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kt.c
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kt.c
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/*!
\file
\brief The various k-truss decomposition routines
\date Started 6/3/2017
\author George
\version\verbatim $Id: cmdline.c 20946 2017-05-10 23:12:48Z karypis $ \endverbatim
*/
#include "kt.h"
#define hfun1(vi, vj, i, range) \
(((ssize_t)(((((ssize_t)vi)+5)^((ssize_t)vj)*(((ssize_t)vi>>32)+1)^((ssize_t)vj<<7)) + (i)*((1+((ssize_t)vi>>3)+1)^((ssize_t)vj<<5))))%range)
#ifndef DYNAMIC_CHUNK
#define DYNAMIC_CHUNK 16
#endif
/*************************************************************************/
/*! Determine the iperm for the key order using counting sort.
*/
/*************************************************************************/
int32_t *gk_i32kvipermi(int32_t n, gk_i32kv_t *cand)
{
int i, j, k, range;
int32_t *counts, *iperm;
for (range=0, i=0; i<n; i++) {
if (cand[i].key > range)
range = cand[i].key;
}
range++;
counts = gk_i32smalloc(range+1, 0, "counts");
for (i=0; i<n; i++)
counts[cand[i].key]++;
MAKECSR(i, range, counts);
iperm = gk_i32smalloc(n, 0, "iperm");
for (i=0; i<n; i++)
iperm[counts[cand[i].key]++] = i;
gk_free((void **)&counts, LTERM);
return iperm;
}
/*************************************************************************/
/*! Reorder the vertices in the graph in inc degree and return the upper
triangular part of the reordered graph in which the adjancency lists
are sorted in increasing order.
*/
/*************************************************************************/
gk_graph_t *kt_PreprocessAndExtractUpper(params_t *params, vault_t *vault)
{
int32_t vi, vj, vk, nvtxs;
ssize_t ei, eiend, ej, ejend, nedges;
ssize_t *xadj, *uxadj;
int32_t *adjncy, *uadjncy, *perm=NULL, *iperm=NULL;
gk_i32kv_t *cand=NULL;
gk_graph_t *graph;
nvtxs = vault->graph->nvtxs;
xadj = vault->graph->xadj;
adjncy = vault->graph->adjncy;
cand = gk_i32kvmalloc(nvtxs, "cand");
for (vi=0; vi<nvtxs; vi++) {
cand[vi].key = (int32_t)(xadj[vi+1]-xadj[vi]);
cand[vi].val = vi;
}
perm = vault->perm = gk_i32smalloc(nvtxs, -1, "perm"); /* perm[old-vtx-num] => new-vtx-num */
iperm = vault->iperm = gk_i32kvipermi(nvtxs, cand); /* iperm[new-vtx-num] => old-vtx-num */
for (vi=0; vi<nvtxs; vi++)
perm[iperm[vi]] = vi;
/* create the reordered/sorted upper triangular portion of the graph */
graph = gk_graph_Create();
graph->nvtxs = nvtxs;
graph->xadj = uxadj = gk_zmalloc(nvtxs+1, "uxadj");
graph->adjncy = uadjncy = gk_i32malloc(10+(xadj[nvtxs]>>1), "uadjncy");
uxadj[0] = nedges = 0;
for (vi=0; vi<nvtxs; vi++) {
vj = iperm[vi];
for (ej=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++) {
assert(adjncy[ej] < nvtxs);
if ((vk = perm[adjncy[ej]]) > vi) /* keep only the upper part */
uadjncy[nedges++] = vk;
}
uxadj[vi+1] = nedges;
if (nedges-uxadj[vi] > 1)
gk_i32sorti(nedges-uxadj[vi], uadjncy+uxadj[vi]); /* sort adjncy list */
}
printf("Upper nedges: %zd out of %zd\n", uxadj[nvtxs], xadj[nvtxs]);
gk_free((void **)&cand, LTERM);
return graph;
}
/*************************************************************************/
/*! Creates the transpose of the upper-triangular graph with location
offsets at +1 locations.
This is used for the JIK algorithm.
