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/* -*- mode: C -*- */
/*
IGraph library.
Copyright (C) 2005-2012 Gabor Csardi <csardi.gabor@gmail.com>
334 Harvard street, Cambridge, MA 02139 USA
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_cliques.h"
#include "igraph_memory.h"
#include "igraph_random.h"
#include "igraph_constants.h"
#include "igraph_adjlist.h"
#include "igraph_interrupt_internal.h"
#include "igraph_interface.h"
#include "igraph_progress.h"
#include "igraph_stack.h"
#include "igraph_types_internal.h"
#include "config.h"
#include <assert.h>
#include <string.h> /* memset */
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, new_member_storage_size;
const igraph_real_t *c1, *c2;
igraph_real_t v1, v2;
igraph_bool_t ok;
/* Allocate the storage */
*new_member_storage=igraph_Realloc(*new_member_storage,
(size_t) (size*old_clique_count),
igraph_real_t);
if (*new_member_storage == 0) {
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
}
new_member_storage_size = size*old_clique_count;
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, (igraph_integer_t) 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;
}
}
/* See if new_member_storage is full. If so, reallocate */
if (m == new_member_storage_size) {
IGRAPH_FINALLY_CLEAN(1);
*new_member_storage = igraph_Realloc(*new_member_storage,
(size_t) new_member_storage_size*2,
igraph_real_t);
if (*new_member_storage == 0)
IGRAPH_ERROR("cliques failed", IGRAPH_ENOMEM);
new_member_storage_size *= 2;
IGRAPH_FINALLY(igraph_free, *new_member_storage);
}
}
}
}
/* 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;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
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_FINALLY(igraph_i_cliques_free_res, res);
/* Will be resized later, if needed. */
member_storage=igraph_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=igraph_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=igraph_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=igraph_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); /* 3 here, +1 is igraph_i_cliques_free_res */
return 0;
}
/**
* \function igraph_cliques
* \brief 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.
*
* </para><para>The current implementation of this function searches
* for maximal independent vertex sets (see \ref
* igraph_maximal_independent_vertex_sets()) in the complementer graph
* using the algorithm published in:
* 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.
*
* \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
*
* \example examples/simple/igraph_cliques.c
*/
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);
}
typedef int(*igraph_i_maximal_clique_func_t)(const igraph_vector_t*, void*, igraph_bool_t*);
typedef struct {
igraph_vector_ptr_t* result;
igraph_integer_t min_size;
igraph_integer_t max_size;
} igraph_i_maximal_clique_data_t;
int igraph_i_maximal_cliques(const igraph_t *graph, igraph_i_maximal_clique_func_t func, void* data);
int igraph_i_maximal_or_largest_cliques_or_indsets(const igraph_t *graph,
igraph_vector_ptr_t *res,
igraph_integer_t *clique_number,
igraph_bool_t keep_only_largest,
igraph_bool_t complementer);
/**
* \function igraph_independent_vertex_sets
* \brief 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.
*
* </para><para>
* The current implementation was ported to igraph from the Very Nauty Graph
* Library by Keith Briggs and uses the algorithm from the 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.
*
* \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
*
* \example examples/simple/igraph_independent_sets.c
*/
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.
*
* </para><para>
* The current implementation was ported to igraph from the Very Nauty Graph
* Library by Keith Briggs and uses the algorithm from the 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.
