int nway_klv(struct vtx_data **graph, /* data structure for graph */
int nvtxs, /* number of vtxs in graph */
struct bilist ** lbuckets, /* array of lists for bucket sort */
struct bilist ** rbuckets, /* array of lists for bucket sort */
struct bilist * llistspace, /* list data structure for each vertex */
struct bilist * rlistspace, /* list data structure for each vertex */
int * ldvals, /* d-values for each transition */
int * rdvals, /* d-values for each transition */
int * sets, /* processor each vertex is assigned to */
int maxdval, /* maximum d-value for a vertex */
double * goal, /* desired set sizes */
int max_dev, /* largest allowed deviation from balance */
int ** bndy_list, /* list of vertices on boundary (0 ends) */
double * weightsum /* sum of vweights in each set (in and out) */
)
{
struct bilist **to_buckets; /* buckets I'm moving to */
struct bilist **from_buckets; /* buckets I'm moving from */
struct bilist * to_listspace; /* list structure I'm moving to */
struct bilist * from_listspace; /* list structure I'm moving from */
struct bilist * out_list; /* list of vtxs moved out of separator */
int * to_dvals; /* d-values I'm moving to */
int * from_dvals; /* d-values I'm moving from */
extern double kl_bucket_time; /* time spent in KL bucketsort */
extern int KL_BAD_MOVES; /* # bad moves in a row to stop KL */
extern int DEBUG_KL; /* debug flag for KL */
extern int KL_NTRIES_BAD; /* number of unhelpful passes before quitting */
extern int KL_MAX_PASS; /* maximum # outer KL loops */
int * bspace; /* list of active vertices for bucketsort */
int * edges; /* edge list for a vertex */
int * edges2; /* edge list for a vertex */
int * bdy_ptr; /* loops through bndy_list */
double total_weight; /* weight of all vertices */
double partial_weight; /* weight of vertices not in separator */
double ratio; /* fraction of weight not in separator */
double time; /* timing parameter */
double delta0; /* largest negative deviation from goal size */
double delta1; /* largest negative deviation from goal size */
double left_imbalance = 0.0; /* imbalance if I move to the left */
double right_imbalance; /* imbalance if I move to the right */
double balance_val; /* how imbalanced is it */
double balance_best; /* best balance yet if trying hard */
int flag; /* condition indicator */
int to = -1, from; /* sets moving into / out of */
int rtop, ltop; /* top of each set of buckets */
int * to_top; /* ptr to top of set moving to */
int lvtx, rvtx; /* next vertex to move left/right */
int lweight, rweight; /* weights of moving vertices */
int weightfrom = 0; /* weight moving out of a set */
int list_length; /* how long is list of vertices to bucketsort? */
int balanced; /* is partition balanced? */
int temp_balanced; /* is intermediate partition balanced? */
int ever_balanced; /* has any partition been balanced? */
int bestvtx = -1; /* best vertex to move */
int bestval = -1; /* best change in value for a vtx move */
int vweight; /* weight of best vertex */
int gtotal; /* sum of changes from moving */
int improved; /* total improvement from KL */
double bestg; /* maximum gtotal found in KL loop */
double bestg_min; /* smaller than any possible bestg */
int beststep; /* step where maximum value occurred */
int bestlength; /* step where maximum value occurred */
int neighbor; /* neighbor of a vertex */
int step_cutoff; /* number of negative steps in a row allowed */
int cost_cutoff; /* amount of negative d-values allowed */
int neg_steps; /* number of negative steps in a row */
int neg_cost; /* decrease in sum of d-values */