*/
/*************************************************************************/
gk_graph_t *kt_TransposeUforJIK(params_t *params, gk_graph_t *graph)
{
int32_t vi, vj, nvtxs;
ssize_t ei, eiend, nedges;
ssize_t *xadj, *txadj;
int32_t *adjncy, *tadjncy;
gk_graph_t *tgraph;
nvtxs = graph->nvtxs;
xadj = graph->xadj;
adjncy = graph->adjncy;
tgraph = gk_graph_Create();
tgraph->nvtxs = nvtxs;
tgraph->xadj = txadj = gk_zsmalloc(nvtxs+1, 0, "txadj");
tgraph->adjncy = tadjncy = gk_i32malloc(2*(xadj[nvtxs]+1), "tadjncy");
for (vi=0; vi<nvtxs; vi++) {
if (xadj[vi+1]-xadj[vi] < 2)
continue;
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend-1; ei++)
txadj[adjncy[ei]] += 2;
}
MAKECSR(vi, nvtxs, txadj);
for (vi=0; vi<nvtxs; vi++) {
if (xadj[vi+1]-xadj[vi] < 2)
continue;
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend-1; ei++) {
vj = adjncy[ei];
tadjncy[txadj[vj]++] = vi;
tadjncy[txadj[vj]++] = ei-xadj[vi]+1; /* row-offset */
}
}
SHIFTCSR(vi, nvtxs, txadj);
return tgraph;
}
/*************************************************************************/
/*! Checks if the supports computed by the TC code is correct.
*/
/*************************************************************************/
void kt_CheckInitialSupport(params_t *params, vault_t *vault)
{
int32_t uvi, vi, vik, vj, vjk, vk, nvtxs, nh;
ssize_t uei, ei, ej;
ssize_t *xadj, *uxadj;
int32_t *adjncy, *uadjncy, *uadjwgt;
int32_t *map;
nvtxs = vault->graph->nvtxs;
xadj = vault->graph->xadj;
adjncy = vault->graph->adjncy;
uxadj = vault->ugraph->xadj;
uadjncy = vault->ugraph->adjncy;
uadjwgt = vault->ugraph->iadjwgt;
map = gk_i32smalloc(nvtxs, -1, "map");
for (uvi=0; uvi<nvtxs; uvi++) {
vi = vault->iperm[uvi];
for (ei=xadj[vi]; ei<xadj[vi+1]; ei++)
map[adjncy[ei]] = vi;
for (uei=uxadj[uvi]; uei<uxadj[uvi+1]; uei++) {
vj = vault->iperm[uadjncy[uei]];
nh = uadjwgt[uei];
for (ej=xadj[vj]; ej<xadj[vj+1]; ej++)
nh -= (map[adjncy[ej]] == vi ? 1 : 0);
GKASSERT(nh == 0);
}
}
gk_free((void **)&map, LTERM);
}
/*************************************************************************/
/*! Checks if the supports computed by the TC code is correct.
*/
/*************************************************************************/
void kt_CheckKTrussDecomposition(params_t *params, vault_t *vault)
{
int32_t k, vi, vj, vk, nvtxs, knvtxs, nh;
ssize_t ei, ej, nedges;
ssize_t *xadj;
int32_t *adjncy;
int32_t *map;
ktedge_t *ktedges;
nvtxs = vault->graph->nvtxs;
nedges = vault->nedges;
ktedges = vault->ktedges;
for (k=1; k<=vault->ktmax; k++) {
xadj = gk_zsmalloc(nvtxs+1, 0, "xadj");
for (ei=0; ei<nedges; ei++) {
if (ktedges[ei].k >= k) {
xadj[ktedges[ei].vi]++;
xadj[ktedges[ei].vj]++;
}
}
for (knvtxs=0, vi=0; vi<nvtxs; vi++)
knvtxs += (xadj[vi] > 0 ? 1 : 0);
MAKECSR(vi, nvtxs, xadj);
adjncy = gk_i32malloc(xadj[nvtxs], "adjncy");
for (ei=0; ei<nedges; ei++) {
if (ktedges[ei].k >= k) {
adjncy[xadj[ktedges[ei].vi]++] = ktedges[ei].vj;
adjncy[xadj[ktedges[ei].vj]++] = ktedges[ei].vi;
}
}
SHIFTCSR(vi, nvtxs, xadj);
map = gk_i32smalloc(nvtxs, -1, "map");
for (vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi]; ei<xadj[vi+1]; ei++)
map[adjncy[ei]] = vi;
for (ei=xadj[vi]; ei<xadj[vi+1]; ei++) {
vj = adjncy[ei];
for (nh=0, ej=xadj[vj]; ej<xadj[vj+1]; ej++)
nh += (map[adjncy[ej]] == vi ? 1 : 0);
GKASSERT(nh >= k);
}
}
printf("k-truss: %4d, nvtxs: %7d, nedges: %8zd\n", k+2, knvtxs, xadj[nvtxs]);
gk_free((void **)&xadj, &adjncy, &map, LTERM);
}
}
/*************************************************************************/
/*! Takes the sups[] array associated with the edges and creates the
ktedges information in the vault.