*
* \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_maximal_or_largest_cliques_or_indsets(graph, res, 0, 1, 0);
}
typedef struct igraph_i_max_ind_vsets_data_t {
igraph_integer_t matrix_size;
igraph_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_bool_t keep_only_largest; /* True if we keep only the largest sets */
} 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_int_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_integer_t size=0;
if (res) {
igraph_vector_t *vec;
vec = igraph_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);
for (v1=0; v1<clqdata->matrix_size; v1++)
if (clqdata->IS[v1] == 0) {
IGRAPH_CHECK(igraph_vector_push_back(vec, v1));
}
size=(igraph_integer_t) igraph_vector_size(vec);
if (!clqdata->keep_only_largest)
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, vec));
else {
if (size > clqdata->largest_set_size) {
/* We are keeping only the largest sets, and we've found one that's
* larger than all previous sets, so we have to clear the list */
j=igraph_vector_ptr_size(res);
for (v1=0; v1<j; v1++) {
igraph_vector_destroy(VECTOR(*res)[v1]);
free(VECTOR(*res)[v1]);
}
igraph_vector_ptr_clear(res);
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, vec));
} else if (size == clqdata->largest_set_size) {
IGRAPH_CHECK(igraph_vector_ptr_push_back(res, vec));
} else {
igraph_vector_destroy(vec);
free(vec);
}
}
IGRAPH_FINALLY_CLEAN(1);
} 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;
} else {
v1 = level+1;
/* Count the number of vertices with an index less than v1 that have
* an IS value of zero */
neis1 = igraph_adjlist_get(&clqdata->adj_list, v1);
c = 0;
j = 0;
while (j<VECTOR(clqdata->deg)[v1] &&
(v2=(long int) 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=(long int) VECTOR(*neis1)[j]) <= level) {
clqdata->IS[v2]++;
j++;
}
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph,res,clqdata, (igraph_integer_t) v1));
j = 0;
while (j<VECTOR(clqdata->deg)[v1] &&
(v2=(long int) 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] = (igraph_integer_t) c;
IGRAPH_CHECK(igraph_i_maximal_independent_vertex_sets_backtrack(graph,res,clqdata, (igraph_integer_t) v1));
clqdata->IS[v1] = 0;
f=1;
j=0;
while (j<VECTOR(clqdata->deg)[v1] &&
(v2=(long int) VECTOR(*neis1)[j]) <= level) {
if (clqdata->IS[v2] == 0) {
IGRAPH_CHECK(igraph_set_add(&clqdata->buckets[v1],
(igraph_integer_t) j));
neis2 = igraph_adjlist_get(&clqdata->adj_list, v2);
k = 0;
while (k<VECTOR(clqdata->deg)[v2] &&
(v3=(long int) 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, (igraph_integer_t) v1));
j=0;
while (j<VECTOR(clqdata->deg)[v1] &&
(v2=(long int) 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=(long int) VECTOR(*neis1)[j];
neis2 = igraph_adjlist_get(&clqdata->adj_list, v2);
k = 0;
while (k<VECTOR(clqdata->deg)[v2] &&
(v3=(long int) 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++;
}
igraph_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;
igraph_integer_t no_of_nodes = (igraph_integer_t) igraph_vcount(graph), i;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
clqdata.matrix_size=no_of_nodes;
clqdata.keep_only_largest=0;
IGRAPH_CHECK(igraph_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = igraph_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_int_size(igraph_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = igraph_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_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.
*
* </para><para>
* The current implementation was ported to igraph from the Very Nauty Graph
* Library by Keith Briggs and uses the algorithm from the 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.
*
* \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;
igraph_integer_t no_of_nodes = (igraph_integer_t) igraph_vcount(graph), i;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
clqdata.matrix_size=no_of_nodes;
clqdata.keep_only_largest=0;
