/*************************************************************************
* This function performs a k-way directed diffusion
**************************************************************************/
real_t WavefrontDiffusion(ctrl_t *ctrl, graph_t *graph, idx_t *home)
{
idx_t ii, i, j, k, l, nvtxs, nedges, nparts;
idx_t from, to, edge, done, nswaps, noswaps, totalv, wsize;
idx_t npasses, first, second, third, mind, maxd;
idx_t *xadj, *adjncy, *adjwgt, *where, *perm;
idx_t *rowptr, *colind, *ed, *psize;
real_t *transfer, *tmpvec;
real_t balance = -1.0, *load, *solution, *workspace;
real_t *nvwgt, *npwgts, flowFactor, cost, ubfactor;
matrix_t matrix;
ikv_t *cand;
idx_t ndirty, nclean, dptr, clean;
nvtxs = graph->nvtxs;
nedges = graph->nedges;
xadj = graph->xadj;
nvwgt = graph->nvwgt;
adjncy = graph->adjncy;
adjwgt = graph->adjwgt;
where = graph->where;
nparts = ctrl->nparts;
ubfactor = ctrl->ubvec[0];
matrix.nrows = nparts;
flowFactor = 0.35;
flowFactor = (ctrl->mype == 2) ? 0.50 : flowFactor;
flowFactor = (ctrl->mype == 3) ? 0.75 : flowFactor;
flowFactor = (ctrl->mype == 4) ? 1.00 : flowFactor;
/* allocate memory */
solution = rmalloc(4*nparts+2*nedges, "WavefrontDiffusion: solution");
tmpvec = solution + nparts;
npwgts = solution + 2*nparts;
load = solution + 3*nparts;
matrix.values = solution + 4*nparts;
transfer = matrix.transfer = solution + 4*nparts + nedges;
perm = imalloc(2*nvtxs+2*nparts+nedges+1, "WavefrontDiffusion: perm");
ed = perm + nvtxs;
psize = perm + 2*nvtxs;
rowptr = matrix.rowptr = perm + 2*nvtxs + nparts;
colind = matrix.colind = perm + 2*nvtxs + 2*nparts + 1;
/*GKTODO - Potential problem with this malloc */
wsize = gk_max(sizeof(real_t)*nparts*6, sizeof(idx_t)*(nvtxs+nparts*2+1));
workspace = (real_t *)gk_malloc(wsize, "WavefrontDiffusion: workspace");
cand = ikvmalloc(nvtxs, "WavefrontDiffusion: cand");
/*****************************/
/* Populate empty subdomains */
/*****************************/
iset(nparts, 0, psize);
for (i=0; i<nvtxs; i++)
psize[where[i]]++;
mind = iargmin(nparts, psize);
maxd = iargmax(nparts, psize);
if (psize[mind] == 0) {
for (i=0; i<nvtxs; i++) {
k = (RandomInRange(nvtxs)+i)%nvtxs;
if (where[k] == maxd) {
where[k] = mind;
psize[mind]++;
psize[maxd]--;
break;
}
}
}
iset(nvtxs, 0, ed);
rset(nparts, 0.0, npwgts);
for (i=0; i<nvtxs; i++) {
npwgts[where[i]] += nvwgt[i];
for (j=xadj[i]; j<xadj[i+1]; j++)
ed[i] += (where[i] != where[adjncy[j]] ? adjwgt[j] : 0);
}
ComputeLoad(graph, nparts, load, ctrl->tpwgts, 0);
done = 0;
/* zero out the tmpvec array */
rset(nparts, 0.0, tmpvec);
npasses = gk_min(nparts/2, NGD_PASSES);
for (l=0; l<npasses; l++) {
/* Set-up and solve the diffusion equation */
nswaps = 0;
/************************/
/* Solve flow equations */
/************************/
SetUpConnectGraph(graph, &matrix, (idx_t *)workspace);
/* check for disconnected subdomains */
for(i=0; i<matrix.nrows; i++) {
if (matrix.rowptr[i]+1 == matrix.rowptr[i+1]) {
