/* Perform KL between two sets. */
int
kl_refine (
struct vtx_data **graph, /* graph data structure */
struct vtx_data **subgraph, /* space for subgraph to refine */
struct bilist *set_list, /* lists of vtxs in each set */
struct bilist *vtx_elems, /* start of storage for lists */
int *new_assign, /* set assignments for all vertices */
int set1,
int set2, /* two sets being refined */
int *glob2loc, /* maps vertices to subgraph vertices */
int *loc2glob, /* maps subgraph vertices to vertices */
int *sub_assign, /* new assignment for subgraphs */
int *old_sub_assign, /* current assignment for subgraphs */
int *degrees, /* space for forming subgraphs */
int using_ewgts, /* are edge weights being used? */
int (*hops)[MAXSETS], /* KL set preferences */
double *goal, /* desired set sizes */
int *sizes, /* number of vertices in different sets */
float *term_wgts[], /* space for terminal propagation weights */
int architecture, /* 0 => hypercube, d => d-dimensional mesh */
int mesh_dims[3] /* if mesh, how big is it? */
)
{
extern int TERM_PROP; /* perform terminal propagation? */
extern double KL_IMBALANCE; /* fractional imbalance allowed in KL */
struct bilist *ptr; /* element in set_list */
double subgoal[2]; /* goal within two subgraphs */
double weights[2]; /* weights for each set */
double maxdeg; /* largest degree of a vertex */
double ratio; /* set sizes / goals */
int *null_ptr; /* argument to klspiff */
int vwgt_max; /* largest vertex weight */
int max_dev; /* largest set deviation allowed in KL */
int subnvtxs; /* number of vtxs in subgraph */
int vwgt_sum1; /* sum of vertex wgts in first set */
int vwgt_sum2; /* sum of vertex wgts in second set */
int subnedges; /* number of edges in subgraph */
int setA, setB; /* two sets being refined */
int nsame; /* number of vertices not moved */
int vtx; /* vertex in subgraph */
int i; /* loop counter */
double find_maxdeg();
void make_maps_ref(), make_subgraph(), remake_graph();
void klspiff(), make_terms_ref(), count_weights();
/* Compute all the quantities I'll need. */
null_ptr = NULL;
make_maps_ref(graph, set_list, vtx_elems, new_assign, sub_assign,
set1, set2, glob2loc, loc2glob, &subnvtxs, &vwgt_max,
&vwgt_sum1, &vwgt_sum2);
for (i = 1; i <= subnvtxs; i++)
old_sub_assign[i] = sub_assign[i];
/* Set up goals for this KL invocation. */
ratio = (vwgt_sum1 + vwgt_sum2) / (goal[set1] + goal[set2]);
subgoal[0] = ratio * goal[set1];
subgoal[1] = ratio * goal[set2];
if (TERM_PROP) {
make_terms_ref(graph, using_ewgts, subnvtxs, loc2glob,
set1, set2, new_assign, architecture, mesh_dims, term_wgts);
}
/* New_assign has overwritten set2 with set1. */
make_subgraph(graph, subgraph, subnvtxs, &subnedges, new_assign, set1,
glob2loc, loc2glob, degrees, using_ewgts);
maxdeg = find_maxdeg(subgraph, subnvtxs, using_ewgts, (float *) NULL);
count_weights(subgraph, subnvtxs, sub_assign, 2, weights, (vwgt_max != 1));
max_dev = vwgt_max;
ratio = (subgoal[0] + subgoal[1]) * KL_IMBALANCE / 2;
if (ratio > max_dev) {
max_dev = ratio;
}
klspiff(subgraph, subnvtxs, sub_assign, 2, hops, subgoal,
term_wgts, max_dev, maxdeg, using_ewgts, &null_ptr, weights);
/* Figure out which modification leaves most vertices intact. */
nsame = 0;
for (i = 1; i <= subnvtxs; i++) {
if (old_sub_assign[i] == sub_assign[i])
nsame++;
}
if (2 * nsame > subnvtxs) {
setA = set1;
setB = set2;
}
else {
setA = set2;
setB = set1;
}
/* Now update the assignments. */
sizes[setA] = sizes[setB] = 0;
for (i = 1; i <= subnvtxs; i++) {
vtx = loc2glob[i];
/* Update the set_lists. */
ptr = &(vtx_elems[vtx]);
if (ptr->next != NULL) {
ptr->next->prev = ptr->prev;
}
if (ptr->prev != NULL) {
ptr->prev->next = ptr->next;
}
if (sub_assign[i] == 0) {
new_assign[vtx] = (int) setA;
++sizes[setA];
ptr->next = set_list[setA].next;