IGRAPH_CHECK(igraph_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = igraph_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_int_size(igraph_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = igraph_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_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
return 0;
}
/*************************************************************************/
/* MAXIMAL CLIQUES, LARGEST CLIQUES */
/*************************************************************************/
int igraph_i_maximal_cliques_store_max_size(const igraph_vector_t* clique, void* data,
igraph_bool_t* cont) {
igraph_integer_t* result = (igraph_integer_t*)data;
IGRAPH_UNUSED(cont);
if (*result < igraph_vector_size(clique))
*result = (igraph_integer_t) igraph_vector_size(clique);
return IGRAPH_SUCCESS;
}
int igraph_i_maximal_cliques_store(const igraph_vector_t* clique, void* data, igraph_bool_t* cont) {
igraph_vector_ptr_t* result = (igraph_vector_ptr_t*)data;
igraph_vector_t* vec;
IGRAPH_UNUSED(cont);
vec = igraph_Calloc(1, igraph_vector_t);
if (vec == 0)
IGRAPH_ERROR("cannot allocate memory for storing next clique", IGRAPH_ENOMEM);
IGRAPH_CHECK(igraph_vector_copy(vec, clique));
IGRAPH_CHECK(igraph_vector_ptr_push_back(result, vec));
return IGRAPH_SUCCESS;
}
int igraph_i_maximal_cliques_store_size_check(const igraph_vector_t* clique, void* data_, igraph_bool_t* cont) {
igraph_i_maximal_clique_data_t* data = (igraph_i_maximal_clique_data_t*)data_;
igraph_vector_t* vec;
igraph_integer_t size = (igraph_integer_t) igraph_vector_size(clique);
IGRAPH_UNUSED(cont);
if (size < data->min_size || size > data->max_size)
return IGRAPH_SUCCESS;
vec = igraph_Calloc(1, igraph_vector_t);
if (vec == 0)
IGRAPH_ERROR("cannot allocate memory for storing next clique", IGRAPH_ENOMEM);
IGRAPH_CHECK(igraph_vector_copy(vec, clique));
IGRAPH_CHECK(igraph_vector_ptr_push_back(data->result, vec));
return IGRAPH_SUCCESS;
}
int igraph_i_largest_cliques_store(const igraph_vector_t* clique, void* data, igraph_bool_t* cont) {
igraph_vector_ptr_t* result = (igraph_vector_ptr_t*)data;
igraph_vector_t* vec;
long int i, n;
IGRAPH_UNUSED(cont);
/* Is the current clique at least as large as the others that we have found? */
if (!igraph_vector_ptr_empty(result)) {
n = igraph_vector_size(clique);
if (n < igraph_vector_size(VECTOR(*result)[0]))
return IGRAPH_SUCCESS;
if (n > igraph_vector_size(VECTOR(*result)[0])) {
for (i = 0; i < igraph_vector_ptr_size(result); i++)
igraph_vector_destroy(VECTOR(*result)[i]);
igraph_vector_ptr_free_all(result);
igraph_vector_ptr_resize(result, 0);
}
}
vec = igraph_Calloc(1, igraph_vector_t);
if (vec == 0)
IGRAPH_ERROR("cannot allocate memory for storing next clique", IGRAPH_ENOMEM);
IGRAPH_CHECK(igraph_vector_copy(vec, clique));
IGRAPH_CHECK(igraph_vector_ptr_push_back(result, vec));
return IGRAPH_SUCCESS;
}
/**
* \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 necessarily the same as a maximal clique,
* ie. the largest cliques are always maximal but a maximal clique is
* not always largest.
*
* </para><para>The current implementation of this function searches
* for maximal cliques using \ref igraph_maximal_cliques() and drops
* those that are not the largest.
*
* </para><para>The implementation of this function changed between
* igraph 0.5 and 0.6, so the order of the cliques and the order of
* vertices within the cliques will almost surely be different between
* these two versions.
*
* \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. Note that
* vertices of a clique may be returned in arbitrary order.
* \return Error code.
*
* \sa \ref igraph_cliques(), \ref igraph_maximal_cliques()
*
* Time complexity: O(3^(|V|/3)) worst case.
*/
int igraph_largest_cliques(const igraph_t *graph, igraph_vector_ptr_t *res) {
igraph_vector_ptr_clear(res);
IGRAPH_FINALLY(igraph_i_cliques_free_res, res);
IGRAPH_CHECK(igraph_i_maximal_cliques(graph, &igraph_i_largest_cliques_store, (void*)res));
IGRAPH_FINALLY_CLEAN(1);
return IGRAPH_SUCCESS;
}
/**
* \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: O(3^(|V|/3)) worst case.
