/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2005 Gabor Csardi <csardi@rmki.kfki.hu>
MTA RMKI, Konkoly-Thege Miklos st. 29-33, Budapest 1121, Hungary
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA
*/
#include "igraph.h"
#include "memory.h"
#include "random.h"
void igraph_i_cliques_free_res(igraph_vector_ptr_t *res) {
long i, n;
n = igraph_vector_ptr_size(res);
for (i=0; i<n; i++) {
if (VECTOR(*res)[i] != 0) {
igraph_vector_destroy(VECTOR(*res)[i]);
igraph_free(VECTOR(*res)[i]);
}
}
igraph_vector_ptr_clear(res);
}
int igraph_i_find_k_cliques(const igraph_t *graph,
long int size,
const igraph_real_t *member_storage,
igraph_real_t **new_member_storage,
long int old_clique_count,
long int *clique_count,
igraph_vector_t *neis,
igraph_bool_t independent_vertices) {
long int j, k, l, m, n;
const igraph_real_t *c1, *c2;
igraph_real_t v1, v2;
igraph_bool_t ok;
/* Allocate the storage */
*new_member_storage=Realloc(*new_member_storage,
size*old_clique_count*(old_clique_count-1)/2,
igraph_real_t);
if (*new_member_storage == 0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, *new_member_storage);
m=n=0;
/* Now consider all pairs of i-1-cliques and see if they can be merged */
for (j=0; j<old_clique_count; j++) {
for (k=j+1; k<old_clique_count; k++) {
IGRAPH_ALLOW_INTERRUPTION();
/* Since cliques are represented by their vertex indices in increasing
* order, two cliques can be merged iff they have exactly the same
* indices excluding one AND there is an edge between the two different
* vertices */
c1 = member_storage+j*(size-1);
c2 = member_storage+k*(size-1);
/* Find the longest prefixes of c1 and c2 that are equal */
for (l=0; l<size-1 && c1[l] == c2[l]; l++)
(*new_member_storage)[m++]=c1[l];
/* Now, if l == size-1, the two vectors are totally equal.
This is a bug */
if (l == size-1) {
IGRAPH_WARNING("possible bug in igraph_cliques");
m=n;
} else {
/* Assuming that j<k, c1[l] is always less than c2[l], since cliques
* are ordered alphabetically. Now add c1[l] and store c2[l] in a
* dummy variable */
(*new_member_storage)[m++]=c1[l];
v1=c1[l];
v2=c2[l];
l++;
/* Copy the remaining part of the two vectors. Every member pair
* found in the remaining parts satisfies the following:
* 1. If they are equal, they should be added.
* 2. If they are not equal, the smaller must be equal to the
* one stored in the dummy variable. If not, the two vectors
* differ in more than one place. The larger will be stored in
* the dummy variable again.
*/
ok=1;
for (; l<size-1; l++) {
if (c1[l] == c2[l]) {
(*new_member_storage)[m++]=c1[l];
ok=0;
} else if (ok) {
if (c1[l] < c2[l]) {
if (c1[l] == v1) {
(*new_member_storage)[m++]=c1[l];
v2 = c2[l];
} else break;
} else {
if (ok && c2[l] == v1) {
(*new_member_storage)[m++]=c2[l];
v2 = c1[l];
} else break;
}
} else break;
}
/* Now, if l != size-1, the two vectors had a difference in more than
* one place, so the whole clique is invalid. */
if (l != size-1) {
/* Step back in new_member_storage */
m=n;
} else {
/* v1 and v2 are the two different vertices. Check for an edge
* if we are looking for cliques and check for the absence of an
* edge if we are looking for independent vertex sets */
IGRAPH_CHECK(igraph_neighbors(graph, neis, v1, IGRAPH_ALL));
l=igraph_vector_search(neis, 0, v2, 0);
if ((l && !independent_vertices) || (!l && independent_vertices)) {
/* Found a new clique, step forward in new_member_storage */
if (m==n || v2>(*new_member_storage)[m-1]) {
(*new_member_storage)[m++]=v2;
n=m;
} else {
m=n;
}
} else {
m=n;
}
}
}
}
}
/* Calculate how many cliques have we found */
*clique_count = n/size;
IGRAPH_FINALLY_CLEAN(1);
return 0;
}
/* Internal function for calculating cliques or independent vertex sets.
* They are practically the same except that the complementer of the graph
* should be used in the latter case.