if (ptr->next != NULL)
ptr->next->prev = ptr;
ptr->prev = &(set_list[setA]);
set_list[setA].next = ptr;
}
else {
new_assign[vtx] = (int) setB;
++sizes[setB];
ptr->next = set_list[setB].next;
if (ptr->next != NULL)
ptr->next->prev = ptr;
ptr->prev = &(set_list[setB]);
set_list[setB].next = ptr;
}
}
remake_graph(subgraph, subnvtxs, loc2glob, degrees, using_ewgts);
return(nsame != subnvtxs);
}
void connect_enforce(struct vtx_data **graph, /* data structure for graph */
int nvtxs, /* number of vertices in full graph */
int using_ewgts, /* are edge weights being used? */
int * assignment, /* set number of each vtx (length n) */
double * goal, /* desired sizes for each set */
int nsets_tot, /* total number sets created */
int * total_move, /* total number of vertices moved */
int * max_move /* largest connected component moved */
)
{
struct vtx_data **subgraph; /* data structure for domain graph */
int subnvtxs; /* number of vertices in a domain */
int subnedges; /* number of edges in a domain */
struct heap * heap; /* data structure for sorting set sizes */
int * heap_map; /* pointers from sets to heap locations */
int * list_ptrs; /* header of vtx list for each domain */
int * setlists; /* linked list of vtxs for each domain */
int * vtxlist; /* space for breadth first search list */
int * comp_lists; /* list of vtxs in each connected comp */
int * clist_ptrs; /* pointers to heads of comp_lists */
int * subsets; /* list of active domains (all of them) */
int * subsets2; /* list of active domains (all of them) */
double * set_size; /* weighted sizes of different partitions */
double size; /* size of subset being moved to new domain */
int * bndy_list; /* list of domains adjacent to component */
double * bndy_size; /* size of these boundaries */
double * comp_size; /* sizes of different connected components */
double comp_size_max; /* size of largest connected component */
int comp_max_index = 0; /* which component is largest? */
int * glob2loc; /* global to domain renumbering */
int * loc2glob; /* domain to global renumbering */
int * degree; /* number of neighbors of a vertex */
int * comp_flag; /* component number for each vtx */
double ewgt; /* edge weight */
int nbndy; /* number of sets adjecent to component */
int domain; /* which subdomain I'm working on */
int new_domain; /* subdomain to move some vertices to */
double max_bndy; /* max connectivity to other domain */
int ncomps; /* number of connected components */
int change; /* how many vertices change set? */
int max_change; /* largest subset moved together */
int vtx; /* vertex in a connected component */
int set; /* set a neighboring vertex is in */
int i, j, k, l; /* loop counters */
double heap_extract_max();
int make_maps(), find_comps();
void make_setlists(), make_subgraph(), remake_graph();
void heap_build(), heap_update_val();
change = 0;
max_change = 0;
/* Allocate space & initialize some values. */
set_size = smalloc(nsets_tot * sizeof(double));
bndy_size = smalloc(nsets_tot * sizeof(double));
bndy_list = smalloc(nsets_tot * sizeof(int));
setlists = smalloc((nvtxs + 1) * sizeof(int));
list_ptrs = smalloc(nsets_tot * sizeof(int));
glob2loc = smalloc((nvtxs + 1) * sizeof(int));
loc2glob = smalloc((nvtxs + 1) * sizeof(int));
subsets = smalloc(nsets_tot * sizeof(int));
heap = (struct heap *)smalloc((nsets_tot + 1) * sizeof(struct heap));
heap_map = smalloc(nsets_tot * sizeof(int));
for (i = 0; i < nsets_tot; i++) {
set_size[i] = 0;
bndy_list[i] = 0;
bndy_size[i] = 0;
subsets[i] = i;
}
for (i = 1; i <= nvtxs; i++) {
set_size[assignment[i]] += graph[i]->vwgt;
}
for (i = 0; i < nsets_tot; i++) {
heap[i + 1].tag = i;
heap[i + 1].val = set_size[i] - goal[i];
}
make_setlists(setlists, list_ptrs, nsets_tot, subsets, assignment, NULL, nvtxs, TRUE);