*/
int igraph_clique_number(const igraph_t *graph, igraph_integer_t *no) {
*no = 0;
return igraph_i_maximal_cliques(graph, &igraph_i_maximal_cliques_store_max_size, (void*)no);
}
typedef struct {
igraph_vector_int_t cand;
igraph_vector_int_t fini;
igraph_vector_int_t cand_filtered;
} igraph_i_maximal_cliques_stack_frame;
void igraph_i_maximal_cliques_stack_frame_destroy(igraph_i_maximal_cliques_stack_frame *frame) {
igraph_vector_int_destroy(&frame->cand);
igraph_vector_int_destroy(&frame->fini);
igraph_vector_int_destroy(&frame->cand_filtered);
}
void igraph_i_maximal_cliques_stack_destroy(igraph_stack_ptr_t *stack) {
igraph_i_maximal_cliques_stack_frame *frame;
while (!igraph_stack_ptr_empty(stack)) {
frame = (igraph_i_maximal_cliques_stack_frame*)igraph_stack_ptr_pop(stack);
igraph_i_maximal_cliques_stack_frame_destroy(frame);
free(frame);
}
igraph_stack_ptr_destroy(stack);
}
int igraph_i_maximal_cliques(const igraph_t *graph, igraph_i_maximal_clique_func_t func, void* data) {
int directed=igraph_is_directed(graph);
long int i, j, k, l;
igraph_integer_t no_of_nodes, nodes_to_check, nodes_done;
igraph_integer_t best_cand = 0, best_cand_degree = 0, best_fini_cand_degree;
igraph_adjlist_t adj_list;
igraph_stack_ptr_t stack;
igraph_i_maximal_cliques_stack_frame frame, *new_frame_ptr;
igraph_vector_t clique;
igraph_vector_int_t new_cand, new_fini, cn, best_cand_nbrs,
best_fini_cand_nbrs;
igraph_bool_t cont = 1;
int assret;
if (directed)
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
no_of_nodes = igraph_vcount(graph);
if (no_of_nodes == 0)
return IGRAPH_SUCCESS;
/* Construct an adjacency list representation */
IGRAPH_CHECK(igraph_adjlist_init(graph, &adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &adj_list);
IGRAPH_CHECK(igraph_adjlist_simplify(&adj_list));
igraph_adjlist_sort(&adj_list);
/* Initialize stack */
IGRAPH_CHECK(igraph_stack_ptr_init(&stack, 0));
IGRAPH_FINALLY(igraph_i_maximal_cliques_stack_destroy, &stack);
/* Create the initial (empty) clique */
IGRAPH_VECTOR_INIT_FINALLY(&clique, 0);
/* Initialize new_cand, new_fini, cn, best_cand_nbrs and best_fini_cand_nbrs (will be used later) */
igraph_vector_int_init(&new_cand, 0);
IGRAPH_FINALLY(igraph_vector_int_destroy, &new_cand);
igraph_vector_int_init(&new_fini, 0);
IGRAPH_FINALLY(igraph_vector_int_destroy, &new_fini);
igraph_vector_int_init(&cn, 0);
IGRAPH_FINALLY(igraph_vector_int_destroy, &cn);
igraph_vector_int_init(&best_cand_nbrs, 0);
IGRAPH_FINALLY(igraph_vector_int_destroy, &best_cand_nbrs);
igraph_vector_int_init(&best_fini_cand_nbrs, 0);
IGRAPH_FINALLY(igraph_vector_int_destroy, &best_fini_cand_nbrs);
/* Find the vertex with the highest degree */
best_cand = 0; best_cand_degree = (igraph_integer_t) igraph_vector_int_size(igraph_adjlist_get(&adj_list, 0));
for (i = 1; i < no_of_nodes; i++) {
j = igraph_vector_int_size(igraph_adjlist_get(&adj_list, i));
if (j > best_cand_degree) {
best_cand = (igraph_integer_t) i;
best_cand_degree = (igraph_integer_t) j;
}
}
/* Create the initial stack frame */
IGRAPH_CHECK(igraph_vector_int_init_seq(&frame.cand, 0, no_of_nodes-1));
IGRAPH_FINALLY(igraph_vector_int_destroy, &frame.cand);
IGRAPH_CHECK(igraph_vector_int_init(&frame.fini, 0));
IGRAPH_FINALLY(igraph_vector_int_destroy, &frame.fini);
IGRAPH_CHECK(igraph_vector_int_init(&frame.cand_filtered, 0));
IGRAPH_FINALLY(igraph_vector_int_destroy, &frame.cand_filtered);
IGRAPH_CHECK(igraph_vector_int_difference_sorted(&frame.cand,
igraph_adjlist_get(&adj_list, best_cand), &frame.cand_filtered));
IGRAPH_FINALLY_CLEAN(3);
IGRAPH_FINALLY(igraph_i_maximal_cliques_stack_frame_destroy, &frame);