*/
/*************************************************************************/
void kt_Sups2KTEdges(params_t *params, vault_t *vault, int32_t ktmax, int32_t *sups)
{
int32_t vi, nvtxs;
ssize_t ei, eiend, ej, nedges;
ssize_t *xadj;
int32_t *adjncy, *adjwgt;
if (params->outfile == NULL)
return;
nvtxs = vault->ugraph->nvtxs;
xadj = vault->ugraph->xadj;
adjncy = vault->ugraph->adjncy;
adjwgt = vault->ugraph->iadjwgt;
vault->nedges = xadj[nvtxs];
vault->ktmax = ktmax;
vault->ktedges = (ktedge_t *)gk_malloc(xadj[nvtxs]*sizeof(ktedge_t), "ktedges");
for (ej=0, nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++, ej++) {
vault->ktedges[ej].vi = gk_min(vault->iperm[vi], vault->iperm[adjncy[ei]]);
vault->ktedges[ej].vj = gk_max(vault->iperm[vi], vault->iperm[adjncy[ei]]);
if (adjwgt[ei] > 0)
vault->ktedges[ej].k = -sups[nedges++] + 2;
else
vault->ktedges[ej].k = 2;
}
}
}
/*************************************************************************/
/*! The hash-map-based edge-triangle-support counting routine that uses
the JIK triangle enumeration scheme.
This is the mapjikv2 tc version.
*/
/*************************************************************************/
int64_t kt_ComputeEdgeSupport(params_t *params, vault_t *vault)
{
int32_t vi, vj, vk, vl, nvtxs, nlocal;
ssize_t ei, eiend, ej, ejstart, ejend;
int64_t ntriangles, ntriangles2;
ssize_t *xadj, *txadj;
int32_t *adjncy, *tadjncy, *adjwgt;
int32_t l, tnc, nc, hmsize, tlsize, tlstart, *hmap, *tmap;
gk_startwctimer(vault->timer_2);
nvtxs = vault->ugraph->nvtxs;
xadj = vault->ugraph->xadj;
adjncy = vault->ugraph->adjncy;
adjwgt = vault->ugraph->iadjwgt;
txadj = vault->lgraph->xadj;
tadjncy = vault->lgraph->adjncy;
/* determine the size of the hash-map and convert it into a format
that is compatible with a bitwise AND operation */
for (hmsize=0, vi=0; vi<nvtxs; vi++)
hmsize = gk_max(hmsize, (int32_t)(xadj[vi+1]-xadj[vi]));
for (l=1; hmsize>(1<<l); l++);
hmsize = (1<<(l+4))-1;
hmap = gk_i32smalloc(hmsize+1, -1, "hmap");
printf("& compatible maximum hmsize: %"PRId32"\n", hmsize);
/* determine the size of the tail-map and allocate memory for it */
for (vi=(nvtxs>>2); vi<nvtxs; vi++) {
if ((txadj[vi+1]-txadj[vi])<<9 > vi)
break;
if ((xadj[vi+1]-xadj[vi])<<4 > nvtxs-vi)
break;
}
tlsize = nvtxs - vi + 100;
tlstart = nvtxs-tlsize;
tmap = gk_i32smalloc(tlsize, -1, "tmap");
tmap -= tlstart; /* make indexing simpler */
printf("tlsize: %"PRId32"\n", tlsize);
/* start counting triangles */
if (params->dbglvl&1)
gk_startwctimer(vault->timer_4);
/* use a combination of hmap and tmap */
ntriangles = 0;
hmsize = 0;
tnc = 0;
for (vj=1; vj<tlstart; vj++) {
if (xadj[vj+1] == xadj[vj] || txadj[vj+1] == txadj[vj])
continue;
/* if needed, increase the working hmsize */
if ((xadj[vj+1]-xadj[vj])<<3 > 1 + (hmsize>>4) + (hmsize>>1)) {
hmsize = xadj[vj+1]-xadj[vj];
for (l=1; hmsize>(1<<l); l++);
hmsize = (1<<(l+4))-1;
if (params->dbglvl&1) {
gk_stopwctimer(vault->timer_4);
printf("vj: %9d tlstart: %d degree: %5zd %7zd hmsize: %6d tnc: %7d time: %5.2lfs\n",