int vtx; /* vertex number */
int dval; /* dval of a vertex */
int group, group2; /* set that a vertex is assigned to */
int left_too_big; /* is left set too large? */
int right_too_big; /* is right set too large? */
int vwgt; /* weight of a vertex */
int gain; /* reduction in separator due to a move */
int neighbor2; /* neighbor of a vertex */
int step; /* loops through movements of vertices */
int parity; /* sort forwards or backwards? */
int done; /* has termination criteria been achieved? */
int nbad; /* number of unhelpful passes in a row */
int npass; /* total number of passes */
int nbadtries; /* number of unhelpful passes before quitting */
int enforce_balance; /* force a balanced partition? */
int enforce_balance_hard; /* really force a balanced partition? */
int i, j, k; /* loop counters */
double seconds(), drandom();
int make_sep_list();
void bucketsortsv(), clear_dvals(), p1bucket();
void removebilist(), movebilist(), add2bilist();
nbadtries = KL_NTRIES_BAD;
enforce_balance = FALSE;
enforce_balance_hard = FALSE;
total_weight = goal[0] + goal[1];
bspace = smalloc_ret((nvtxs + 1) * sizeof(int));
if (bspace == NULL) {
return (1);
}
bdy_ptr = *bndy_list;
list_length = 0;
while (*bdy_ptr != 0) {
bspace[list_length++] = *bdy_ptr++;
}
sfree(*bndy_list);
clear_dvals(graph, nvtxs, ldvals, rdvals, bspace, list_length);
step_cutoff = KL_BAD_MOVES;
cost_cutoff = maxdval * step_cutoff / 7;
if (cost_cutoff < step_cutoff)
cost_cutoff = step_cutoff;
partial_weight = weightsum[0] + weightsum[1];
ratio = partial_weight / total_weight;
delta0 = fabs(weightsum[0] - goal[0] * ratio);
delta1 = fabs(weightsum[1] - goal[1] * ratio);
balanced =
(delta0 + delta1 <= max_dev) && weightsum[0] != total_weight && weightsum[1] != total_weight;
bestg_min = -2.0 * nvtxs * maxdval;
parity = FALSE;
nbad = 0;
npass = 0;
improved = 0;
done = FALSE;
while (!done) {
npass++;
ever_balanced = FALSE;
balance_best = delta0 + delta1;
/* Initialize various quantities. */
ltop = rtop = 2 * maxdval;
gtotal = 0;
bestg = bestg_min;
beststep = -1;
bestlength = list_length;
out_list = NULL;
neg_steps = 0;
/* Compute the initial d-values, and bucket-sort them. */
time = seconds();
bucketsortsv(graph, nvtxs, lbuckets, rbuckets, llistspace, rlistspace, ldvals, rdvals, sets,
maxdval, parity, bspace, list_length);
parity = !parity;
kl_bucket_time += seconds() - time;
if (DEBUG_KL > 2) {
printf("After sorting, left buckets:\n");
p1bucket(lbuckets, llistspace, maxdval);
printf(" right buckets:\n");
p1bucket(rbuckets, rlistspace, maxdval);
}
/* Now determine the set of vertex moves. */
for (step = 1;; step++) {
/* Find the highest d-value in each set. */
/* But only consider moves from large to small sets, or moves */
/* in which balance is preserved. */
/* Break ties in some nonarbitrary manner. */
bestval = -maxdval - 1;
partial_weight = weightsum[0] + weightsum[1];
ratio = partial_weight / total_weight;
left_too_big = (weightsum[0] > (goal[0] + .5 * max_dev) * ratio);
right_too_big = (weightsum[1] > (goal[1] + .5 * max_dev) * ratio);
while (ltop >= 0 && lbuckets[ltop] == NULL) {
--ltop;
}
if (ltop >= 0 && !left_too_big) {
lvtx = ((long)lbuckets[ltop] - (long)llistspace) / sizeof(struct bilist);
lweight = graph[lvtx]->vwgt;
rweight = lweight - (ltop - maxdval);
weightfrom = rweight;
to = 0;
bestvtx = lvtx;
bestval = ltop - maxdval;
partial_weight = weightsum[0] + lweight + weightsum[1] - rweight;
ratio = partial_weight / total_weight;
left_imbalance = max(fabs(weightsum[0] + lweight - goal[0] * ratio),
fabs(weightsum[1] - rweight - goal[1] * ratio));
}
