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tc.c
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tc.c
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#include "types.h"
#include "queue.h"
#include "graph.h"
#include "bfs.h"
#include "tc.h"
/* Algorithm from
T. A. Davis, "Graph algorithms via SuiteSparse: GraphBLAS: triangle counting and K-truss," 2018 IEEE High Performance extreme Computing Conference (HPEC), Waltham, MA, USA, 2018, pp. 1-6, doi: 10.1109/HPEC.2018.8547538.
*/
UINT_t tc_davis // # of triangles
(
#if 1
const GRAPH_TYPE *graph
#else
const UINT_t *restrict Ap, // column pointers, size n+1
const UINT_t *restrict Ai, // row indices
const UINT_t n // A is n-by-n
#endif
)
{
#if 1
UINT_t *Ap = graph->rowPtr;
UINT_t *Ai = graph->colInd;
UINT_t n = graph->numVertices;
#endif
bool *restrict Mark = (bool *) calloc (n, sizeof (bool)) ;
if (Mark == NULL) return (-1) ;
UINT_t ntri = 0 ;
for (UINT_t j = 0 ; j < n ; j++) {
// scatter A(:,j) into Mark
for (UINT_t p = Ap [j] ; p < Ap [j+1] ; p++)
Mark [Ai [p]] = 1 ;
// sum(C(:,j)) where C(:,j) = (A * A(:,j)) .* Mark
for (UINT_t p = Ap [j] ; p < Ap [j+1] ; p++) {
const UINT_t k = Ai [p] ;
// C(:,j) += (A(:,k) * A(k,j)) .* Mark
for (UINT_t pa = Ap [k] ; pa < Ap [k+1] ; pa++)
// C(i,j) += (A(i,k) * A(k,j)) .* Mark
ntri += Mark [Ai [pa]] ;
}
for (UINT_t p = Ap [j] ; p < Ap [j+1] ; p++)
Mark [Ai [p]] = 0 ;
}
free (Mark) ;
return (ntri/6) ;
}
UINT_t tc_wedge(const GRAPH_TYPE *graph) {
/* Algorithm: For each vertex i, for each open wedge (j, i, k), determine if there's a closing edge (j, k) */
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (UINT_t i = 0; i < n; i++) {
UINT_t s = Ap[i];
UINT_t e = Ap[i + 1];
for (UINT_t j = s; j < e; j++) {
UINT_t neighbor1 = Ai[j];
for (UINT_t k = s; k < e; k++) {
UINT_t neighbor2 = Ai[k];
if (neighbor1 != neighbor2) {
UINT_t s_n1 = Ap[neighbor1];
UINT_t e_n1 = Ap[neighbor1 + 1];
for (UINT_t l = s_n1; l < e_n1; l++) {
if (Ai[l] == neighbor2) {
count++;
break;
}
}
}
}
}
}
return (count/6);
}
UINT_t tc_wedge_DO(const GRAPH_TYPE *graph) {
/* Algorithm: For each vertex i, for each open wedge (j, i, k), determine if there's a closing edge (j, k) */
/* Direction oriented. */
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (UINT_t i = 0; i < n; i++) {
UINT_t s = Ap[i];
UINT_t e = Ap[i + 1];
for (UINT_t j = s; j < e; j++) {
UINT_t neighbor1 = Ai[j];
if (neighbor1 > i) {
for (UINT_t k = s; k < e; k++) {
UINT_t neighbor2 = Ai[k];
if ((neighbor1 != neighbor2) && (neighbor2 > neighbor1)) {
UINT_t s_n1 = Ap[neighbor1];
UINT_t e_n1 = Ap[neighbor1 + 1];
for (UINT_t l = s_n1; l < e_n1; l++) {
if (Ai[l] == neighbor2) {
count++;
break;
}
}
}
}
}
}
}
return count;
}
UINT_t tc_triples(const GRAPH_TYPE *graph) {
/* Algorithm: for each triple (i, j, k), determine if the three triangle edges exist. */
register UINT_t i, j, k;
UINT_t count = 0;
const UINT_t n = graph->numVertices;
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
for (k = 0; k < n; k++) {
if (check_edge(graph, i, j) && check_edge(graph, j, k) && check_edge(graph, k, i))
count++;