vj, tlstart, xadj[vj+1]-xadj[vj], txadj[vj+1]-txadj[vj],
hmsize, tnc, gk_getwctimer(vault->timer_4));
tnc = 0;
gk_clearwctimer(vault->timer_4);
gk_startwctimer(vault->timer_4);
}
}
/* hash Adj(vj) using hmap for the front and tmap for the last tlsize indices */
for (nc=0, ej=ejstart=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++) {
if ((vk = adjncy[ej]) >= tlstart)
break;
for (l=(vk&hmsize); hmap[l]!=-1; l=((l+1)&hmsize), nc++);
hmap[l] = ej-ejstart;
}
for (; ej<ejend; ej++)
tmap[adjncy[ej]] = ej-ejstart;
tnc += nc;
/* find intersections */
if (nc > 0) { /* we had collisions */
for (ej=txadj[vj], ejend=txadj[vj+1]; ej<ejend; ej+=2) {
vi = tadjncy[ej];
for (nlocal=0, ei=xadj[vi]+tadjncy[ej+1], eiend=xadj[vi+1]; ei<eiend; ei++) {
if ((vk = adjncy[ei]) >= tlstart)
break;
l = vk&hmsize;
if (hmap[l] == -1)
continue;
if (adjncy[ejstart+hmap[l]] == vk) {
adjwgt[ei]++;
adjwgt[ejstart+hmap[l]]++;
nlocal++;
continue;
}
for (l=((l+1)&hmsize); hmap[l]!=-1 && adjncy[ejstart+hmap[l]]!=vk; l=((l+1)&hmsize));
if (hmap[l]!=-1 && adjncy[ejstart+hmap[l]] == vk) {
adjwgt[ei]++;
adjwgt[ejstart+hmap[l]]++;
nlocal++;
}
}
for (; ei<eiend; ei++) {
if (tmap[adjncy[ei]] != -1) {
assert(adjncy[ejstart+tmap[adjncy[ei]]] == adjncy[ei]);
adjwgt[ei]++;
adjwgt[ejstart+tmap[adjncy[ei]]]++;
nlocal++;
}
}
if (nlocal > 0) {
ntriangles += nlocal;
assert(adjncy[xadj[vi]+tadjncy[ej+1]-1] == vj);
adjwgt[xadj[vi]+tadjncy[ej+1]-1] += nlocal;
}
}
/* reset hmap/tmap */
for (ej=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++) {
if ((vk = adjncy[ej]) >= tlstart)
break;
for (l=(vk&hmsize); hmap[l]==-1 || adjncy[ejstart+hmap[l]]!=vk; l=((l+1)&hmsize));
hmap[l] = -1;
}
for (; ej<ejend; ej++)
tmap[adjncy[ej]] = -1;
}
else { /* there were no collisons */
for (ej=txadj[vj], ejend=txadj[vj+1]; ej<ejend; ej+=2) {
vi = tadjncy[ej];
for (nlocal=0, ei=xadj[vi]+tadjncy[ej+1], eiend=xadj[vi+1]; ei<eiend; ei++) {
if ((vk = adjncy[ei]) >= tlstart)
break;
if (hmap[vk&hmsize]!=-1 && adjncy[ejstart+hmap[vk&hmsize]] == vk) {
adjwgt[ei]++;
adjwgt[ejstart+hmap[vk&hmsize]]++;
nlocal++;
}
}
for (; ei<eiend; ei++) {
if (tmap[adjncy[ei]] != -1) {
assert(adjncy[ejstart+tmap[adjncy[ei]]] == adjncy[ei]);
adjwgt[ei]++;
adjwgt[ejstart+tmap[adjncy[ei]]]++;
nlocal++;
}
}
if (nlocal > 0) {
ntriangles += nlocal;
assert(adjncy[xadj[vi]+tadjncy[ej+1]-1] == vj);
adjwgt[xadj[vi]+tadjncy[ej+1]-1] += nlocal;
}
}
/* reset hmap/tmap */
for (ej=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++) {
if ((vk = adjncy[ej]) >= tlstart)
break;
hmap[vk&hmsize] = -1;
}
for (; ej<ejend; ej++)
tmap[adjncy[ej]] = -1;
}
}
printf("ntriangles: %zd\n", ntriangles);
if (params->dbglvl&1) {
gk_stopwctimer(vault->timer_4);
printf("vj: %9d tlstart: %d degree: %5zd %7zd hmsize: %6d tnc: %7d time: %5.2lfs\n",
vj, tlstart, xadj[vj+1]-xadj[vj], txadj[vj+1]-txadj[vj],
hmsize, tnc, gk_getwctimer(vault->timer_4));
tnc = 0;
gk_clearwctimer(vault->timer_4);
gk_startwctimer(vault->timer_4);
}
/* use tmap for the last tlsize rows */
for (; vj<nvtxs; vj++) {
if (1 || xadj[vj+1]-xadj[vj] < nvtxs-vj-1) {
/* hash Adj(vj) */