/* TODO: frame.cand and frame.fini should be a set instead of a vector */
/* Main loop starts here */
nodes_to_check = (igraph_integer_t) igraph_vector_int_size(&frame.cand_filtered); nodes_done = 0;
while (!igraph_vector_int_empty(&frame.cand_filtered) || !igraph_stack_ptr_empty(&stack)) {
if (igraph_vector_int_empty(&frame.cand_filtered)) {
/* No candidates left to check in this stack frame, pop out the previous stack frame */
igraph_i_maximal_cliques_stack_frame *newframe = igraph_stack_ptr_pop(&stack);
igraph_i_maximal_cliques_stack_frame_destroy(&frame);
frame = *newframe;
free(newframe);
if (igraph_stack_ptr_size(&stack) == 1) {
/* We will be using the next candidate node in the next iteration, so we can increase
* nodes_done by 1 */
nodes_done++;
}
/* For efficiency reasons, we only check for interruption and show progress here */
IGRAPH_PROGRESS("Maximal cliques: ", 100.0 * nodes_done / nodes_to_check, NULL);
IGRAPH_ALLOW_INTERRUPTION();
igraph_vector_pop_back(&clique);
continue;
}
/* Try the next node in the clique */
i = (long int) igraph_vector_int_pop_back(&frame.cand_filtered);
IGRAPH_CHECK(igraph_vector_push_back(&clique, i));
/* Remove the node from the candidate list */
assret=igraph_vector_int_binsearch(&frame.cand, i, &j); assert(assret);
igraph_vector_int_remove(&frame.cand, j);
/* Add the node to the finished list */
assret = !igraph_vector_int_binsearch(&frame.fini, i, &j); assert(assret);
IGRAPH_CHECK(igraph_vector_int_insert(&frame.fini, j, i));
/* Create new_cand and new_fini */
IGRAPH_CHECK(igraph_vector_int_intersect_sorted(&frame.cand, igraph_adjlist_get(&adj_list, i), &new_cand));
IGRAPH_CHECK(igraph_vector_int_intersect_sorted(&frame.fini, igraph_adjlist_get(&adj_list, i), &new_fini));
/* Do we have anything more to search? */
if (igraph_vector_int_empty(&new_cand)) {
if (igraph_vector_int_empty(&new_fini)) {
/* We have a maximal clique here */
IGRAPH_CHECK(func(&clique, data, &cont));
if (!cont) {
/* The callback function requested to stop the search */
break;
}
}
igraph_vector_pop_back(&clique);
continue;
}
if (igraph_vector_int_empty(&new_fini) &&
igraph_vector_int_size(&new_cand) == 1) {
/* Shortcut: only one node left */
IGRAPH_CHECK(igraph_vector_push_back(&clique, VECTOR(new_cand)[0]));
IGRAPH_CHECK(func(&clique, data, &cont));
if (!cont) {
/* The callback function requested to stop the search */
break;
}
igraph_vector_pop_back(&clique);
igraph_vector_pop_back(&clique);
continue;
}
/* Find the next best candidate node in new_fini */
l = igraph_vector_int_size(&new_cand);
best_cand_degree = -1;
j = igraph_vector_int_size(&new_fini);
for (i = 0; i < j; i++) {
k = (long int)VECTOR(new_fini)[i];
IGRAPH_CHECK(igraph_vector_int_intersect_sorted(&new_cand, igraph_adjlist_get(&adj_list, k), &cn));
if (igraph_vector_int_size(&cn) > best_cand_degree) {
best_cand_degree = (igraph_integer_t) igraph_vector_int_size(&cn);
IGRAPH_CHECK(igraph_vector_int_update(&best_fini_cand_nbrs, &cn));
if (best_cand_degree == l) {
/* Cool, we surely have the best candidate node here as best_cand_degree can't get any better */
break;
}
}
}
/* Shortcut here: we don't have to examine new_cand */
if (best_cand_degree == l) {
igraph_vector_pop_back(&clique);
continue;
}
/* Still finding best candidate node */
best_fini_cand_degree = best_cand_degree;
best_cand_degree = -1;
j = igraph_vector_int_size(&new_cand);
l = l - 1;
for (i = 0; i < j; i++) {
k = (long int)VECTOR(new_cand)[i];
IGRAPH_CHECK(igraph_vector_int_intersect_sorted(&new_cand, igraph_adjlist_get(&adj_list, k), &cn));