*/
int igraph_i_cliques(const igraph_t *graph, igraph_vector_ptr_t *res,
igraph_integer_t min_size, igraph_integer_t max_size,
igraph_bool_t independent_vertices) {
igraph_integer_t no_of_nodes;
igraph_vector_t neis;
igraph_real_t *member_storage=0, *new_member_storage, *c1;
long int i, j, k, clique_count, old_clique_count;
no_of_nodes = igraph_vcount(graph);
if (min_size < 0) { min_size = 0; }
if (max_size > no_of_nodes || max_size <= 0) { max_size = no_of_nodes; }
igraph_vector_ptr_clear(res);
IGRAPH_VECTOR_INIT_FINALLY(&neis, 0);
igraph_vector_ptr_clear(res);
IGRAPH_FINALLY(igraph_i_cliques_free_res, res);
/* Will be resized later, if needed. */
member_storage=Calloc(1, igraph_real_t);
if (member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, member_storage);
/* Find all 1-cliques: every vertex will be a clique */
new_member_storage=Calloc(no_of_nodes, igraph_real_t);
if (new_member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, new_member_storage);
for (i=0; i<no_of_nodes; i++) {
new_member_storage[i] = i;
}
clique_count = no_of_nodes;
old_clique_count = 0;
/* Add size 1 cliques if requested */
if (min_size <= 1) {
IGRAPH_CHECK(igraph_vector_ptr_resize(res, no_of_nodes));
igraph_vector_ptr_null(res);
for (i=0; i<no_of_nodes; i++) {
igraph_vector_t *p=Calloc(1, igraph_vector_t);
if (p==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, p);
IGRAPH_CHECK(igraph_vector_init(p, 1));
VECTOR(*p)[0]=i;
VECTOR(*res)[i]=p;
IGRAPH_FINALLY_CLEAN(1);
}
}
for (i=2; i<=max_size && clique_count > 1; i++) {
/* Here new_member_storage contains the cliques found in the previous
iteration. Save this into member_storage, might be needed later */
c1=member_storage;
member_storage=new_member_storage;
new_member_storage=c1;
old_clique_count=clique_count;
IGRAPH_ALLOW_INTERRUPTION();
/* Calculate the cliques */
IGRAPH_FINALLY_CLEAN(2);
IGRAPH_CHECK(igraph_i_find_k_cliques(graph, i, member_storage,
&new_member_storage,
old_clique_count,
&clique_count,
&neis,
independent_vertices));
IGRAPH_FINALLY(igraph_free, member_storage);
IGRAPH_FINALLY(igraph_free, new_member_storage);
/* Add the cliques just found to the result if requested */
if (i>=min_size && i<=max_size) {
for (j=0, k=0; j<clique_count; j++, k+=i) {
igraph_vector_t *p=Calloc(1, igraph_vector_t);
if (p==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, p);
IGRAPH_CHECK(igraph_vector_init_copy(p, &new_member_storage[k], i));
IGRAPH_FINALLY(igraph_vector_destroy, p);
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, p));
IGRAPH_FINALLY_CLEAN(2);
}
}
} /* i <= max_size && clique_count != 0 */
igraph_free(member_storage);
igraph_free(new_member_storage);
igraph_vector_destroy(&neis);
IGRAPH_FINALLY_CLEAN(4); /* 2 here, +1 is igraph_i_cliques_free_res */
return 0;
}
/**
* \function igraph_cliques
* Find all or some cliques in a graph
*
* </para><para>
* Cliques are fully connected subgraphs of a graph.
*
* </para><para>
* If you are only interested in the size of the largest clique in the graph,
* use \ref igraph_clique_number() instead.
*
* \param graph The input graph.
* \param res Pointer to a pointer vector, the result will be stored
* here, ie. \c res will contain pointers to \c igraph_vector_t
* objects which contain the indices of vertices involved in a clique.
* The pointer vector will be resized if needed but note that the
* objects in the pointer vector will not be freed.
* \param min_size Integer giving the minimum size of the cliques to be
* returned. If negative or zero, no lower bound will be used.
* \param max_size Integer giving the maximum size of the cliques to be
* returned. If negative or zero, no upper bound will be used.
* \return Error code.
*
* \sa \ref igraph_largest_cliques() and \ref igraph_clique_number().