for (ej=ejstart=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++)
tmap[adjncy[ej]] = ej-ejstart;
/* find intersections */
for (ej=txadj[vj], ejend=txadj[vj+1]; ej<ejend; ej+=2) {
vi = tadjncy[ej];
for (nlocal=0, ei=xadj[vi]+tadjncy[ej+1], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (tmap[adjncy[ei]] != -1) {
adjwgt[ei]++;
adjwgt[ejstart+tmap[adjncy[ei]]]++;
nlocal++;
}
}
if (nlocal > 0) {
ntriangles += nlocal;
assert(adjncy[xadj[vi]+tadjncy[ej+1]-1] == vj);
adjwgt[xadj[vi]+tadjncy[ej+1]-1] += nlocal;
}
}
/* reset tmap */
for (ej=xadj[vj], ejend=xadj[vj+1]; ej<ejend; ej++)
tmap[adjncy[ej]] = -1;
}
else { /* the row is dense */ /* TODO: This has not been updated */
tnc++;
/* find intersections */
for (nlocal=0, ej=txadj[vj], ejend=txadj[vj+1]; ej<ejend; ej+=2) {
vi = tadjncy[ej];
nlocal += xadj[vi+1]-xadj[vi]-tadjncy[ej+1];
}
ntriangles += nlocal;
}
}
gk_stopwctimer(vault->timer_2);
if (params->dbglvl&1) {
gk_stopwctimer(vault->timer_4);
vj = nvtxs-2;
printf("vj: %9d tlstart: %d degree: %5zd %7zd hmsize: %6d tnc: %7d time: %5.2lfs\n",
vj, tlstart, xadj[vj+1]-xadj[vj], txadj[vj+1]-txadj[vj],
hmsize, tnc, gk_getwctimer(vault->timer_4));
for (ntriangles2=0, ei=0; ei<xadj[nvtxs]; ei++)
ntriangles2 += adjwgt[ei];
printf("Sanity check: ntriangles: %zd %zd %zd\n", ntriangles, ntriangles2/3, ntriangles2%3);
}
tmap += tlstart;
gk_free((void **)&hmap, &tmap, LTERM);
return ntriangles;
}
/*************************************************************************/
/*! This is the initial baseline version of k-truss decomposition.
*/
/*************************************************************************/
int64_t kt_Baseline1(params_t *params, vault_t *vault)
{
struct edge_s {
int32_t vi, vj, sup;
} *edges;
struct aii_s {
int32_t vj, inc;
size_t id;
} *aii;
struct xaii_s {
int64_t start, end;
} *xaii;
gk_ipq_t *queue;
int32_t k, vi, vik, vj, vjk, vk, nvtxs, nlocal, nltriangles, sup;
ssize_t ti, ei, eip, eiend, ej, ejp, ejend;
int64_t nedges, ntriangles;
ssize_t *xadj;
int32_t *adjncy, *adjwgt;
gk_startwctimer(vault->timer_tcsetup);
vault->ugraph = kt_PreprocessAndExtractUpper(params, vault);
vault->lgraph = kt_TransposeUforJIK(params, vault->ugraph);
nvtxs = vault->ugraph->nvtxs;
xadj = vault->ugraph->xadj;
adjncy = vault->ugraph->adjncy;
/* where the support values will be stored */
adjwgt = vault->ugraph->iadjwgt = gk_i32smalloc(xadj[nvtxs], 0, "adjwgt");
gk_stopwctimer(vault->timer_tcsetup);
gk_startwctimer(vault->timer_esupport);
ntriangles = kt_ComputeEdgeSupportPar(params, vault);
gk_stopwctimer(vault->timer_esupport);
gk_startwctimer(vault->timer_ktsetup);
/* determine the number of edges with non-zero support */
for (nedges=0, ei=0, eiend=xadj[nvtxs]; ei<eiend; ei++) {
if (adjwgt[ei] > 0)
nedges++;
}
/* allocate memory for the adjancency lists, which in addition to the
adjancent vertex it will store the increment (for skip-list) and
the ID for priority queue */
xaii = (struct xaii_s *)gk_malloc((nvtxs+1)*sizeof(struct xaii_s), "xaii");
aii = (struct aii_s *)gk_malloc((2*nedges+1)*sizeof(struct aii_s), "aii");