}
return (count/6);
}
UINT_t tc_triples_DO(const GRAPH_TYPE *graph) {
/* Algorithm: for each triple (i, j, k), determine if the three triangle edges exist. */
/* Direction oriented. */
register UINT_t i, j, k;
UINT_t count = 0;
const UINT_t n = graph->numVertices;
for (i = 0; i < n; i++)
for (j = i; j < n; j++)
for (k = j; k < n; k++) {
if (check_edge(graph, i, j) && check_edge(graph, j, k) && check_edge(graph, k, i))
count++;
}
return count;
}
UINT_t tc_intersectMergePath(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a linear scan. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
count += intersectSizeMergePath(graph, v, w);
}
}
return (count/6);
}
UINT_t tc_intersectMergePath_DO(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a linear scan. */
/* Direction oriented. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
if (v < w)
count += intersectSizeMergePath(graph, v, w);
}
}
return (count/3);
}
UINT_t tc_intersectBinarySearch(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a binary search. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
count += intersectSizeBinarySearch(graph, v, w);
}
}
return (count/6);
}
UINT_t tc_intersectBinarySearch_DO(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a binary search. */
/* Direction oriented. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
if (v < w)
count += intersectSizeBinarySearch(graph, v, w);
}
}
return (count/3);
}
UINT_t tc_intersectPartition(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a binary search-based partition. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n ; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
count += searchLists_with_partitioning((UINT_t *)Ai, (INT_t) Ap[v], (INT_t)Ap[v+1]-1, (UINT_t *)Ai, (INT_t)Ap[w], (INT_t)Ap[w+1]-1);
}
}
return (count/6);
}
UINT_t tc_intersectPartition_DO(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a binary search-based partition. */
/* Direction oriented. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (v = 0; v < n; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
if (v < w)
count += searchLists_with_partitioning((UINT_t *)Ai, (INT_t) Ap[v], (INT_t)Ap[v+1]-1, (UINT_t *)Ai, (INT_t)Ap[w], (INT_t)Ap[w+1]-1);
}
}
return (count/3);
}
UINT_t tc_intersectHash(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a hash. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
bool *Hash;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
Hash = (bool *)calloc(n, sizeof(bool));
assert_malloc(Hash);
for (v = 0; v < n ; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
count += intersectSizeHash(graph, Hash, v, w);
}
}
free(Hash);
return (count/6);
}
UINT_t tc_intersectHash_DO(const GRAPH_TYPE *graph) {
/* Algorithm: For each edge (i, j), find the size of its intersection using a hash. */
/* Direction oriented. */
register UINT_t v, w;
register UINT_t b, e;
UINT_t count = 0;
bool *Hash;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
Hash = (bool *)calloc(n, sizeof(bool));
assert_malloc(Hash);
for (v = 0; v < n ; v++) {
b = Ap[v ];
e = Ap[v+1];
for (UINT_t i=b ; i<e ; i++) {