*
* Time complexity: TODO
*/
int igraph_cliques(const igraph_t *graph, igraph_vector_ptr_t *res,
igraph_integer_t min_size, igraph_integer_t max_size) {
return igraph_i_cliques(graph, res, min_size, max_size, 0);
}
int igraph_i_largest_cliques(const igraph_t *graph, igraph_vector_ptr_t *res,
igraph_bool_t independent_vertices) {
igraph_integer_t no_of_nodes;
igraph_vector_t neis;
igraph_real_t *member_storage=0, *new_member_storage, *c1;
long int i, j, k, clique_count, old_clique_count;
no_of_nodes = igraph_vcount(graph);
IGRAPH_VECTOR_INIT_FINALLY(&neis, 0);
igraph_vector_ptr_clear(res);
IGRAPH_FINALLY(igraph_i_cliques_free_res, res);
/* Will be resized later, if needed. */
member_storage=Calloc(1, igraph_real_t);
if (member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, member_storage);
new_member_storage=Calloc(no_of_nodes, igraph_real_t);
if (new_member_storage==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, new_member_storage);
for (i=0; i<no_of_nodes; i++) {
new_member_storage[i] = i;
}
clique_count = no_of_nodes;
old_clique_count = 0;
for (i=2; i<=no_of_nodes && clique_count > 1; i++) {
c1=member_storage;
member_storage=new_member_storage;
new_member_storage=c1;
old_clique_count=clique_count;
IGRAPH_ALLOW_INTERRUPTION();
/* Calculate the cliques */
IGRAPH_FINALLY_CLEAN(2);
IGRAPH_CHECK(igraph_i_find_k_cliques(graph, i, member_storage,
&new_member_storage,
old_clique_count,
&clique_count,
&neis,
independent_vertices));
IGRAPH_FINALLY(igraph_free, member_storage);
IGRAPH_FINALLY(igraph_free, new_member_storage);
}
/* Where is the result? */
if (clique_count != 0) {
c1=new_member_storage;
i=no_of_nodes;
} else {
c1=member_storage;
i=i-2;
clique_count=old_clique_count;
}
/* Ok, the result is in c1, there are clique_count cliques and
i is the size of the cliques
*/
for (j=0, k=0; j<clique_count; j++, k+=i) {
igraph_vector_t *p=Calloc(1, igraph_vector_t);
if (p==0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, p);
IGRAPH_CHECK(igraph_vector_init_copy(p, &c1[k], i));
IGRAPH_FINALLY(igraph_vector_destroy, p);
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, p));
IGRAPH_FINALLY_CLEAN(2);
}
igraph_free(member_storage);
igraph_free(new_member_storage);
igraph_vector_destroy(&neis);
IGRAPH_FINALLY_CLEAN(4); /* 2 here, +1 is igraph_i_cliques_free_res */
return 0;
}
/**
* \function igraph_largest_cliques
* \brief Finds the largest clique(s) in a graph.
*
* </para><para>
* A clique is largest (quite intuitively) if there is no other clique
* in the graph which contains more vertices.
*
* </para><para>
* Note that this is not neccessarily the same as a maximal clique,
* ie. the largest cliques are always maximal but a maximal clique is
* not always largest.
* \param graph The input graph.
* \param res Pointer to an initialized pointer vector, the result
* will be stored here. It will be resized as needed.
* \return Error code.
*
* \sa \ref igraph_cliques(), \ref igraph_maximal_cliques()
*
* Time complexity: TODO.
*/
int igraph_largest_cliques(const igraph_t *graph, igraph_vector_ptr_t *res) {
return igraph_i_largest_cliques(graph, res, 0);
}
/**
* \function igraph_independent_vertex_sets
* Find all independent vertex sets in a graph
*
* </para><para>
* A vertex set is considered independent if there are no edges between
* them.
*
* </para><para>
* If you are interested in the size of the largest independent vertex set,
* use \ref igraph_independence_number() instead.
*
* \param graph The input graph.
* \param res Pointer to a pointer vector, the result will be stored
* here, ie. \c res will contain pointers to \c igraph_vector_t
* objects which contain the indices of vertices involved in an independent
* vertex set. The pointer vector will be resized if needed but note that the
* objects in the pointer vector will not be freed.
* \param min_size Integer giving the minimum size of the sets to be
* returned. If negative or zero, no lower bound will be used.
* \param max_size Integer giving the maximum size of the sets to be
* returned. If negative or zero, no upper bound will be used.
* \return Error code.
*
* \sa \ref igraph_largest_independent_vertex_sets(),
* \ref igraph_independence_number().