cost = (real_t)(ctrl->mype);
goto CleanUpAndExit;
}
}
ConjGrad2(&matrix, load, solution, 0.001, workspace);
ComputeTransferVector(1, &matrix, solution, transfer, 0);
GetThreeMax(nparts, load, &first, &second, &third);
if (l%3 == 0) {
FastRandomPermute(nvtxs, perm, 1);
}
else {
/*****************************/
/* move dirty vertices first */
/*****************************/
ndirty = 0;
for (i=0; i<nvtxs; i++) {
if (where[i] != home[i])
ndirty++;
}
dptr = 0;
for (i=0; i<nvtxs; i++) {
if (where[i] != home[i])
perm[dptr++] = i;
else
perm[ndirty++] = i;
}
PASSERT(ctrl, ndirty == nvtxs);
ndirty = dptr;
nclean = nvtxs-dptr;
FastRandomPermute(ndirty, perm, 0);
FastRandomPermute(nclean, perm+ndirty, 0);
}
if (ctrl->mype == 0) {
for (j=nvtxs, k=0, ii=0; ii<nvtxs; ii++) {
i = perm[ii];
if (ed[i] != 0) {
cand[k].key = -ed[i];
cand[k++].val = i;
}
else {
cand[--j].key = 0;
cand[j].val = i;
}
}
ikvsorti(k, cand);
}
for (ii=0; ii<nvtxs/3; ii++) {
i = (ctrl->mype == 0) ? cand[ii].val : perm[ii];
from = where[i];
/* don't move out the last vertex in a subdomain */
if (psize[from] == 1)
continue;
clean = (from == home[i]) ? 1 : 0;
/* only move from top three or dirty vertices */
if (from != first && from != second && from != third && clean)
continue;
/* Scatter the sparse transfer row into the dense tmpvec row */
for (j=rowptr[from]+1; j<rowptr[from+1]; j++)
tmpvec[colind[j]] = transfer[j];
for (j=xadj[i]; j<xadj[i+1]; j++) {
to = where[adjncy[j]];
if (from != to) {
if (tmpvec[to] > (flowFactor * nvwgt[i])) {
tmpvec[to] -= nvwgt[i];
INC_DEC(psize[to], psize[from], 1);
INC_DEC(npwgts[to], npwgts[from], nvwgt[i]);
INC_DEC(load[to], load[from], nvwgt[i]);
where[i] = to;
nswaps++;
/* Update external degrees */
ed[i] = 0;
for (k=xadj[i]; k<xadj[i+1]; k++) {
edge = adjncy[k];
ed[i] += (to != where[edge] ? adjwgt[k] : 0);
if (where[edge] == from)
ed[edge] += adjwgt[k];
if (where[edge] == to)
ed[edge] -= adjwgt[k];
}
break;
}
}
}
/* Gather the dense tmpvec row into the sparse transfer row */
for (j=rowptr[from]+1; j<rowptr[from+1]; j++) {
transfer[j] = tmpvec[colind[j]];
tmpvec[colind[j]] = 0.0;
}
ASSERT(fabs(rsum(nparts, tmpvec, 1)) < .0001)
}
if (l % 2 == 1) {
balance = rmax(nparts, npwgts)*nparts;
if (balance < ubfactor + 0.035)
done = 1;
if (GlobalSESum(ctrl, done) > 0)
break;
noswaps = (nswaps > 0) ? 0 : 1;
if (GlobalSESum(ctrl, noswaps) > ctrl->npes/2)
break;
}
}
graph->mincut = ComputeSerialEdgeCut(graph);
totalv = Mc_ComputeSerialTotalV(graph, home);
cost = ctrl->ipc_factor * (real_t)graph->mincut + ctrl->redist_factor * (real_t)totalv;
CleanUpAndExit:
gk_free((void **)&solution, (void **)&perm, (void **)&workspace, (void **)&cand, LTERM);
return cost;
}
/*************************************************************************
* This function is the entry point of the initial balancing algorithm.
* This algorithm assembles the graph to all the processors and preceeds
* with the balancing step.