w = Ai[i];
if (v < w)
count += intersectSizeHash(graph, Hash, v, w);
}
}
free(Hash);
return (count/3);
}
/* T. M. Low, V. N. Rao, M. Lee, D. Popovici, F. Franchetti and S. McMillan,
"First look: Linear algebra-based triangle counting without matrix multiplication,"
2017 IEEE High Performance Extreme Computing Conference (HPEC),
Waltham, MA, USA, 2017, pp. 1-6,
doi: 10.1109/HPEC.2017.8091046. */
UINT_t tc_low(
#if 1
const GRAPH_TYPE *graph
#else
UINT_t *IA , // row indices
UINT_t *JA // column indices
#endif
)
{
#if 1
UINT_t* IA = graph->rowPtr;
UINT_t* JA = graph->colInd;
UINT_t N = graph->numVertices;
#endif
UINT_t delta = 0 ; // number of triangles
// for every vertex in V_{BR}
// # pragma omp parallel for schedule (dynamic) reduction (+ : delta)
for ( UINT_t i = 1 ; i<N-1; i ++ )
{
UINT_t *curr_row_x = IA + i ;
UINT_t *curr_row_A = IA + i + 1;
UINT_t num_nnz_curr_row_x = *curr_row_A - *curr_row_x;
UINT_t *x_col_begin = ( JA + *curr_row_x);
UINT_t *x_col_end = x_col_begin;
UINT_t *row_bound = x_col_begin + num_nnz_curr_row_x;
// UINT_t col_x_min = 0;
UINT_t col_x_max = i - 1;
// partition the current row into x and y, where x == a01 ^ T == a10t and y == a12t
while (x_col_end < row_bound && *x_col_end < col_x_max)
++x_col_end;
x_col_end -= (*x_col_end > col_x_max || x_col_end == row_bound);
UINT_t *y_col_begin = x_col_end + 1;
UINT_t *y_col_end = row_bound - 1;
UINT_t num_nnz_y = (y_col_end - y_col_begin) + 1;
UINT_t num_nnz_x = (x_col_end - x_col_begin) + 1;
UINT_t y_col_first = i + 1;
UINT_t x_col_first = 0;
UINT_t *y_col = y_col_begin;
// compute y*A20*x ( Equation 5 )
for (UINT_t j = 0 ; j< num_nnz_y ; ++j ,++ y_col)
{
UINT_t row_index_A = *y_col - y_col_first;
UINT_t *x_col = x_col_begin;
UINT_t num_nnz_A = *( curr_row_A + row_index_A + 1 ) - *( curr_row_A + row_index_A );
UINT_t *A_col = ( JA + *( curr_row_A + row_index_A ) );
UINT_t *A_col_max = A_col + num_nnz_A ;
for (UINT_t k = 0 ; k < num_nnz_x && *A_col <= col_x_max ; ++k )
{
UINT_t row_index_x = *x_col - x_col_first;
while ( (* A_col < *x_col ) && ( A_col < A_col_max ) )
++A_col;
delta += (* A_col == row_index_x ) ;
++x_col ;
}
}
}
return delta ;
}
void bfs_treelist(const GRAPH_TYPE *graph, const bool* E, UINT_t* parent /* , UINT_t* component */) {
/* UINT_t c; */
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
bool *visited = (bool *)malloc(n * sizeof(bool));
assert_malloc(visited);
for (UINT_t i=0 ; i<n ; i++)
visited[i] = false;
// c = 0;
for (UINT_t v=0 ; v<n ; v++) {
if (!visited[v]) {
// c++;
Queue *queue = createQueue(n);
visited[v] = true;
// component[v] = c;
enqueue(queue, v);
while (!isEmpty(queue)) {
UINT_t currentVertex = dequeue(queue);
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e ; i++) {
if (E[i]) {
UINT_t adjacentVertex = Ai[i];
if (!visited[adjacentVertex]) {
visited[adjacentVertex] = true;
// component[adjacentVertex] = c;
parent[adjacentVertex] = currentVertex;
enqueue(queue, adjacentVertex);
}
}
}
}
free_queue(queue);
}
}
free(visited);
}
static bool and_E(const bool* E, const UINT_t m) {
for (UINT_t i = 0 ; i<m ; i++)