edges = (struct edge_s *)gk_malloc((nedges+1)*sizeof(struct edge_s), "edges");
for (vi=0; vi<nvtxs; vi++)
xaii[vi].start = 0;
/* determine sizes */
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
xaii[vi].start++;
xaii[adjncy[ei]].start++;
edges[nedges].vi = vi;
edges[nedges].vj = adjncy[ei];
edges[nedges].sup = adjwgt[ei];
nedges++;
}
}
}
/* the MAKECSR equivalent */
for (vi=1; vi<nvtxs; vi++)
xaii[vi].start += xaii[vi-1].start;
for (vi=nvtxs; vi>0; vi--)
xaii[vi].start = xaii[vi-1].start;
xaii[0].start = 0;
/* populate it into two steps to ensure that the sorted order is maintained */
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
vj = adjncy[ei];
aii[xaii[vj].start].vj = vi;
aii[xaii[vj].start].inc = 1;
aii[xaii[vj].start].id = nedges;
xaii[vj].start++;
nedges++;
}
}
}
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
aii[xaii[vi].start].vj = adjncy[ei];
aii[xaii[vi].start].inc = 1;
aii[xaii[vi].start].id = nedges;
xaii[vi].start++;
nedges++;
}
}
}
/* the SHIFTCSR equivalent */
for (vi=nvtxs; vi>0; vi--)
xaii[vi].start = xaii[vi-1].start;
xaii[0].start = 0;
/* record the end in xaii[vi] and from now own, you will be using that */
for (vi=0; vi<nvtxs; vi++)
xaii[vi].end = xaii[vi+1].start;
printf("Edges with non-zero support: %zd (%.2f%%)\n", nedges, (float)100.00*nedges/xadj[nvtxs]);
gk_startwctimer(vault->timer_1);
/* create and populate the priority queue
[the negative on the key is because my priority queues are max priority queues */
queue = gk_ipqCreate(nedges);
for (ei=0; ei<nedges; ei++)
gk_ipqInsert(queue, ei, -edges[ei].sup);
gk_stopwctimer(vault->timer_1);
printf("Pqueue stats: nnodes: %zu, nedges: %zd\n", gk_ipqLength(queue), nedges);
gk_stopwctimer(vault->timer_ktsetup);
printf("#triangles before peeling: %zd\n", ntriangles);
ntriangles = 0;
gk_startwctimer(vault->timer_ktpeeling);
/* get into the k-truss enumeration loop */
for (k=1;;k++) {
if (gk_ipqLength(queue) == 0)
break;
nlocal = 0;
nltriangles = 0;
while (k >= -gk_ipqSeeTopKey(queue)) {
if (gk_ipqLength(queue) == 0)
break;
nlocal++;
ti = gk_ipqGetTop(queue);
vi = edges[ti].vi;
vj = edges[ti].vj;
if (edges[ti].sup > 0) {
gk_startwctimer(vault->timer_3);
sup = edges[ti].sup;
/*
printf("%d %d %d %zd %zd %d\n",
vi, vj, edges[ti].sup,
xaii[vi].end-xaii[vi].start,
xaii[vj].end-xaii[vj].start,
nltriangles);
*/
ei = xaii[vi].start;
eiend = xaii[vi].end;
vik = aii[ei].vj;
ej = xaii[vj].start;
ejend = xaii[vj].end;
vjk = aii[ej].vj;
/* decrease the support of the intersection */
while (ei < eiend && ej < ejend) {
//printf(" vik: %d vjk: %d\n", vik, vjk);
if (vik < vjk) {
ei += aii[ei].inc;
vik = aii[ei].vj;
}
else if (vjk < vik) {
ej += aii[ej].inc;
vjk = aii[ej].vj;
}
else {
//printf(" ** vk: %d\n", vik);
nltriangles++;
edges[aii[ei].id].sup--;
gk_ipqUpdate(queue, aii[ei].id, -edges[aii[ei].id].sup);
ei += aii[ei].inc;
vik = aii[ei].vj;
edges[aii[ej].id].sup--;
gk_ipqUpdate(queue, aii[ej].id, -edges[aii[ej].id].sup);
ej += aii[ej].inc;
vjk = aii[ej].vj;
if (--sup == 0)
break;
}
}