**************************************************************************/
void Balance_Partition(CtrlType *ctrl, GraphType *graph, WorkSpaceType *wspace)
{
int i, j, mype, npes, nvtxs, nedges, ncon;
idxtype *vtxdist, *xadj, *adjncy, *adjwgt, *vwgt, *vsize;
idxtype *part, *lwhere, *home;
GraphType *agraph, cgraph;
CtrlType myctrl;
int lnparts, fpart, fpe, lnpes, ngroups, srnpes, srmype;
int twoparts=2, numflag = 0, wgtflag = 3, moptions[10], edgecut, max_cut;
int sr_pe, gd_pe, sr, gd, who_wins, *rcounts, *rdispls;
float my_cut, my_totalv, my_cost = -1.0, my_balance = -1.0, wsum;
float rating, max_rating, your_cost = -1.0, your_balance = -1.0;
float lbvec[MAXNCON], lbsum, min_lbsum, *mytpwgts, mytpwgts2[2], buffer[2];
MPI_Status status;
MPI_Comm ipcomm, srcomm;
struct {
float cost;
int rank;
} lpecost, gpecost;
IFSET(ctrl->dbglvl, DBG_TIME, starttimer(ctrl->InitPartTmr));
vtxdist = graph->vtxdist;
agraph = Mc_AssembleAdaptiveGraph(ctrl, graph, wspace);
nvtxs = cgraph.nvtxs = agraph->nvtxs;
nedges = cgraph.nedges = agraph->nedges;
ncon = cgraph.ncon = agraph->ncon;
xadj = cgraph.xadj = idxmalloc(nvtxs*(5+ncon)+1+nedges*2, "U_IP: xadj");
vwgt = cgraph.vwgt = xadj + nvtxs+1;
vsize = cgraph.vsize = xadj + nvtxs*(1+ncon)+1;
cgraph.where = agraph->where = part = xadj + nvtxs*(2+ncon)+1;
lwhere = xadj + nvtxs*(3+ncon)+1;
home = xadj + nvtxs*(4+ncon)+1;
adjncy = cgraph.adjncy = xadj + nvtxs*(5+ncon)+1;
adjwgt = cgraph.adjwgt = xadj + nvtxs*(5+ncon)+1 + nedges;
/* ADD: this assumes that tpwgts for all constraints is the same */
/* ADD: this is necessary because serial metis does not support the general case */
mytpwgts = fsmalloc(ctrl->nparts, 0.0, "mytpwgts");
for (i=0; i<ctrl->nparts; i++)
for (j=0; j<ncon; j++)
mytpwgts[i] += ctrl->tpwgts[i*ncon+j];
for (i=0; i<ctrl->nparts; i++)
mytpwgts[i] /= (float)ncon;
idxcopy(nvtxs+1, agraph->xadj, xadj);
idxcopy(nvtxs*ncon, agraph->vwgt, vwgt);
idxcopy(nvtxs, agraph->vsize, vsize);
idxcopy(nedges, agraph->adjncy, adjncy);
idxcopy(nedges, agraph->adjwgt, adjwgt);
/****************************************/
/****************************************/
if (ctrl->ps_relation == DISCOUPLED) {
rcounts = imalloc(ctrl->npes, "rcounts");
rdispls = imalloc(ctrl->npes+1, "rdispls");
for (i=0; i<ctrl->npes; i++) {
rdispls[i] = rcounts[i] = vtxdist[i+1]-vtxdist[i];
}
MAKECSR(i, ctrl->npes, rdispls);
MPI_Allgatherv((void *)graph->home, graph->nvtxs, IDX_DATATYPE,
(void *)part, rcounts, rdispls, IDX_DATATYPE, ctrl->comm);
for (i=0; i<agraph->nvtxs; i++)
home[i] = part[i];
GKfree((void **)&rcounts, (void **)&rdispls, LTERM);
}
else {
for (i=0; i<ctrl->npes; i++)
for (j=vtxdist[i]; j<vtxdist[i+1]; j++)
part[j] = home[j] = i;
}
/* Ensure that the initial partitioning is legal */
for (i=0; i<agraph->nvtxs; i++) {
if (part[i] >= ctrl->nparts)