while (rtop >= 0 && rbuckets[rtop] == NULL) {
--rtop;
}
if (rtop >= 0 && !right_too_big) {
rvtx = ((long)rbuckets[rtop] - (long)rlistspace) / sizeof(struct bilist);
rweight = graph[rvtx]->vwgt;
lweight = rweight - (rtop - maxdval);
partial_weight = weightsum[0] - lweight + weightsum[1] + rweight;
ratio = partial_weight / total_weight;
right_imbalance = max(fabs(weightsum[0] - lweight - goal[0] * ratio),
fabs(weightsum[1] + rweight - goal[1] * ratio));
if (rtop - maxdval > bestval || (rtop - maxdval == bestval &&
(right_imbalance < left_imbalance ||
(right_imbalance == left_imbalance && drandom() < .5)))) {
to = 1;
weightfrom = lweight;
bestvtx = rvtx;
bestval = rtop - maxdval;
}
}
if (bestval == -maxdval - 1) { /* No allowed moves */
if (DEBUG_KL > 0) {
printf("No KLV moves at step %d. bestg = %g at step %d.\n", step, bestg, beststep);
}
break;
}
if (to == 0) {
from = 1;
to_listspace = llistspace;
from_listspace = rlistspace;
to_dvals = ldvals;
from_dvals = rdvals;
to_buckets = lbuckets;
from_buckets = rbuckets;
to_top = <op;
}
else {
from = 0;
to_listspace = rlistspace;
from_listspace = llistspace;
to_dvals = rdvals;
from_dvals = ldvals;
to_buckets = rbuckets;
from_buckets = lbuckets;
to_top = &rtop;
}
vweight = graph[bestvtx]->vwgt;
weightsum[to] += vweight;
weightsum[from] -= weightfrom;
/* Check if this partition is balanced. */
partial_weight = weightsum[0] + weightsum[1];
ratio = partial_weight / total_weight;
delta0 = fabs(weightsum[0] - goal[0] * ratio);
delta1 = fabs(weightsum[1] - goal[1] * ratio);
temp_balanced = (delta0 + delta1 <= max_dev) && weightsum[0] != total_weight &&
weightsum[1] != total_weight;
ever_balanced = (ever_balanced || temp_balanced);
balance_val = delta0 + delta1;
gtotal += bestval;
if ((gtotal > bestg && temp_balanced) ||
(enforce_balance_hard && balance_val < balance_best)) {
bestg = gtotal;
beststep = step;
if (balance_val < balance_best) {
balance_best = balance_val;
}
if (temp_balanced) {
enforce_balance_hard = FALSE;
}
}
if (DEBUG_KL > 1) {
printf("At KLV step %d, bestvtx=%d, bestval=%d (2->%d), wt0 = %g, wt1 = %g\n", step,
bestvtx, bestval, to, weightsum[0], weightsum[1]);
}
/* Monitor the stopping criteria. */
if (bestval < 0) {
if (!enforce_balance || ever_balanced)
neg_steps++;
if (bestg != bestg_min)
neg_cost = bestg - gtotal;
else
neg_cost = -maxdval - 1;
if ((neg_steps > step_cutoff || neg_cost > cost_cutoff) &&
!(enforce_balance && bestg == bestg_min)) {
if (DEBUG_KL > 0) {
if (neg_steps > step_cutoff) {
printf("KLV step cutoff at step %d. bestg = %g at step %d.\n", step, bestg,
beststep);
}
else if (neg_cost > cost_cutoff) {
printf("KLV cost cutoff at step %d. bestg = %g at step %d.\n", step, bestg,
beststep);
}
}
gtotal -= bestval;
weightsum[to] -= vweight;
weightsum[from] += weightfrom;
break;
}
}
else if (bestval > 0) {
neg_steps = 0;
}
/* Remove vertex from its buckets, and flag it as finished. */
sets[bestvtx] = to;
removebilist(&to_listspace[bestvtx], &to_buckets[bestval + maxdval]);
/*
printf("After to removebilist\n");
p1bucket(to_buckets, to_listspace, maxdval);
*/
if (from_dvals[bestvtx] != -maxdval - 1) {
removebilist(&from_listspace[bestvtx], &from_buckets[from_dvals[bestvtx] + maxdval]);
/*
printf("After from removebilist\n");
p1bucket(from_buckets, from_listspace, maxdval);
*/
}
from_dvals[bestvtx] = -maxdval - 1;
/* Now keep track of vertices moved out of separator so */
/* I can restore them as needed. */
llistspace[bestvtx].next = out_list;
out_list = &(llistspace[bestvtx]);
/* Now update the d-values of all the neighbors */
/* And neighbors of neighbors ... */
/* If left move:
1. Separator neighbors right gain => infinity
2. Left neighbors unaffected.
3. Right neighbors move into separator.
A. Right gain = infinity.
B. Left gain = computed.
C. For any of their neighbors in separator increase left gain.
*/
edges = graph[bestvtx]->edges;
for (j = graph[bestvtx]->nedges - 1; j; j--) {
neighbor = *(++edges);
group = sets[neighbor];
if (group == 2) { /* In separator. */
gain = from_dvals[neighbor] + maxdval;
/* Gain in the from direction => -infinity */
if (gain >= 0) {
removebilist(&from_listspace[neighbor], &from_buckets[gain]);
/*
printf("\n After removing %d\n", neighbor);
p1bucket(from_buckets, from_listspace, maxdval);
*/
from_dvals[neighbor] = -maxdval - 1;
}
}
else if (group == from) {
/* Gain in the from direction => -infinity */
sets[neighbor] = 2;
from_dvals[neighbor] = -maxdval - 1;
if (to == 0) {
bspace[list_length++] = -neighbor;
}
else {
bspace[list_length++] = neighbor;
}
edges2 = graph[neighbor]->edges;
vwgt = graph[neighbor]->vwgt;
gain = graph[neighbor]->vwgt;
flag = FALSE;
for (k = graph[neighbor]->nedges - 1; k; k--) {
neighbor2 = *(++edges2);
group2 = sets[neighbor2];
if (group2 == 2) {
dval = to_dvals[neighbor2] + maxdval;
if (dval >= 0) {
movebilist(&to_listspace[neighbor2], &to_buckets[dval], &to_buckets[dval + vwgt]);
/*
printf("\n After moving %d from bucket %d to bucket
%d\n", neighbor2, dval, dval + vwgt);
p1bucket(to_buckets, to_listspace, maxdval);
*/
to_dvals[neighbor2] += vwgt;
dval += vwgt;
if (dval > *to_top) {
*to_top = dval;
}
}
}
else if (group2 == from) {
gain -= graph[neighbor2]->vwgt;
if (to_dvals[neighbor2] + maxdval < 0) {
flag = TRUE;
}
}
}
if (flag) { /* Not allowed to move further. */
to_dvals[neighbor] = -maxdval - 1;
}
else {
to_dvals[neighbor] = gain;
/* place in appropriate bucket */
gain += maxdval;
add2bilist(&to_listspace[neighbor], &to_buckets[gain]);
/*
printf("\nAfter adding %d to bucket %d\n", neighbor, gain -
maxdval);
p1bucket(to_buckets, to_listspace, maxdval);
*/
if (gain > *to_top)
*to_top = gain;
}
}
}
if (beststep == step) {
bestlength = list_length;
}
if (DEBUG_KL > 2) {
printf("\n-- After step, left buckets:\n");
p1bucket(lbuckets, llistspace, maxdval);
printf(" right buckets:\n");
p1bucket(rbuckets, rlistspace, maxdval);
}
}
/* Done with a pass; should we actually perform any swaps? */
if (bestg > 0 || (bestg != bestg_min && !balanced && enforce_balance)) {
improved += bestg;
}
else {
if (enforce_balance_hard) {
/* I've done the best I can, give up. */
done = TRUE;
}
if (enforce_balance) {
enforce_balance_hard = TRUE;
}
enforce_balance = TRUE;
nbad++;
}
/* Work backwards, undoing all the undesirable moves. */
/* First reset vertices moved out of the separator. */
if (out_list) {
if (beststep < 0)
beststep = 0;
for (i = step - 1; i > beststep; i--) {
vtx = ((long)out_list - (long)llistspace) / sizeof(struct bilist);
if (sets[vtx] != 2) {
weightsum[sets[vtx]] -= graph[vtx]->vwgt;
}
sets[vtx] = 2;
out_list = out_list->next;
}
}
for (i = list_length - 1; i >= bestlength; i--) {
vtx = bspace[i];
if (vtx < 0) {
if (sets[-vtx] == 2) {
weightsum[1] += graph[-vtx]->vwgt;
}
sets[-vtx] = 1;
}
else {
if (sets[vtx] == 2) {
weightsum[0] += graph[vtx]->vwgt;
}
sets[vtx] = 0;
}
}
partial_weight = weightsum[0] + weightsum[1];
ratio = partial_weight / total_weight;
delta0 = fabs(weightsum[0] - goal[0] * ratio);
delta1 = fabs(weightsum[1] - goal[1] * ratio);
balanced = (delta0 + delta1 <= max_dev) && weightsum[0] != total_weight &&
weightsum[1] != total_weight;
done = done || (nbad >= nbadtries && balanced);
if (KL_MAX_PASS > 0) {
done = done || (npass == KL_MAX_PASS && balanced);
}
if (!done) { /* Rezero dval values. */
clear_dvals(graph, nvtxs, ldvals, rdvals, bspace, list_length);
}
/* Construct list of separator vertices to pass to buckets or return */
list_length = make_sep_list(bspace, list_length, sets);
if (done) {
bspace[list_length] = 0;