if (igraph_vector_int_size(&cn) > best_cand_degree) {
best_cand_degree = (igraph_integer_t) igraph_vector_int_size(&cn);
IGRAPH_CHECK(igraph_vector_int_update(&best_cand_nbrs, &cn));
if (best_cand_degree == l) {
/* Cool, we surely have the best candidate node here as best_cand_degree can't get any better */
break;
}
}
}
/* Create a new stack frame in case we back out later */
new_frame_ptr = igraph_Calloc(1, igraph_i_maximal_cliques_stack_frame);
if (new_frame_ptr == 0) {
IGRAPH_ERROR("cannot allocate new stack frame", IGRAPH_ENOMEM);
}
IGRAPH_FINALLY(igraph_free, new_frame_ptr);
*new_frame_ptr = frame;
memset(&frame, 0, sizeof(frame));
IGRAPH_CHECK(igraph_stack_ptr_push(&stack, new_frame_ptr));
IGRAPH_FINALLY_CLEAN(1); /* ownership of new_frame_ptr taken by the stack */
/* Ownership of the current frame and its vectors (frame.cand, frame.done, frame.cand_filtered)
* is taken by the stack from now on. Vectors in frame must be re-initialized with new_cand,
* new_fini and stuff. The old frame.cand and frame.fini won't be leaked because they are
* managed by the stack now. */
frame.cand = new_cand;
frame.fini = new_fini;
IGRAPH_CHECK(igraph_vector_int_init(&new_cand, 0));
IGRAPH_CHECK(igraph_vector_int_init(&new_fini, 0));
IGRAPH_CHECK(igraph_vector_int_init(&frame.cand_filtered, 0));
/* Adjust frame.cand_filtered */
if (best_cand_degree < best_fini_cand_degree) {
IGRAPH_CHECK(igraph_vector_int_difference_sorted(&frame.cand, &best_fini_cand_nbrs, &frame.cand_filtered));
} else {
IGRAPH_CHECK(igraph_vector_int_difference_sorted(&frame.cand, &best_cand_nbrs, &frame.cand_filtered));
}
}
IGRAPH_PROGRESS("Maximal cliques: ", 100.0, NULL);
igraph_adjlist_destroy(&adj_list);
igraph_vector_destroy(&clique);
igraph_vector_int_destroy(&new_cand);
igraph_vector_int_destroy(&new_fini);
igraph_vector_int_destroy(&cn);
igraph_vector_int_destroy(&best_cand_nbrs);
igraph_vector_int_destroy(&best_fini_cand_nbrs);
igraph_i_maximal_cliques_stack_frame_destroy(&frame);
igraph_i_maximal_cliques_stack_destroy(&stack);
IGRAPH_FINALLY_CLEAN(9);
return IGRAPH_SUCCESS;
}
int igraph_i_maximal_or_largest_cliques_or_indsets(const igraph_t *graph,
igraph_vector_ptr_t *res,
igraph_integer_t *clique_number,
igraph_bool_t keep_only_largest,
igraph_bool_t complementer) {
igraph_i_max_ind_vsets_data_t clqdata;
igraph_integer_t no_of_nodes = (igraph_integer_t) igraph_vcount(graph), i;
if (igraph_is_directed(graph))
IGRAPH_WARNING("directionality of edges is ignored for directed graphs");
clqdata.matrix_size=no_of_nodes;
clqdata.keep_only_largest=keep_only_largest;
if (complementer)
IGRAPH_CHECK(igraph_adjlist_init_complementer(graph, &clqdata.adj_list, IGRAPH_ALL, 0));
else
IGRAPH_CHECK(igraph_adjlist_init(graph, &clqdata.adj_list, IGRAPH_ALL));
IGRAPH_FINALLY(igraph_adjlist_destroy, &clqdata.adj_list);
clqdata.IS = igraph_Calloc(no_of_nodes, igraph_integer_t);
if (clqdata.IS == 0)
IGRAPH_ERROR("igraph_i_maximal_or_largest_cliques_or_indsets 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_int_size(igraph_adjlist_get(&clqdata.adj_list, i));
clqdata.buckets = igraph_Calloc(no_of_nodes+1, igraph_set_t);
if (clqdata.buckets == 0)
IGRAPH_ERROR("igraph_maximal_or_largest_cliques_or_indsets 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));
if (res) 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_adjlist_destroy(&clqdata.adj_list);
igraph_vector_destroy(&clqdata.deg);
igraph_free(clqdata.IS);
igraph_free(clqdata.buckets);
IGRAPH_FINALLY_CLEAN(4);
if (clique_number) *clique_number = clqdata.largest_set_size;
return 0;
}
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