part[i] = home[i] = part[i] % ctrl->nparts;
if (part[i] < 0)
part[i] = home[i] = (-1*part[i]) % ctrl->nparts;
}
/****************************************/
/****************************************/
IFSET(ctrl->dbglvl, DBG_REFINEINFO, Mc_ComputeSerialBalance(ctrl, agraph, agraph->where, lbvec));
IFSET(ctrl->dbglvl, DBG_REFINEINFO, rprintf(ctrl, "input cut: %d, balance: ", ComputeSerialEdgeCut(agraph)));
for (i=0; i<agraph->ncon; i++)
IFSET(ctrl->dbglvl, DBG_REFINEINFO, rprintf(ctrl, "%.3f ", lbvec[i]));
IFSET(ctrl->dbglvl, DBG_REFINEINFO, rprintf(ctrl, "\n"));
/****************************************/
/* Split the processors into two groups */
/****************************************/
sr = (ctrl->mype % 2 == 0) ? 1 : 0;
gd = (ctrl->mype % 2 == 1) ? 1 : 0;
if (graph->ncon > MAX_NCON_FOR_DIFFUSION || ctrl->npes == 1) {
sr = 1;
gd = 0;
}
sr_pe = 0;
gd_pe = 1;
MPI_Comm_split(ctrl->gcomm, sr, 0, &ipcomm);
MPI_Comm_rank(ipcomm, &mype);
MPI_Comm_size(ipcomm, &npes);
myctrl.dbglvl = 0;
myctrl.mype = mype;
myctrl.npes = npes;
myctrl.comm = ipcomm;
myctrl.sync = ctrl->sync;
myctrl.seed = ctrl->seed;
myctrl.nparts = ctrl->nparts;
myctrl.ipc_factor = ctrl->ipc_factor;
myctrl.redist_factor = ctrl->redist_base;
myctrl.partType = ADAPTIVE_PARTITION;
myctrl.ps_relation = DISCOUPLED;
myctrl.tpwgts = ctrl->tpwgts;
icopy(ncon, ctrl->tvwgts, myctrl.tvwgts);
icopy(ncon, ctrl->ubvec, myctrl.ubvec);
if (sr == 1) {
/*******************************************/
/* Half of the processors do scratch-remap */
/*******************************************/
ngroups = amax(amin(RIP_SPLIT_FACTOR, npes), 1);
MPI_Comm_split(ipcomm, mype % ngroups, 0, &srcomm);
MPI_Comm_rank(srcomm, &srmype);
MPI_Comm_size(srcomm, &srnpes);
moptions[0] = 0;
moptions[7] = ctrl->sync + (mype % ngroups) + 1;
idxset(nvtxs, 0, lwhere);
lnparts = ctrl->nparts;
fpart = fpe = 0;
lnpes = srnpes;
while (lnpes > 1 && lnparts > 1) {
ASSERT(ctrl, agraph->nvtxs > 1);
/* Determine the weights of the partitions */
mytpwgts2[0] = ssum(lnparts/2, mytpwgts+fpart);
mytpwgts2[1] = 1.0-mytpwgts2[0];
if (agraph->ncon == 1) {
METIS_WPartGraphKway2(&agraph->nvtxs, agraph->xadj, agraph->adjncy, agraph->vwgt,
agraph->adjwgt, &wgtflag, &numflag, &twoparts, mytpwgts2, moptions, &edgecut,
part);
}
else {
METIS_mCPartGraphRecursive2(&agraph->nvtxs, &ncon, agraph->xadj, agraph->adjncy,
agraph->vwgt, agraph->adjwgt, &wgtflag, &numflag, &twoparts, mytpwgts2,
moptions, &edgecut, part);
}
wsum = ssum(lnparts/2, mytpwgts+fpart);
sscale(lnparts/2, 1.0/wsum, mytpwgts+fpart);
sscale(lnparts-lnparts/2, 1.0/(1.0-wsum), mytpwgts+fpart+lnparts/2);
/* I'm picking the left branch */
if (srmype < fpe+lnpes/2) {
Mc_KeepPart(agraph, wspace, part, 0);
lnpes = lnpes/2;
lnparts = lnparts/2;
}
else {
Mc_KeepPart(agraph, wspace, part, 1);