bspace = srealloc(bspace, (list_length + 1) * sizeof(int));
*bndy_list = bspace;
}
gain = 0;
j = k = 0;
for (i = 1; i <= nvtxs; i++) {
if (sets[i] == 0)
j += graph[i]->vwgt;
else if (sets[i] == 1)
k += graph[i]->vwgt;
else if (sets[i] == 2)
gain += graph[i]->vwgt;
}
/*
printf("\nAfter pass of KLV: sets = %d/%d, sep = %d (bestg = %g)\n\n\n",
j, k, gain, bestg);
*/
}
if (DEBUG_KL > 0) {
printf(" KLV required %d passes to improve by %d.\n", npass, improved);
}
return (0);
}
int
nway_kl (
struct vtx_data **graph, /* data structure for graph */
int nvtxs, /* number of vtxs in graph */
struct bilist ****buckets, /* array of lists for bucket sort */
struct bilist **listspace, /* list data structure for each vertex */
int **tops, /* 2-D array of top of each set of buckets */
int **dvals, /* d-values for each transition */
int *sets, /* processor each vertex is assigned to */
int maxdval, /* maximum d-value for a vertex */
int nsets, /* number of sets divided into */
double *goal, /* desired set sizes */
float *term_wgts[], /* weights for terminal propogation */
int (*hops)[MAXSETS], /* cost of set transitions */
int max_dev, /* largest allowed deviation from balance */
int using_ewgts, /* are edge weights being used? */
int **bndy_list, /* list of vertices on boundary (0 ends) */
double *startweight /* sum of vweights in each set (in and out) */
)
/* Suaris and Kedem algorithm for quadrisection, generalized to an */
/* arbitrary number of sets, with intra-set cost function specified by hops. */
/* Note: this is for a single divide step. */
/* Also, sets contains an intial (possibly crummy) partitioning. */
{
extern double kl_bucket_time; /* time spent in KL bucketsort */
extern int KL_BAD_MOVES; /* # bad moves in a row to stop KL */
extern int DEBUG_KL; /* debug flag for KL */
extern int KL_RANDOM; /* use randomness in KL? */
extern int KL_NTRIES_BAD; /* number of unhelpful passes before quitting */
extern int KL_UNDO_LIST; /* should I back out of changes or start over? */
extern int KL_MAX_PASS; /* maximum number of outer KL loops */
extern double CUT_TO_HOP_COST; /* if term_prop; cut/hop importance */
struct bilist *movelist; /* list of vtxs to be moved */
struct bilist **endlist; /* end of movelists */
struct bilist *bestptr; /* best vertex in linked list */
struct bilist *bptr; /* loops through bucket list */
float *ewptr=NULL; /* loops through edge weights */
double *locked=NULL; /* weight of vertices locked in a set */
double *loose=NULL; /* weight of vtxs that can move from a set */
int *bspace=NULL; /* list of active vertices for bucketsort */
double *weightsum=NULL; /* sum of vweights for each partition */
int *edges=NULL; /* edge list for a vertex */
int *bdy_ptr=NULL; /* loops through bndy_list */
double time; /* timing parameter */
double delta; /* desire of sets to change size */
double bestdelta=-1; /* strongest delta value */
double deltaplus; /* largest negative deviation from goal size */
double deltaminus; /* largest negative deviation from goal size */
int list_length; /* how long is list of vertices to bucketsort? */
int balanced; /* is partition balanced? */
int temp_balanced; /* is intermediate partition balanced? */
int ever_balanced; /* has any partition been balanced? */
int bestvtx=-1; /* best vertex to move */
int bestval=-1; /* best change in value for a vtx move */
int bestfrom=-1, bestto=-1; /* sets best vertex moves between */
int vweight; /* weight of best vertex */
int gtotal; /* sum of changes from moving */
int improved; /* total improvement from KL */
double balance_val=0.0; /* how imbalanced is it */
double balance_best; /* best balance yet if trying hard */
double bestg; /* maximum gtotal found in KL loop */
double bestg_min; /* smaller than any possible bestg */
int beststep; /* step where maximum value occurred */
int neighbor; /* neighbor of a vertex */