if (E[i]) return true;
return false;
}
static bool check_edge_treelist(const GRAPH_TYPE *graph, const bool* E, const UINT_t v, const UINT_t w) {
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
if ((v==n) || (w==n)) return false;
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e; i++)
if (E[i] && (Ai[i] == w))
return true;
return false;
}
static void remove_treelist(const GRAPH_TYPE* graph, bool *E, const UINT_t *parent) {
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
for (UINT_t v=0 ; v<n ; v++) {
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e; i++) {
if (E[i]) {
UINT_t w = Ai[i];
if (parent[w] == v) {
E[i] = false;
UINT_t ws = Ap[w];
UINT_t we = Ap[w+1];
for (UINT_t j=ws ; j<we ; j++) {
if (Ai[j] == v) {
E[j] = false;
break;
}
}
}
}
}
}
return;
}
UINT_t tc_treelist(const GRAPH_TYPE *graph) {
/* Itai and Rodeh, SIAM Journal of Computing, 1978 */
UINT_t count = 0;
UINT_t *parent;
// UINT_t* component;
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
// 1. While there remains an edge in E:
// 1a. compute a covering tree for each connected component of G;
// 1b. for each edge (u, v) in none of these trees:
// 1ba. If (father(u), v) in E then output triangle (u, v, father(u))
// 1bb. else If (father(v), u) in E then output triangle (u, v, father (v)
// 1c. remove from E all the edges in these trees
bool* E = (bool *)malloc(m * sizeof(bool));
assert_malloc(E);
for (UINT_t i=0 ; i<m ; i++)
E[i] = true;
// component = (UINT_t *)malloc(n * sizeof(UINT_t));
// assert_malloc(component);
parent = (UINT_t *)malloc(n * sizeof(UINT_t));
assert_malloc(parent);
while (and_E(E, m)) {
for (UINT_t i=0 ; i<n ; i++) {
// component[i] = 0;
parent[i] = n;
}
bfs_treelist(graph, E, parent /* , component */);
for (UINT_t u=0 ; u<n ; u++) {
UINT_t s = Ap[u];
UINT_t e = Ap[u+1];
for (UINT_t j=s; j<e ; j++) {
if (E[j]) {
UINT_t v = Ai[j];
if (parent[u] != v) {
if (check_edge_treelist(graph, E, parent[u], v))
count++;
else if (check_edge_treelist(graph, E, parent[v], u))
count++;
}
}
}
}
remove_treelist(graph, E, parent);
}
free(parent);
// free(component);
free(E);
return count/2;
}
static void bfs_treelist2(const GRAPH_TYPE *graph, UINT_t* parent /* , UINT_t* component */) {
/* UINT_t c; */
const UINT_t *restrict Ap = graph->rowPtr;
const UINT_t *restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
bool *visited = (bool *)malloc(n * sizeof(bool));
assert_malloc(visited);
for (UINT_t i=0 ; i<n ; i++)
visited[i] = false;
// c = 0;
for (UINT_t v=0 ; v<n ; v++) {
if (!visited[v]) {
// c++;
Queue *queue = createQueue(n);
visited[v] = true;
// component[v] = c;
enqueue(queue, v);
while (!isEmpty(queue)) {
UINT_t currentVertex = dequeue(queue);
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e ; i++) {
UINT_t adjacentVertex = Ai[i];
if (!visited[adjacentVertex]) {
visited[adjacentVertex] = true;
// component[adjacentVertex] = c;
parent[adjacentVertex] = currentVertex;
enqueue(queue, adjacentVertex);
}
}
}
free_queue(queue);
}
}
free(visited);
}
static void remove_treelist2(GRAPH_TYPE* graph, const UINT_t *parent) {
