FM / graph

/usr/include/boost/graph

Name	Size	Mode	Actions
detail/	-	0755	rm
distributed/	-	0755	rm
parallel/	-	0755	rm
planar_detail/	-	0755	rm
property_maps/	-	0755	rm
accounting.hpp	876	0644	edit dl rm
adjacency_iterator.hpp	2899	0644	edit dl rm
adjacency_list.hpp	13692	0644	edit dl rm
adjacency_list_io.hpp	11849	0644	edit dl rm
adjacency_matrix.hpp	45743	0644	edit dl rm
adj_list_serialize.hpp	4523	0644	edit dl rm
astar_search.hpp	26736	0644	edit dl rm
bandwidth.hpp	2992	0644	edit dl rm
bc_clustering.hpp	5937	0644	edit dl rm
bellman_ford_shortest_paths.hpp	8229	0644	edit dl rm
betweenness_centrality.hpp	26290	0644	edit dl rm
biconnected_components.hpp	16701	0644	edit dl rm
bipartite.hpp	13492	0644	edit dl rm
boyer_myrvold_planar_test.hpp	9849	0644	edit dl rm
boykov_kolmogorov_max_flow.hpp	47342	0644	edit dl rm
breadth_first_search.hpp	14751	0644	edit dl rm
bron_kerbosch_all_cliques.hpp	11736	0644	edit dl rm
buffer_concepts.hpp	2429	0644	edit dl rm
chrobak_payne_drawing.hpp	8641	0644	edit dl rm
circle_layout.hpp	1924	0644	edit dl rm
closeness_centrality.hpp	6057	0644	edit dl rm
clustering_coefficient.hpp	5726	0644	edit dl rm
compressed_sparse_row_graph.hpp	69887	0644	edit dl rm
connected_components.hpp	4134	0644	edit dl rm
copy.hpp	21225	0644	edit dl rm
core_numbers.hpp	13663	0644	edit dl rm
create_condensation_graph.hpp	3159	0644	edit dl rm
cuthill_mckee_ordering.hpp	5992	0644	edit dl rm
cycle_canceling.hpp	6645	0644	edit dl rm
dag_shortest_paths.hpp	6064	0644	edit dl rm
degree_centrality.hpp	4236	0644	edit dl rm
depth_first_search.hpp	15430	0644	edit dl rm
dijkstra_shortest_paths.hpp	23687	0644	edit dl rm
dijkstra_shortest_paths_no_color_map.hpp	9620	0644	edit dl rm
dimacs.hpp	10448	0644	edit dl rm
directed_graph.hpp	24214	0644	edit dl rm
dll_import_export.hpp	892	0644	edit dl rm
dominator_tree.hpp	17553	0644	edit dl rm
eccentricity.hpp	4611	0644	edit dl rm
edge_coloring.hpp	6809	0644	edit dl rm
edge_connectivity.hpp	6796	0644	edit dl rm
edge_list.hpp	9948	0644	edit dl rm
edmonds_karp_max_flow.hpp	10177	0644	edit dl rm
edmunds_karp_max_flow.hpp	982	0644	edit dl rm
erdos_renyi_generator.hpp	7257	0644	edit dl rm
exception.hpp	1466	0644	edit dl rm
exterior_property.hpp	4289	0644	edit dl rm
filtered_graph.hpp	20098	0644	edit dl rm
find_flow_cost.hpp	1859	0644	edit dl rm
floyd_warshall_shortest.hpp	8510	0644	edit dl rm
fruchterman_reingold.hpp	17325	0644	edit dl rm
geodesic_distance.hpp	8015	0644	edit dl rm
graphml.hpp	13460	0644	edit dl rm
graphviz.hpp	33503	0644	edit dl rm
graph_archetypes.hpp	11008	0644	edit dl rm
graph_as_tree.hpp	4532	0644	edit dl rm
graph_concepts.hpp	19785	0644	edit dl rm
graph_mutability_traits.hpp	4995	0644	edit dl rm
graph_selectors.hpp	1274	0644	edit dl rm
graph_stats.hpp	4394	0644	edit dl rm
graph_traits.hpp	13065	0644	edit dl rm
graph_utility.hpp	16182	0644	edit dl rm
grid_graph.hpp	33830	0644	edit dl rm
gursoy_atun_layout.hpp	13248	0644	edit dl rm
hawick_circuits.hpp	14593	0644	edit dl rm
howard_cycle_ratio.hpp	23107	0644	edit dl rm
incremental_components.hpp	8224	0644	edit dl rm
isomorphism.hpp	26308	0644	edit dl rm
is_kuratowski_subgraph.hpp	10260	0644	edit dl rm
is_straight_line_drawing.hpp	7230	0644	edit dl rm
iteration_macros.hpp	11659	0644	edit dl rm
iteration_macros_undef.hpp	673	0644	edit dl rm
johnson_all_pairs_shortest.hpp	7646	0644	edit dl rm
kamada_kawai_spring_layout.hpp	28048	0644	edit dl rm
king_ordering.hpp	12101	0644	edit dl rm
kruskal_min_spanning_tree.hpp	5743	0644	edit dl rm
labeled_graph.hpp	30914	0644	edit dl rm
leda_graph.hpp	28789	0644	edit dl rm
lookup_edge.hpp	1894	0644	edit dl rm