int step_cutoff; /* number of negative steps in a row allowed */
int cost_cutoff; /* amount of negative d-values allowed */
int neg_steps; /* number of negative steps in a row */
int neg_cost; /* decrease in sum of d-values */
int vtx; /* vertex number */
int dval; /* dval of a vertex */
int group; /* set that a vertex is assigned to */
double cut_cost; /* if term_prop; relative cut/hop importance */
int diff; /* change in a d-value */
int stuck1st, stuck2nd; /* how soon will moves be disallowed? */
int beststuck1=-1, beststuck2=-1; /* best stuck values for tie-breaking */
int eweight; /* a particular edge weight */
int worth_undoing; /* is it worth undoing list? */
float undo_frac; /* fraction of vtxs indicating worth of undoing */
int step; /* loops through movements of vertices */
int parity; /* sort forwards or backwards? */
int done; /* has termination criteria been achieved? */
int nbad; /* number of unhelpful passes in a row */
int npass; /* total number of passes */
int nbadtries; /* number of unhelpful passes before quitting */
int enforce_balance; /* force a balanced partition? */
int enforce_balance_hard; /* really force a balanced partition? */
int balance_trouble; /* even balance_hard isn't working */
int size; /* array spacing */
int i, j, k, l; /* loop counters */
double drandom(), seconds();
int make_kl_list();
void bucketsorts(), bucketsorts_bi(), bucketsort1();
void pbuckets(), removebilist(), movebilist(), make_bndy_list();
nbadtries = KL_NTRIES_BAD;
enforce_balance = FALSE;
temp_balanced = FALSE;
enforce_balance_hard = FALSE;
balance_trouble = FALSE;
size = (int) (&(listspace[0][1]) - &(listspace[0][0]));
undo_frac = .3;
cut_cost = 1;
if (term_wgts[1] != NULL) {
if (CUT_TO_HOP_COST > 1) {
cut_cost = CUT_TO_HOP_COST;
}
}
bspace = smalloc_ret(nvtxs * sizeof(int));
weightsum = smalloc_ret(nsets * sizeof(double));
locked = smalloc_ret(nsets * sizeof(double));
loose = smalloc_ret(nsets * sizeof(double));
if (bspace == NULL || weightsum == NULL || locked == NULL || loose == NULL) {
sfree(loose);
sfree(locked);
sfree(weightsum);
sfree(bspace);
return(1);
}
if (*bndy_list != NULL) {
bdy_ptr = *bndy_list;
list_length = 0;
while (*bdy_ptr != 0) {
bspace[list_length++] = *bdy_ptr++;
}
sfree(*bndy_list);
if (list_length == 0) { /* No boundary -> make everybody bndy. */
for (i = 0; i < nvtxs; i++) {
bspace[i] = i + 1;
}
list_length = nvtxs;
}
/* Set dvals to flag uninitialized vertices. */
for (i = 1; i <= nvtxs; i++) {
dvals[i][0] = 3 * maxdval;
}
}
else {
list_length = nvtxs;
}
step_cutoff = KL_BAD_MOVES;
cost_cutoff = maxdval * step_cutoff / 7;
if (cost_cutoff < step_cutoff)
cost_cutoff = step_cutoff;
deltaminus = deltaplus = 0;
for (i = 0; i < nsets; i++) {
if (startweight[i] - goal[i] > deltaplus) {
deltaplus = startweight[i] - goal[i];
}
else if (goal[i] - startweight[i] > deltaminus) {
deltaminus = goal[i] - startweight[i];
}
}
balanced = (deltaplus + deltaminus <= max_dev);
bestg_min = -2.0 * nvtxs * maxdval;
parity = FALSE;
eweight = cut_cost + .5;
nbad = 0;
npass = 0;
improved = 0;
done = FALSE;
while (!done) {
npass++;
ever_balanced = FALSE;
/* Initialize various quantities. */
balance_best = 0;
for (i = 0; i < nsets; i++) {
for (j = 0; j < nsets; j++)
tops[i][j] = 2 * maxdval;
weightsum[i] = startweight[i];
loose[i] = weightsum[i];
locked[i] = 0;
balance_best += goal[i];
}
gtotal = 0;
bestg = bestg_min;
beststep = -1;
movelist = NULL;
endlist = &movelist;
neg_steps = 0;
/* Compute the initial d-values, and bucket-sort them. */
time = seconds();
if (nsets == 2) {
bucketsorts_bi(graph, nvtxs, buckets, listspace, dvals, sets, term_wgts,
maxdval, nsets, parity, hops, bspace, list_length, npass,
using_ewgts);
}
else {
bucketsorts(graph, nvtxs, buckets, listspace, dvals, sets, term_wgts,
maxdval, nsets, parity, hops, bspace, list_length, npass,
using_ewgts);
}
parity = !parity;
kl_bucket_time += seconds() - time;
