)) {
k = j;
cto = to;
}
}
to = cto;
if (mynbrs[k].ed-myrinfo->id < 0 &&
!BetterBalanceKWay(ncon, vwgt+i*ncon, ubfactors,
-1, pwgts+from*ncon, pijbm+from*ncon,
+1, pwgts+to*ncon, pijbm+to*ncon))
continue;
}
/*=====================================================================
* If we got here, we can now move the vertex from 'from' to 'to'
*======================================================================*/
graph->mincut -= mynbrs[k].ed-myrinfo->id;
nmoved++;
IFSET(ctrl->dbglvl, METIS_DBG_MOVEINFO,
printf("\t\tMoving %6"PRIDX" to %3"PRIDX". Gain: %4"PRIDX". Cut: %6"PRIDX"\n",
i, to, mynbrs[k].ed-myrinfo->id, graph->mincut));
/* Update the subdomain connectivity information */
if (ctrl->minconn) {
/* take care of i's move itself */
UpdateEdgeSubDomainGraph(ctrl, from, to, myrinfo->id-mynbrs[k].ed, &maxndoms);
/* take care of the adjacent vertices */
for (j=xadj[i]; j<xadj[i+1]; j++) {
me = where[adjncy[j]];
if (me != from && me != to) {
UpdateEdgeSubDomainGraph(ctrl, from, me, -adjwgt[j], &maxndoms);
UpdateEdgeSubDomainGraph(ctrl, to, me, adjwgt[j], &maxndoms);
}
}
}
/* Update ID/ED and BND related information for the moved vertex */
iaxpy(ncon, 1, vwgt+i*ncon, 1, pwgts+to*ncon, 1);
iaxpy(ncon, -1, vwgt+i*ncon, 1, pwgts+from*ncon, 1);
UpdateMovedVertexInfoAndBND(i, from, k, to, myrinfo, mynbrs, where,
nbnd, bndptr, bndind, bndtype);
/* Update the degrees of adjacent vertices */
for (j=xadj[i]; j<xadj[i+1]; j++) {
ii = adjncy[j];
me = where[ii];
myrinfo = graph->ckrinfo+ii;
oldnnbrs = myrinfo->nnbrs;
UpdateAdjacentVertexInfoAndBND(ctrl, ii, xadj[ii+1]-xadj[ii], me,
from, to, myrinfo, adjwgt[j], nbnd, bndptr, bndind, bndtype);