gk_stopwctimer(vault->timer_3);
}
/* remove the edge from both adjacency lists */
for (eip=-1, ei=xaii[vi].start; aii[ei].vj<vj; eip=ei, ei+=aii[ei].inc);
ASSERT(aii[ei].vj == vj);
if (eip == -1)
xaii[vi].start += aii[ei].inc;
else
aii[eip].inc += aii[ei].inc;
edges[aii[ei].id].sup = -k; /* this is used for encoding the maximal value of k of that edge */
for (ejp=-1, ej=xaii[vj].start; aii[ej].vj<vi; ejp=ej, ej+=aii[ej].inc);
ASSERT(aii[ej].vj == vi);
if (ejp == -1)
xaii[vj].start += aii[ej].inc;
else
aii[ejp].inc += aii[ej].inc;
edges[aii[ej].id].sup = -k; /* this is used for encoding the maximal value of k of that edge */
}
if (nlocal > 0 && params->dbglvl&1)
printf("k: %7d; nlocal: %7d, nltriangles: %7d\n", k, nlocal, nltriangles);
ntriangles += nltriangles;
}
gk_stopwctimer(vault->timer_ktpeeling);
printf("#triangles after peeling: %zd\n", ntriangles);
gk_free((void **)&edges, &aii, &xaii, LTERM);
return ntriangles;
}
/*************************************************************************/
/*! This is the initial baseline version of k-truss decomposition.
*/
/*************************************************************************/
int64_t kt_Baseline2(params_t *params, vault_t *vault)
{
struct edge_s {
int32_t vi, vj, sup;
} *edges;
struct aii_s {
int32_t vj, inc;
size_t id;
} *aii;
struct xaii_s {
int64_t start, end;
} *xaii;
gk_ipq_t *queue;
int32_t k, vi, vik, vj, vjk, vk, nvtxs, nlocal, nltriangles, sup;
ssize_t ti, ei, eip, eiend, ej, ejp, ejend;
int64_t nedges, ntriangles;
ssize_t *xadj;
int32_t *adjncy, *adjwgt;
ssize_t nupdates, *updindices, *updmark;
gk_startwctimer(vault->timer_tcsetup);
vault->ugraph = kt_PreprocessAndExtractUpper(params, vault);
vault->lgraph = kt_TransposeUforJIK(params, vault->ugraph);
nvtxs = vault->ugraph->nvtxs;
xadj = vault->ugraph->xadj;
adjncy = vault->ugraph->adjncy;
/* where the support values will be stored */
adjwgt = vault->ugraph->iadjwgt = gk_i32smalloc(xadj[nvtxs], 0, "adjwgt");
gk_stopwctimer(vault->timer_tcsetup);
gk_startwctimer(vault->timer_esupport);
ntriangles = kt_ComputeEdgeSupportPar(params, vault);
gk_stopwctimer(vault->timer_esupport);
gk_startwctimer(vault->timer_ktsetup);
/* determine the number of edges with non-zero support */
for (nedges=0, ei=0, eiend=xadj[nvtxs]; ei<eiend; ei++) {
if (adjwgt[ei] > 0)
nedges++;
}
/* allocate memory for the adjancency lists, which in addition to the
adjancent vertex it will store the increment (for skip-list) and
the ID for priority queue */
xaii = (struct xaii_s *)gk_malloc((nvtxs+1)*sizeof(struct xaii_s), "xaii");
aii = (struct aii_s *)gk_malloc((2*nedges+1)*sizeof(struct aii_s), "aii");
edges = (struct edge_s *)gk_malloc((nedges+1)*sizeof(struct edge_s), "edges");
for (vi=0; vi<nvtxs; vi++)
xaii[vi].start = 0;
/* determine sizes */
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
xaii[vi].start++;
xaii[adjncy[ei]].start++;
edges[nedges].vi = vi;
edges[nedges].vj = adjncy[ei];
edges[nedges].sup = adjwgt[ei];
nedges++;
}
}
}
/* the MAKECSR equivalent */
for (vi=1; vi<nvtxs; vi++)
xaii[vi].start += xaii[vi-1].start;