if (DEBUG_KL > 2) {
pbuckets(buckets, listspace, maxdval, nsets);
}
/* Now determine the set of K-L moves. */
for (step = 1;; step++) {
/* Find the highest d-value in each set. */
/* But only consider moves from large to small sets, or moves */
/* in which balance is preserved. */
/* Break ties in some nonarbitrary manner. */
bestval = -maxdval - 1;
for (i = 0; i < nsets; i++)
for (j = 0; j < nsets; j++)
/* Only allow moves from large sets to small sets, or */
/* moves which preserve balance. */
if (i != j) {
/* Find the best move from i to j. */
for (k = tops[i][j]; k >= 0 && buckets[i][j][k] == NULL;
k--) ;
tops[i][j] = k;
if (k >= 0) {
l = (j > i) ? j - 1 : j;
vtx = ((int) (buckets[i][j][k] - listspace[l])) / size;
vweight = graph[vtx]->vwgt;
if ((enforce_balance_hard &&
weightsum[i] >= goal[i] && weightsum[j] <= goal[j] &&
weightsum[i] - goal[i] - (weightsum[j] - goal[j]) >
max_dev) ||
(!enforce_balance_hard &&
weightsum[i] >= goal[i] && weightsum[j] <= goal[j]) ||
(!enforce_balance_hard &&
weightsum[i] - vweight - goal[i] > -(double)((max_dev + 1) / 2) &&
weightsum[j] + vweight - goal[j] < (double)((max_dev + 1) / 2))) {
/* Is it the best move seen so far? */
if (k - maxdval > bestval) {
bestval = k - maxdval;
bestvtx = vtx;
bestto = j;
/* DO I NEED ALL THIS DATA? Just to break ties. */
bestdelta = fabs(weightsum[i] - vweight - goal[i]) +
fabs(weightsum[j] + vweight - goal[j]);
beststuck1 = min(loose[i], goal[j] - locked[j]);
beststuck2 = max(loose[i], goal[j] - locked[j]);
}
else if (k - maxdval == bestval) {
/* Tied. Is better balanced than current best? */
/* If tied, move among sets with most freedom. */
stuck1st = min(loose[i], goal[j] - locked[j]);
stuck2nd = max(loose[i], goal[j] - locked[j]);
delta = fabs(weightsum[i] - vweight - goal[i]) +
fabs(weightsum[j] + vweight - goal[j]);
/* NOTE: Randomization in this check isn't ideal */
/* if more than two guys are tied. */
if (delta < bestdelta ||
(delta == bestdelta && (stuck1st > beststuck1 ||
(stuck1st == beststuck1 &&
(stuck2nd > beststuck2 ||
(stuck2nd == beststuck2 &&
(KL_RANDOM && drandom() < .5))))))) {
bestval = k - maxdval;
bestvtx = vtx;
bestto = j;
bestdelta = delta;
beststuck1 = stuck1st;
beststuck2 = stuck2nd;
}
}
}
}
}
if (bestval == -maxdval - 1) { /* No allowed moves */
if (DEBUG_KL > 0) {
printf("No KL moves at step %d. bestg = %g at step %d.\n",
step, bestg, beststep);
}
break;
}
bestptr = &(listspace[0][bestvtx]);
bestfrom = sets[bestvtx];
vweight = graph[bestvtx]->vwgt;
weightsum[bestto] += vweight;
weightsum[bestfrom] -= vweight;
loose[bestfrom] -= vweight;
locked[bestto] += vweight;
if (enforce_balance) { /* Check if this partition is balanced. */
deltaminus = deltaplus = 0;
for (i = 0; i < nsets; i++) {
if (weightsum[i] - goal[i] > deltaplus) {
deltaplus = weightsum[i] - goal[i];
}
else if (goal[i] - weightsum[i] > deltaminus) {
deltaminus = goal[i] - weightsum[i];
}
}
balance_val = deltaminus + deltaplus;
temp_balanced = (balance_val <= max_dev);
ever_balanced = (ever_balanced || temp_balanced);
}
gtotal += bestval;
if (((gtotal > bestg && (!enforce_balance || temp_balanced)) ||
(enforce_balance_hard && balance_val < balance_best)) &&
step != nvtxs) {
bestg = gtotal;
beststep = step;
if (enforce_balance_hard) {
balance_best = balance_val;
}
if (temp_balanced) {
enforce_balance_hard = FALSE;
}
}
if (DEBUG_KL > 1) {
printf("At KL step %d, bestvtx=%d, bestval=%d (%d-> %d)\n",
step, bestvtx, bestval, bestfrom, bestto);
}
/* Monitor the stopping criteria. */
if (bestval < 0) {
if (!enforce_balance || ever_balanced)
neg_steps++;
if (bestg != bestg_min)
neg_cost = bestg - gtotal;
else
neg_cost = -maxdval - 1;
if ((neg_steps > step_cutoff || neg_cost > cost_cutoff) &&
!(enforce_balance && bestg == bestg_min) &&
(beststep != step)) {
if (DEBUG_KL > 0) {
if (neg_steps > step_cutoff) {
printf("KL step cutoff at step %d. bestg = %g at step %d.\n",