fpart = fpart + lnparts/2;
fpe = fpe + lnpes/2;
lnpes = lnpes - lnpes/2;
lnparts = lnparts - lnparts/2;
}
}
/* In case srnpes is greater than or equal to nparts */
if (lnparts == 1) {
/* Only the first process will assign labels (for the reduction to work) */
if (srmype == fpe) {
for (i=0; i<agraph->nvtxs; i++)
lwhere[agraph->label[i]] = fpart;
}
}
/* In case srnpes is smaller than nparts */
else {
if (ncon == 1)
METIS_WPartGraphKway2(&agraph->nvtxs, agraph->xadj, agraph->adjncy, agraph->vwgt,
agraph->adjwgt, &wgtflag, &numflag, &lnparts, mytpwgts+fpart, moptions,
&edgecut, part);
else
METIS_mCPartGraphRecursive2(&agraph->nvtxs, &ncon, agraph->xadj, agraph->adjncy,
agraph->vwgt, agraph->adjwgt, &wgtflag, &numflag, &lnparts, mytpwgts+fpart,
moptions, &edgecut, part);
for (i=0; i<agraph->nvtxs; i++)
lwhere[agraph->label[i]] = fpart + part[i];
}
MPI_Allreduce((void *)lwhere, (void *)part, nvtxs, IDX_DATATYPE, MPI_SUM, srcomm);
edgecut = ComputeSerialEdgeCut(&cgraph);
Mc_ComputeSerialBalance(ctrl, &cgraph, part, lbvec);
lbsum = ssum(ncon, lbvec);
MPI_Allreduce((void *)&edgecut, (void *)&max_cut, 1, MPI_INT, MPI_MAX, ipcomm);
MPI_Allreduce((void *)&lbsum, (void *)&min_lbsum, 1, MPI_FLOAT, MPI_MIN, ipcomm);
lpecost.rank = ctrl->mype;
lpecost.cost = lbsum;
if (min_lbsum < UNBALANCE_FRACTION * (float)(ncon)) {
if (lbsum < UNBALANCE_FRACTION * (float)(ncon))
lpecost.cost = (float)edgecut;
else
lpecost.cost = (float)max_cut + lbsum;
}
MPI_Allreduce((void *)&lpecost, (void *)&gpecost, 1, MPI_FLOAT_INT, MPI_MINLOC, ipcomm);
if (ctrl->mype == gpecost.rank && ctrl->mype != sr_pe) {
MPI_Send((void *)part, nvtxs, IDX_DATATYPE, sr_pe, 1, ctrl->comm);
}
if (ctrl->mype != gpecost.rank && ctrl->mype == sr_pe) {
MPI_Recv((void *)part, nvtxs, IDX_DATATYPE, gpecost.rank, 1, ctrl->comm, &status);
}
if (ctrl->mype == sr_pe) {
idxcopy(nvtxs, part, lwhere);
SerialRemap(&cgraph, ctrl->nparts, home, lwhere, part, ctrl->tpwgts);
}
MPI_Comm_free(&srcomm);
}
/**************************************/
/* The other half do global diffusion */
/**************************************/
else {
/******************************************************************/
/* The next stmt is required to balance out the sr MPI_Comm_split */
/******************************************************************/
MPI_Comm_split(ipcomm, MPI_UNDEFINED, 0, &srcomm);
if (ncon == 1) {
rating = WavefrontDiffusion(&myctrl, agraph, home);
Mc_ComputeSerialBalance(ctrl, &cgraph, part, lbvec);
lbsum = ssum(ncon, lbvec);
/* Determine which PE computed the best partitioning */
MPI_Allreduce((void *)&rating, (void *)&max_rating, 1, MPI_FLOAT, MPI_MAX, ipcomm);
MPI_Allreduce((void *)&lbsum, (void *)&min_lbsum, 1, MPI_FLOAT, MPI_MIN, ipcomm);
lpecost.rank = ctrl->mype;
lpecost.cost = lbsum;
if (min_lbsum < UNBALANCE_FRACTION * (float)(ncon)) {