*
* Time complexity: TODO
*/
int igraph_independent_vertex_sets(const igraph_t *graph,
igraph_vector_ptr_t *res,
igraph_integer_t min_size,
igraph_integer_t max_size) {
return igraph_i_cliques(graph, res, min_size, max_size, 1);
}
/**
* \function igraph_largest_independent_vertex_sets
* \brief Finds the largest independent vertex set(s) in a graph.
*
* </para><para>
* An independent vertex set is largest if there is no other
* independent vertex set with more vertices in the graph.
* \param graph The input graph.
* \param res Pointer to a pointer vector, the result will be stored
* here. It will be resized as needed.
* \return Error code.
*
* \sa \ref igraph_independent_vertex_sets(), \ref
* igraph_maximal_independent_vertex_sets().
*
* Time complexity: TODO
*/
int igraph_largest_independent_vertex_sets(const igraph_t *graph,
igraph_vector_ptr_t *res) {
return igraph_i_largest_cliques(graph, res, 1);
}
typedef struct igraph_i_max_ind_vsets_data_t {
igraph_integer_t matrix_size;
igraph_i_adjlist_t adj_list; /* Adjacency list of the graph */
igraph_vector_t deg; /* Degrees of individual nodes */
igraph_set_t* buckets; /* Bucket array */
/* The IS value for each node. Still to be explained :) */
igraph_integer_t* IS;
igraph_integer_t largest_set_size; /* Size of the largest set encountered */
} igraph_i_max_ind_vsets_data_t;
int igraph_i_maximal_independent_vertex_sets_backtrack(const igraph_t *graph,
igraph_vector_ptr_t *res,
igraph_i_max_ind_vsets_data_t *clqdata,
igraph_integer_t level) {
long int v1, v2, v3, c, j, k;
igraph_vector_t *neis1, *neis2;
igraph_bool_t f;
igraph_integer_t j1;
long int it_state;
IGRAPH_ALLOW_INTERRUPTION();
if (level >= clqdata->matrix_size-1) {
igraph_vector_t *vec;
igraph_integer_t size=0;
vec = Calloc(1, igraph_vector_t);
if (vec == 0)
IGRAPH_ERROR("igraph_i_maximal_independent_vertex_sets failed", IGRAPH_ENOMEM);
IGRAPH_VECTOR_INIT_FINALLY(vec, 0);
if (res) {
for (v1=0; v1<clqdata->matrix_size; v1++)
if (clqdata->IS[v1] == 0) {
IGRAPH_CHECK(igraph_vector_push_back(vec, v1));
}
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, vec));
size=igraph_vector_size(vec);
} else {
for (v1=0, size=0; v1<clqdata->matrix_size; v1++)
if (clqdata->IS[v1] == 0) size++;
}
if (size>clqdata->largest_set_size) clqdata->largest_set_size=size;
IGRAPH_FINALLY_CLEAN(1);
} else {
v1 = level+1;
/* Count the number of vertices with an index less than v1 that have
* an IS value of zero */
neis1 = igraph_i_adjlist_get(&clqdata->adj_list, v1);
c = 0;
j = 0;
while (j<VECTOR(clqdata->deg)[v1] && (v2=VECTOR(*neis1)[j]) <= level) {
if (clqdata->IS[v2] == 0) c++;
j++;
}
if (c == 0) {
/* If there are no such nodes... */
j = 0;
while (j<VECTOR(clqdata->deg)[v1] && (v2=VECTOR(*neis1)[j]) <= level) {
clqdata->IS[v2]++;
j++;
}
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph,res,clqdata,v1));
j = 0;
while (j<VECTOR(clqdata->deg)[v1] && (v2=VECTOR(*neis1)[j]) <= level) {
clqdata->IS[v2]--;
j++;
}
} else {
/* If there are such nodes, store the count in the IS value of v1 */
clqdata->IS[v1] = c;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph,res,clqdata,v1));
clqdata->IS[v1] = 0;
f=1;
j=0;
while (j<VECTOR(clqdata->deg)[v1] && (v2=VECTOR(*neis1)[j]) <= level) {
if (clqdata->IS[v2] == 0) {
IGRAPH_CHECK(igraph_set_add(&clqdata->buckets[v1], j));
neis2 = igraph_i_adjlist_get(&clqdata->adj_list, v2);
k = 0;
while (k<VECTOR(clqdata->deg)[v2] && (v3=VECTOR(*neis2)[k])<=level) {
clqdata->IS[v3]--;
if (clqdata->IS[v3] == 0) f=0;
k++;
}
}
clqdata->IS[v2]++;
j++;
}
if (f)
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph,res,clqdata,v1));
j=0;
while (j<VECTOR(clqdata->deg)[v1] && (v2=VECTOR(*neis1)[j]) <= level) {
clqdata->IS[v2]--;
j++;
}
it_state=0;
while (igraph_set_iterate(&clqdata->buckets[v1], &it_state, &j1)) {
j=(long)j1;
v2=VECTOR(*neis1)[j];
neis2 = igraph_i_adjlist_get(&clqdata->adj_list, v2);
k = 0;
while (k<VECTOR(clqdata->deg)[v2] && (v3=VECTOR(*neis2)[k])<=level) {
clqdata->IS[v3]++;
k++;
}
}
igraph_set_clear(&clqdata->buckets[v1]);
}
}
return 0;
}
void igraph_i_free_set_array(igraph_set_t* array) {
long int i = 0;
while (igraph_set_inited(array+i)) {
igraph_set_destroy(array+i);
i++;
}
Free(array);
}
/**
* \function igraph_maximal_independent_vertex_sets
* \brief Find all maximal independent vertex sets of a graph
*
* </para><para>
* A maximal independent vertex set is an independent vertex set which
* can't be extended any more by adding a new vertex to it.