heap_build(heap, nsets_tot, heap_map);
for (i = 0; i < nsets_tot; i++) {
/* Find largest remaining set to work on next */
size = heap_extract_max(heap, nsets_tot - i, &domain, heap_map);
/* Construct subdomain graph. */
subnvtxs = make_maps(setlists, list_ptrs, domain, glob2loc, loc2glob);
if (subnvtxs > 1) {
subgraph = (struct vtx_data **)smalloc((subnvtxs + 1) * sizeof(struct vtx_data *));
degree = smalloc((subnvtxs + 1) * sizeof(int));
make_subgraph(graph, subgraph, subnvtxs, &subnedges, assignment, domain, glob2loc, loc2glob,
degree, using_ewgts);
/* Find connected components. */
comp_flag = smalloc((subnvtxs + 1) * sizeof(int));
vtxlist = smalloc(subnvtxs * sizeof(int));
ncomps = find_comps(subgraph, subnvtxs, comp_flag, vtxlist);
sfree(vtxlist);
/* Restore original graph */
remake_graph(subgraph, subnvtxs, loc2glob, degree, using_ewgts);
sfree(degree);
sfree(subgraph);
if (ncomps > 1) {
/* Figure out sizes of components */
comp_size = smalloc(ncomps * sizeof(double));
for (j = 0; j < ncomps; j++) {
comp_size[j] = 0;
}
for (j = 1; j <= subnvtxs; j++) {
comp_size[comp_flag[j]] += graph[loc2glob[j]]->vwgt;
}
comp_size_max = 0;
for (j = 0; j < ncomps; j++) {
if (comp_size[j] > comp_size_max) {
comp_size_max = comp_size[j];
comp_max_index = j;
}
}
for (j = 0; j < ncomps; j++) {
if (j != comp_max_index) {
change += comp_size[j];
if (comp_size[j] > max_change)
max_change = comp_size[j];
}
}
sfree(comp_size);
/* Make data structures for traversing components */
comp_lists = smalloc((subnvtxs + 1) * sizeof(int));
clist_ptrs = smalloc(ncomps * sizeof(int));
if (ncomps > nsets_tot) {
subsets2 = smalloc(ncomps * sizeof(int));
for (j = 0; j < ncomps; j++)
subsets2[j] = j;
}
else
subsets2 = subsets;
make_setlists(comp_lists, clist_ptrs, ncomps, subsets2, comp_flag, NULL, subnvtxs, TRUE);
if (ncomps > nsets_tot) {
sfree(subsets2);
}
/* Move all but the largest component. */
ewgt = 1;
for (j = 0; j < ncomps; j++)
if (j != comp_max_index) {
/* Figure out to which other domain it is most connected. */
nbndy = 0;
k = clist_ptrs[j];
while (k != 0) {
vtx = loc2glob[k];
for (l = 1; l <= graph[vtx]->nedges; l++) {
set = assignment[graph[vtx]->edges[l]];
if (set != domain) {
if (bndy_size[set] == 0)
bndy_list[nbndy++] = set;
if (using_ewgts)
ewgt = graph[vtx]->ewgts[l];
bndy_size[set] += ewgt;
}
}
k = comp_lists[k];
}
/* Select a new domain. */
/* Instead of just big boundary, penalize too-large sets. */
/* Could be more aggressive to improve balance. */
max_bndy = 0;
new_domain = -1;
for (k = 0; k < nbndy; k++) {
l = bndy_list[k];
if (bndy_size[l] * goal[l] / (set_size[l] + 1) > max_bndy) {
new_domain = bndy_list[k];
max_bndy = bndy_size[l] * goal[l] / (set_size[l] + 1);
}
}
if (new_domain == -1) {
printf("Error in connect_enforce: new_domain = -1. Disconnected graph?\n");
new_domain = domain;
}
/* Clear bndy_size array */
for (k = 0; k < nbndy; k++)
bndy_size[bndy_list[k]] = 0;
k = clist_ptrs[j];
size = 0;
while (k != 0) {
vtx = loc2glob[k];
assignment[vtx] = new_domain;
size += graph[vtx]->vwgt;
/* Finally, update setlists and list_ptrs */
/* Note: current domain setlist now bad, but not used
again */
setlists[vtx] = list_ptrs[new_domain];
list_ptrs[new_domain] = vtx;
k = comp_lists[k];
}
/*
printf("Updating set %d (from %d) to size %g\n", new_domain, domain,
set_size[new_domain] + size - goal[new_domain]);
*/
if (heap_map[new_domain] > 0) {
set_size[new_domain] += size;
heap_update_val(heap, heap_map[new_domain], set_size[new_domain] - goal[new_domain],
heap_map);
}
}
sfree(clist_ptrs);
sfree(comp_lists);
}
sfree(comp_flag);
}
}
sfree(heap_map);
sfree(heap);
sfree(subsets);
sfree(loc2glob);
sfree(glob2loc);
sfree(list_ptrs);
sfree(setlists);
sfree(bndy_list);
sfree(bndy_size);
sfree(set_size);
*total_move = change;
*max_move = max_change;
}