if (lbsum < UNBALANCE_FRACTION * (float)(ncon))
lpecost.cost = rating;
else
lpecost.cost = max_rating + lbsum;
}
MPI_Allreduce((void *)&lpecost, (void *)&gpecost, 1, MPI_FLOAT_INT, MPI_MINLOC, ipcomm);
/* Now send this to the coordinating processor */
if (ctrl->mype == gpecost.rank && ctrl->mype != gd_pe)
MPI_Send((void *)part, nvtxs, IDX_DATATYPE, gd_pe, 1, ctrl->comm);
if (ctrl->mype != gpecost.rank && ctrl->mype == gd_pe)
MPI_Recv((void *)part, nvtxs, IDX_DATATYPE, gpecost.rank, 1, ctrl->comm, &status);
if (ctrl->mype == gd_pe) {
idxcopy(nvtxs, part, lwhere);
SerialRemap(&cgraph, ctrl->nparts, home, lwhere, part, ctrl->tpwgts);
}
}
else {
Mc_Diffusion(&myctrl, agraph, graph->vtxdist, agraph->where, home, wspace, N_MOC_GD_PASSES);
}
}
if (graph->ncon <= MAX_NCON_FOR_DIFFUSION) {
if (ctrl->mype == sr_pe || ctrl->mype == gd_pe) {
/********************************************************************/
/* The coordinators from each group decide on the best partitioning */
/********************************************************************/
my_cut = (float) ComputeSerialEdgeCut(&cgraph);
my_totalv = (float) Mc_ComputeSerialTotalV(&cgraph, home);
Mc_ComputeSerialBalance(ctrl, &cgraph, part, lbvec);
my_balance = ssum(cgraph.ncon, lbvec);
my_balance /= (float) cgraph.ncon;
my_cost = ctrl->ipc_factor * my_cut + REDIST_WGT * ctrl->redist_base * my_totalv;
IFSET(ctrl->dbglvl, DBG_REFINEINFO, printf("%s initial cut: %.1f, totalv: %.1f, balance: %.3f\n",
(ctrl->mype == sr_pe ? "scratch-remap" : "diffusion"), my_cut, my_totalv, my_balance));
if (ctrl->mype == gd_pe) {
buffer[0] = my_cost;
buffer[1] = my_balance;
MPI_Send((void *)buffer, 2, MPI_FLOAT, sr_pe, 1, ctrl->comm);
}
else {
MPI_Recv((void *)buffer, 2, MPI_FLOAT, gd_pe, 1, ctrl->comm, &status);
your_cost = buffer[0];
your_balance = buffer[1];
}
}
if (ctrl->mype == sr_pe) {
who_wins = gd_pe;
if ((my_balance < 1.1 && your_balance > 1.1) ||
(my_balance < 1.1 && your_balance < 1.1 && my_cost < your_cost) ||
(my_balance > 1.1 && your_balance > 1.1 && my_balance < your_balance)) {
who_wins = sr_pe;
}
}
MPI_Bcast((void *)&who_wins, 1, MPI_INT, sr_pe, ctrl->comm);
}
else {
who_wins = sr_pe;
}
MPI_Bcast((void *)part, nvtxs, IDX_DATATYPE, who_wins, ctrl->comm);
idxcopy(graph->nvtxs, part+vtxdist[ctrl->mype], graph->where);
MPI_Comm_free(&ipcomm);
GKfree((void **)&xadj, (void **)&mytpwgts, LTERM);
/* For whatever reason, FreeGraph crashes here...so explicitly free the memory.
FreeGraph(agraph);
*/
GKfree((void **)&agraph->xadj, (void **)&agraph->adjncy, (void **)&agraph->vwgt, (void **)&agraph->nvwgt, LTERM);
GKfree((void **)&agraph->vsize, (void **)&agraph->adjwgt, (void **)&agraph->label, LTERM);
GKfree((void **)&agraph, LTERM);
IFSET(ctrl->dbglvl, DBG_TIME, stoptimer(ctrl->InitPartTmr));
}