*
* </para><para>
* The algorithm used here is based on the following paper:
* S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm for
* generating all the maximal independent sets. SIAM J Computing,
* 6:505--517, 1977.
*
* </para><para>
* The implementation was originally written by Kevin O'Neill and modified
* by K M Briggs in the Very Nauty Graph Library. I simply re-wrote it to
* use igraph's data structures.
*
* </para><para>
* If you are interested in the size of the largest independent vertex set,
* use \ref igraph_independence_number() instead.
*
* \param graph The input graph.
* \param res Pointer to a pointer vector, the result will be stored
* here, ie. \c res will contain pointers to \c igraph_vector_t
* objects which contain the indices of vertices involved in an independent
* vertex set. The pointer vector will be resized if needed but note that the
* objects in the pointer vector will not be freed.
* \return Error code.
*
* \sa \ref igraph_maximal_cliques(), \ref
* igraph_independence_number()
*
* Time complexity: TODO.
*/
int igraph_maximal_independent_vertex_sets(const igraph_t *graph,
igraph_vector_ptr_t *res) {
igraph_i_max_ind_vsets_data_t clqdata;
long int no_of_nodes = igraph_vcount(graph), i;
clqdata.matrix_size=no_of_nodes;
IGRAPH_CHECK(igraph_i_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_i_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_maximal_independent_vertex_sets failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_free, clqdata.IS);
IGRAPH_VECTOR_INIT_FINALLY(&clqdata.deg, no_of_nodes);
for (i=0; i<no_of_nodes; i++)
VECTOR(clqdata.deg)[i] = igraph_vector_size(igraph_i_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_maximal_independent_vertex_sets failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_i_free_set_array, clqdata.buckets);
for (i=0; i<no_of_nodes; i++)
IGRAPH_CHECK(igraph_set_init(&clqdata.buckets[i], 0));
igraph_vector_ptr_clear(res);
/* Do the show */
clqdata.largest_set_size=0;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph, res, &clqdata, 0));
/* Cleanup */
for (i=0; i<no_of_nodes; i++) igraph_set_destroy(&clqdata.buckets[i]);
igraph_i_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
return 0;
}
/**
* \function igraph_independence_number
* \brief Find the independence number of the graph
*
* </para><para>
* The independence number of a graph is the cardinality of the largest
* independent vertex set.
*
* \param graph The input graph.
* \param no The independence number will be returned to the \c
* igraph_integer_t pointed by this variable.
* \return Error code.
*
* \sa \ref igraph_independent_vertex_sets().
*
* Time complexity: TODO.