UINT_t *restrict Ap = graph->rowPtr;
UINT_t *restrict Ai = graph->colInd;
UINT_t n = graph->numVertices;
UINT_t m = graph->numEdges;
bool *E = (bool *)malloc(m * sizeof(bool));
assert_malloc(E);
UINT_t *Degree = (UINT_t *)malloc(n * sizeof(UINT_t));
assert_malloc(Degree);
for (UINT_t i=0 ; i<m ; i++)
E[i] = true;
for (UINT_t v=0 ; v<n ; v++) {
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e; i++) {
UINT_t w = Ai[i];
if (parent[w] == v) {
E[i] = false;
UINT_t ws = Ap[w];
UINT_t we = Ap[w+1];
for (UINT_t j=ws ; j<we ; j++) {
if (Ai[j] == v) {
E[j] = false;
break;
}
}
}
}
}
UINT_t numEdges_new=0;
for (UINT_t i=0 ; i<m ; i++) {
if (E[i]) {
Ai[numEdges_new] = Ai[i];
numEdges_new++;
}
}
for (UINT_t v=0 ; v<n ; v++) {
Degree[v] = 0;
UINT_t s = Ap[v];
UINT_t e = Ap[v+1];
for (UINT_t i = s; i < e; i++) {
if (E[i]) {
Degree[v]++;
}
}
}
Ap[0] = 0;
for (UINT_t i=1 ; i<=n ; i++) {
Ap[i] = Ap[i-1] + Degree[i-1];
}
graph->numEdges = numEdges_new;
free(Degree);
free(E);
return;
}
UINT_t tc_treelist2(const GRAPH_TYPE *graph) {
/* Itai and Rodeh, SIAM Journal of Computing, 1978 */
UINT_t edges;
UINT_t count = 0;
UINT_t *parent;
// UINT_t* component;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
// 1. While there remains an edge in E:
// 1a. compute a covering tree for each connected component of G;
// 1b. for each edge (u, v) in none of these trees:
// 1ba. If (father(u), v) in E then output triangle (u, v, father(u))
// 1bb. else If (father(v), u) in E then output triangle (u, v, father (v)
// 1c. remove from E all the edges in these trees
GRAPH_TYPE* graph2;
graph2 = (GRAPH_TYPE *)malloc(sizeof(GRAPH_TYPE));
assert_malloc(graph2);
graph2->numVertices = n;
graph2->numEdges = m;
allocate_graph(graph2);
copy_graph(graph, graph2);
const UINT_t *restrict Ap2 = graph2->rowPtr;
const UINT_t *restrict Ai2 = graph2->colInd;
// component = (UINT_t *)malloc(n * sizeof(UINT_t));
// assert_malloc(component);
parent = (UINT_t *)malloc(n * sizeof(UINT_t));
assert_malloc(parent);
edges = m;
while (edges>0) {
for (UINT_t i=0 ; i<n ; i++) {
// component[i] = 0;
parent[i] = n;
}
bfs_treelist2(graph2, parent /* , component */);
for (UINT_t u=0 ; u<n ; u++) {
UINT_t s = Ap2[u];
UINT_t e = Ap2[u+1];
for (UINT_t j=s; j<e ; j++) {
UINT_t v = Ai2[j];
if (parent[u] != v) {
if ((parent[u] < n) && (check_edge(graph2, parent[u], v)))
count++;
else if ((parent[v] < n) && (check_edge(graph2, parent[v], u)))
count++;
}
}
}
remove_treelist2(graph2, parent);
edges = graph2->numEdges;
}
free(parent);
// free(component);
free_graph(graph2);
return count/2;
}
UINT_t tc_forward(const GRAPH_TYPE *graph) {
/* Schank, T., Wagner, D. (2005). Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_54 */
register UINT_t s, t;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
UINT_t* Size = (UINT_t *)calloc(n, sizeof(UINT_t));
assert_malloc(Size);
UINT_t* A = (UINT_t *)calloc(m, sizeof(UINT_t));
assert_malloc(A);
for (s = 0; s < n ; s++) {
b = Ap[s ];
e = Ap[s+1];
for (UINT_t i=b ; i<e ; i++) {
t = Ai[i];
if (s<t) {
count += intersectSizeMergePath_forward(graph, s, t, A, Size);