step, bestg, beststep);
}
else if (neg_cost > cost_cutoff) {
printf("KL cost cutoff at step %d. bestg = %g at step %d.\n",
step, bestg, beststep);
}
}
break;
}
}
else if (bestval > 0) {
neg_steps = 0;
}
/* Remove vertex from its buckets, and flag it as finished. */
l = 0;
for (k = 0; k < nsets; k++) {
if (k != bestfrom) {
dval = dvals[bestvtx][l] + maxdval;
removebilist(&listspace[l][bestvtx],
&buckets[bestfrom][k][dval]);
l++;
}
}
/* Is there a better way to do this? */
sets[bestvtx] = -sets[bestvtx] - 1;
/* Set up the linked list of moved vertices. */
bestptr->next = NULL;
bestptr->prev = (struct bilist *) (unsigned long) bestto;
*endlist = bestptr;
endlist = &(bestptr->next);
/* Now update the d-values of all the neighbors */
edges = graph[bestvtx]->edges;
if (using_ewgts)
ewptr = graph[bestvtx]->ewgts;
for (j = graph[bestvtx]->nedges - 1; j; j--) {
neighbor = *(++edges);
if (using_ewgts)
eweight = *(++ewptr) * cut_cost + .5;
/* First make sure neighbor is alive. */
if (sets[neighbor] >= 0) {
group = sets[neighbor];
if (dvals[neighbor][0] >= 3 * maxdval) {
/* New vertex, not yet in buckets. */
/* Can't be neighbor of moved vtx, so compute */
/* inital dvals and buckets, then update. */
bucketsort1(graph, neighbor, buckets, listspace, dvals, sets,
term_wgts, maxdval, nsets, hops, using_ewgts);
}
l = 0;
for (k = 0; k < nsets; k++) {
if (k != group) {
diff = eweight * (
hops[k][bestfrom] - hops[group][bestfrom] +
hops[group][bestto] - hops[k][bestto]);
dval = dvals[neighbor][l] + maxdval;
movebilist(&listspace[l][neighbor],
&buckets[group][k][dval],
&buckets[group][k][dval + diff]);
dvals[neighbor][l] += diff;
dval += diff;
if (dval > tops[group][k])
tops[group][k] = dval;
l++;
}
}
}
}
if (DEBUG_KL > 2) {
pbuckets(buckets, listspace, maxdval, nsets);
}
}
/* Done with a pass; should we actually perform any swaps? */
bptr = movelist;
if (bestg > 0 || (bestg != bestg_min && !balanced && enforce_balance) ||
(bestg != bestg_min && balance_trouble)) {
improved += bestg;
for (i = 1; i <= beststep; i++) {
vtx = ((int) (bptr - listspace[0])) / size;
bestto = (int) (unsigned long) bptr->prev;
startweight[bestto] += graph[vtx]->vwgt;
startweight[-sets[vtx] - 1] -= graph[vtx]->vwgt;
sets[vtx] = (int) bestto;
bptr = bptr->next;
}
deltaminus = deltaplus = 0;
for (i = 0; i < nsets; i++) {
if (startweight[i] - goal[i] > deltaplus) {
deltaplus = startweight[i] - goal[i];
}
else if (goal[i] - startweight[i] > deltaminus) {
deltaminus = goal[i] - startweight[i];
}
}
/*
printf(" deltaplus = %f, deltaminus = %f, max_dev = %d\n", deltaplus, deltaminus, max_dev);
*/
balanced = (deltaplus + deltaminus <= max_dev);
}
else {
nbad++;
}
if (!balanced || bptr == movelist) {
if (enforce_balance) {
if (enforce_balance_hard) {
balance_trouble = TRUE;
}
enforce_balance_hard = TRUE;
}
enforce_balance = TRUE;
nbad++;
}
worth_undoing = (step < undo_frac * nvtxs);
done = (nbad >= nbadtries && balanced);
if (KL_MAX_PASS > 0) {
done = done || (npass == KL_MAX_PASS && balanced);
}
if (!done) { /* Prepare for next pass. */
if (KL_UNDO_LIST && worth_undoing && !balance_trouble) {
/* Make a list of modified vertices for next bucketsort. */
/* Also, ensure these vertices are removed from their buckets. */
list_length = make_kl_list(graph, movelist, buckets, listspace,
sets, nsets, bspace, dvals, maxdval);
}
}
if (done || !(KL_UNDO_LIST && worth_undoing && !balance_trouble)) {
/* Restore set numbers of remaining, altered vertices. */
while (bptr != NULL) {
vtx = ((int) (bptr - listspace[0])) / size;
sets[vtx] = -sets[vtx] - 1;
bptr = bptr->next;
}
list_length = nvtxs;
}
if (done && *bndy_list != NULL) {
make_bndy_list(graph, movelist, buckets, listspace, sets, nsets,
bspace, tops, bndy_list);
}
}
if (DEBUG_KL > 0) {
printf(" KL required %d passes to improve by %d.\n", npass, improved);
}
sfree(loose);
sfree(locked);
sfree(weightsum);
sfree(bspace);
return(0);
}