*/
int igraph_independence_number(const igraph_t *graph, igraph_integer_t *no) {
igraph_i_max_ind_vsets_data_t clqdata;
long int no_of_nodes = igraph_vcount(graph), i;
clqdata.matrix_size=no_of_nodes;
IGRAPH_CHECK(igraph_i_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_i_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_independence_number failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_free, clqdata.IS);
IGRAPH_VECTOR_INIT_FINALLY(&clqdata.deg, no_of_nodes);
for (i=0; i<no_of_nodes; i++)
VECTOR(clqdata.deg)[i] = igraph_vector_size(igraph_i_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_independence_number failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_i_free_set_array, clqdata.buckets);
for (i=0; i<no_of_nodes; i++)
IGRAPH_CHECK(igraph_set_init(&clqdata.buckets[i], 0));
/* Do the show */
clqdata.largest_set_size=0;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph, 0, &clqdata, 0));
*no = clqdata.largest_set_size;
/* Cleanup */
for (i=0; i<no_of_nodes; i++) igraph_set_destroy(&clqdata.buckets[i]);
igraph_i_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
return 0;
}
/**
* \function igraph_maximal_cliques
* \brief Find all maximal cliques of a graph
*
* </para><para>
* A maximal clique is a clique which
* can't be extended any more by adding a new vertex to it. This is actually
* implemented by looking for a maximal independent vertex set in the
* complementer of the graph.
*
* </para><para>
* If you are only interested in the size of the largest clique in the graph,
* use \ref igraph_clique_number() instead.
*
* \param graph The input graph.
* \param res Pointer to a pointer vector, the result will be stored
* here, ie. \c res will contain pointers to \c igraph_vector_t
* objects which contain the indices of vertices involved in a clique.
* The pointer vector will be resized if needed but note that the
* objects in the pointer vector will not be freed.
* \return Error code.
*
* \sa \ref igraph_maximal_independent_vertex_sets(), \ref
* igraph_clique_number()
*
* Time complexity: TODO.
*/
int igraph_maximal_cliques(const igraph_t *graph, igraph_vector_ptr_t *res) {
igraph_i_max_ind_vsets_data_t clqdata;
long int no_of_nodes = igraph_vcount(graph), i;
clqdata.matrix_size=no_of_nodes;
IGRAPH_CHECK(igraph_i_adjlist_init_complementer(graph, &clqdata.adj_list,
IGRAPH_ALL, 0));
IGRAPH_FINALLY(igraph_i_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_maximal_cliques failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_free, clqdata.IS);
IGRAPH_VECTOR_INIT_FINALLY(&clqdata.deg, no_of_nodes);
for (i=0; i<no_of_nodes; i++)
VECTOR(clqdata.deg)[i] = igraph_vector_size(igraph_i_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_maximal_cliques failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_i_free_set_array, clqdata.buckets);
for (i=0; i<no_of_nodes; i++)
IGRAPH_CHECK(igraph_set_init(&clqdata.buckets[i], 0));
igraph_vector_ptr_clear(res);
/* Do the show */
clqdata.largest_set_size=0;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph, res, &clqdata, 0));
/* Cleanup */
for (i=0; i<no_of_nodes; i++) igraph_set_destroy(&clqdata.buckets[i]);
igraph_i_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
return 0;
}
/**
* \function igraph_clique_number
* \brief Find the clique number of the graph
*
* </para><para>
* The clique number of a graph is the size of the largest clique.
*
* \param graph The input graph.
* \param no The clique number will be returned to the \c igraph_integer_t
* pointed by this variable.
* \return Error code.
*
* \sa \ref igraph_cliques(), \ref igraph_largest_cliques().
*
* Time complexity: TODO.
*/
int igraph_clique_number(const igraph_t *graph, igraph_integer_t *no) {
igraph_i_max_ind_vsets_data_t clqdata;
long int no_of_nodes = igraph_vcount(graph), i;
clqdata.matrix_size=no_of_nodes;
IGRAPH_CHECK(igraph_i_adjlist_init_complementer(graph, &clqdata.adj_list,
IGRAPH_ALL, 0));
IGRAPH_FINALLY(igraph_i_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_clique_number failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_free, clqdata.IS);
IGRAPH_VECTOR_INIT_FINALLY(&clqdata.deg, no_of_nodes);
for (i=0; i<no_of_nodes; i++)
VECTOR(clqdata.deg)[i] = igraph_vector_size(igraph_i_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_clique_number failed", IGRAPH_ENOMEM);
IGRAPH_FINALLY(igraph_i_free_set_array, clqdata.buckets);
for (i=0; i<no_of_nodes; i++)
IGRAPH_CHECK(igraph_set_init(&clqdata.buckets[i], 0));
/* Do the show */
clqdata.largest_set_size=0;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph, 0, &clqdata, 0));
*no = clqdata.largest_set_size;
/* Cleanup */
for (i=0; i<no_of_nodes; i++) igraph_set_destroy(&clqdata.buckets[i]);
igraph_i_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
return 0;
}
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