A[Ap[t] + Size[t]] = s;
Size[t]++;
}
}
}
free(A);
free(Size);
return count;
}
static UINT_t tc_forward_hash_config_size(const GRAPH_TYPE *graph, UINT_t hashSize) {
/* Schank, T., Wagner, D. (2005). Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_54 */
register UINT_t s, t;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
bool* Hash = (bool *)calloc( (hashSize == 0)? m: hashSize, sizeof(bool));
assert_malloc(Hash);
UINT_t* Size = (UINT_t *)calloc(n, sizeof(UINT_t));
assert_malloc(Size);
UINT_t* A = (UINT_t *)calloc(m, sizeof(UINT_t));
assert_malloc(A);
for (s = 0; s < n ; s++) {
b = Ap[s ];
e = Ap[s+1];
for (UINT_t i=b ; i<e ; i++) {
t = Ai[i];
if (s<t) {
count += intersectSizeHash_forward(graph, Hash, s, t, A, Size);
A[Ap[t] + Size[t]] = s;
Size[t]++;
}
}
}
free(A);
free(Size);
free(Hash);
return count;
}
UINT_t tc_forward_hash(const GRAPH_TYPE *graph) {
return tc_forward_hash_config_size(graph, 0);
}
static UINT_t tc_forward_hash_skip_config_size(const GRAPH_TYPE *graph, UINT_t hashSize) {
/* Schank, T., Wagner, D. (2005). Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_54 */
register UINT_t s, t;
register UINT_t b, e;
UINT_t count = 0;
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
const UINT_t m = graph->numEdges;
bool* Hash = (bool *)calloc( (hashSize == 0)? m: hashSize, sizeof(bool));
assert_malloc(Hash);
UINT_t* Size = (UINT_t *)calloc(n, sizeof(UINT_t));
assert_malloc(Size);
UINT_t* A = (UINT_t *)calloc(m, sizeof(UINT_t));
assert_malloc(A);
for (s = 0 ; s < n ; s++) {
b = Ap[s ];
e = Ap[s+1];
for (UINT_t i=b ; i<e ; i++) {
t = Ai[i];
if (s<t) {
count += intersectSizeHashSkip_forward(graph, Hash, s, t, A, Size);
A[Ap[t] + Size[t]] = s;
Size[t]++;
}
}
}
free(A);
free(Size);
free(Hash);
return count;
}
UINT_t tc_forward_hash_skip(const GRAPH_TYPE *graph) {
return tc_forward_hash_skip_config_size(graph, 0);
}
UINT_t tc_forward_hash_degreeOrder(const GRAPH_TYPE *graph) {
/* Schank, T., Wagner, D. (2005). Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_54 */
UINT_t count = 0;
GRAPH_TYPE *graph2;
graph2 = reorder_graph_by_degree(graph, REORDER_HIGHEST_DEGREE_FIRST);
count = tc_forward_hash(graph2);
free_graph(graph2);
return count;
}
UINT_t tc_forward_hash_degreeOrderReverse(const GRAPH_TYPE *graph) {
/* Schank, T., Wagner, D. (2005). Finding, Counting and Listing All Triangles in Large Graphs, an Experimental Study. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_54 */
UINT_t count = 0;
GRAPH_TYPE *graph2;
graph2 = reorder_graph_by_degree(graph, REORDER_LOWEST_DEGREE_FIRST);
count = tc_forward_hash(graph2);
free_graph(graph2);
return count;
}
/**** COMPACT FORWARD ***/
UINT_t firstNeighborIndex(const GRAPH_TYPE *graph, UINT_t i) {
const UINT_t* restrict Ap = graph->rowPtr;
const UINT_t* restrict Ai = graph->colInd;
const UINT_t n = graph->numVertices;
UINT_t s = Ap[i];
UINT_t e = Ap[i+1];
UINT_t index = n-1;
for (UINT_t w=s ; w<e ; w++)
if (Ai[w] < index)
index = Ai[w];
return index;
}
UINT_t nextNeighborIndex(const GRAPH_TYPE *graph, UINT_t i, UINT_t j) {
const UINT_t* restrict Ap = graph->rowPtr;