for (vi=nvtxs; vi>0; vi--)
xaii[vi].start = xaii[vi-1].start;
xaii[0].start = 0;
/* populate it into two steps to ensure that the sorted order is maintained */
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
vj = adjncy[ei];
aii[xaii[vj].start].vj = vi;
aii[xaii[vj].start].inc = 1;
aii[xaii[vj].start].id = nedges;
xaii[vj].start++;
nedges++;
}
}
}
for (nedges=0, vi=0; vi<nvtxs; vi++) {
for (ei=xadj[vi], eiend=xadj[vi+1]; ei<eiend; ei++) {
if (adjwgt[ei] > 0) {
aii[xaii[vi].start].vj = adjncy[ei];
aii[xaii[vi].start].inc = 1;
aii[xaii[vi].start].id = nedges;
xaii[vi].start++;
nedges++;
}
}
}
/* the SHIFTCSR equivalent */
for (vi=nvtxs; vi>0; vi--)
xaii[vi].start = xaii[vi-1].start;
xaii[0].start = 0;
/* record the end in xaii[vi] and from now own, you will be using that */
for (vi=0; vi<nvtxs; vi++)
xaii[vi].end = xaii[vi+1].start;
printf("Edges with non-zero support: %zd (%.2f%%)\n", nedges, (float)100.00*nedges/xadj[nvtxs]);
gk_startwctimer(vault->timer_1);
/* create and populate the priority queue
[the negative on the key is because my priority queues are max priority queues */
queue = gk_ipqCreate(nedges);
for (ei=0; ei<nedges; ei++)
gk_ipqInsert(queue, ei, -edges[ei].sup);
gk_stopwctimer(vault->timer_1);
printf("Pqueue stats: nnodes: %zu, nedges: %zd\n", gk_ipqLength(queue), nedges);
updindices = gk_zmalloc(nedges, "updindices");
updmark = gk_zsmalloc(nedges, -1, "updmark");
gk_stopwctimer(vault->timer_ktsetup);
printf("#triangles before peeling: %zd\n", ntriangles);
ntriangles = 0;
gk_startwctimer(vault->timer_ktpeeling);
/* get into the k-truss enumeration loop */
for (k=1;;k++) {
if (gk_ipqLength(queue) == 0)
break;
nlocal = 0;
nltriangles = 0;
BACK:
nupdates = 0;
while (k >= -gk_ipqSeeTopKey(queue)) {
if (gk_ipqLength(queue) == 0)
break;
nlocal++;
ti = gk_ipqGetTop(queue);
vi = edges[ti].vi;
vj = edges[ti].vj;
if (edges[ti].sup > 0) {
gk_startwctimer(vault->timer_3);
sup = edges[ti].sup;
/*
printf("%d %d %d %zd %zd %d\n",
vi, vj, edges[ti].sup,
xaii[vi].end-xaii[vi].start,
xaii[vj].end-xaii[vj].start,
nltriangles);
*/
ei = xaii[vi].start;
eiend = xaii[vi].end;
vik = aii[ei].vj;
ej = xaii[vj].start;
ejend = xaii[vj].end;
vjk = aii[ej].vj;
/* decrease the support of the intersection */
while (ei < eiend && ej < ejend) {
//printf(" vik: %d vjk: %d\n", vik, vjk);
if (vik < vjk) {
ei += aii[ei].inc;
vik = aii[ei].vj;
}
else if (vjk < vik) {
ej += aii[ej].inc;
vjk = aii[ej].vj;
}
else {
//printf(" ** vk: %d\n", vik);
nltriangles++;
edges[aii[ei].id].sup--;
if (updmark[aii[ei].id] == -1 ) {
updindices[nupdates++] = aii[ei].id;
updmark[aii[ei].id] = 1;
}
ei += aii[ei].inc;
vik = aii[ei].vj;
edges[aii[ej].id].sup--;
if (updmark[aii[ej].id] == -1 ) {
updindices[nupdates++] = aii[ej].id;
updmark[aii[ej].id] = 1;
}
ej += aii[ej].inc;
vjk = aii[ej].vj;
if (--sup == 0)
break;
}
}
gk_stopwctimer(vault->timer_3);
}
/* remove the edge from both adjacency lists */
gk_startwctimer(vault->timer_5);
for (eip=-1, ei=xaii[vi].start; aii[ei].vj<vj; eip=ei, ei+=aii[ei].inc);
ASSERT(aii[ei].vj == vj);