loop_erased_random_walk.hpp	4436	0644	edit dl rm
make_biconnected_planar.hpp	3513	0644	edit dl rm
make_connected.hpp	2645	0644	edit dl rm
make_maximal_planar.hpp	7578	0644	edit dl rm
matrix_as_graph.hpp	7227	0644	edit dl rm
maximum_adjacency_search.hpp	15125	0644	edit dl rm
maximum_weighted_matching.hpp	49722	0644	edit dl rm
max_cardinality_matching.hpp	31000	0644	edit dl rm
mcgregor_common_subgraphs.hpp	43470	0644	edit dl rm
mesh_graph_generator.hpp	5616	0644	edit dl rm
metis.hpp	10982	0644	edit dl rm
metric_tsp_approx.hpp	10809	0644	edit dl rm
minimum_degree_ordering.hpp	27087	0644	edit dl rm
named_function_params.hpp	39639	0644	edit dl rm
named_graph.hpp	20614	0644	edit dl rm
neighbor_bfs.hpp	11763	0644	edit dl rm
numeric_values.hpp	1814	0644	edit dl rm
one_bit_color_map.hpp	3277	0644	edit dl rm
overloading.hpp	1584	0644	edit dl rm
page_rank.hpp	6164	0644	edit dl rm
planar_canonical_ordering.hpp	7203	0644	edit dl rm
planar_face_traversal.hpp	6020	0644	edit dl rm
plod_generator.hpp	7708	0644	edit dl rm
point_traits.hpp	782	0644	edit dl rm
prim_minimum_spanning_tree.hpp	2960	0644	edit dl rm
profile.hpp	1327	0644	edit dl rm
properties.hpp	12417	0644	edit dl rm
property_iter_range.hpp	4345	0644	edit dl rm
push_relabel_max_flow.hpp	34737	0644	edit dl rm
random.hpp	9672	0644	edit dl rm
random_layout.hpp	988	0644	edit dl rm
random_spanning_tree.hpp	5775	0644	edit dl rm
read_dimacs.hpp	12080	0644	edit dl rm
relax.hpp	4400	0644	edit dl rm
reverse_graph.hpp	22402	0644	edit dl rm
rmat_graph_generator.hpp	19291	0644	edit dl rm
r_c_shortest_paths.hpp	30673	0644	edit dl rm
sequential_vertex_coloring.hpp	4562	0644	edit dl rm
simple_point.hpp	628	0644	edit dl rm
sloan_ordering.hpp	15540	0644	edit dl rm
smallest_last_ordering.hpp	5458	0644	edit dl rm
small_world_generator.hpp	3670	0644	edit dl rm
ssca_graph_generator.hpp	6564	0644	edit dl rm
stanford_graph.hpp	20126	0644	edit dl rm
stoer_wagner_min_cut.hpp	12415	0644	edit dl rm
strong_components.hpp	13009	0644	edit dl rm
st_connected.hpp	2852	0644	edit dl rm
subgraph.hpp	39996	0644	edit dl rm
successive_shortest_path_nonnegative_weights.hpp	10413	0644	edit dl rm
tiernan_all_cycles.hpp	12547	0644	edit dl rm
topological_sort.hpp	2611	0644	edit dl rm
topology.hpp	20389	0644	edit dl rm
transitive_closure.hpp	14260	0644	edit dl rm
transitive_reduction.hpp	5326	0644	edit dl rm
transpose_graph.hpp	1198	0644	edit dl rm
tree_traits.hpp	1338	0644	edit dl rm
two_bit_color_map.hpp	3510	0644	edit dl rm
two_graphs_common_spanning_trees.hpp	34996	0644	edit dl rm
undirected_dfs.hpp	10672	0644	edit dl rm
undirected_graph.hpp	25276	0644	edit dl rm
use_mpi.hpp	437	0644	edit dl rm
vector_as_graph.hpp	10474	0644	edit dl rm
vertex_and_edge_range.hpp	5528	0644	edit dl rm
vf2_sub_graph_iso.hpp	48585	0644	edit dl rm
visitors.hpp	11318	0644	edit dl rm
wavefront.hpp	3932	0644	edit dl rm
write_dimacs.hpp	2889	0644	edit dl rm

Edit: /usr/include/boost/graph/bron_kerbosch_all_cliques.hpp (11736B)

// (C) Copyright 2007-2009 Andrew Sutton
//
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0 (See accompanying file
// LICENSE_1_0.txt or http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_GRAPH_CLIQUE_HPP
#define BOOST_GRAPH_CLIQUE_HPP

#include <vector>
#include <deque>
#include <boost/config.hpp>

#include <boost/concept/assert.hpp>

#include <boost/graph/graph_concepts.hpp>
#include <boost/graph/lookup_edge.hpp>

#include <boost/concept/detail/concept_def.hpp>
namespace boost
{
namespace concepts
{
    BOOST_concept(CliqueVisitor, (Visitor)(Clique)(Graph))
    {
        BOOST_CONCEPT_USAGE(CliqueVisitor) { vis.clique(k, g); }

private:
        Visitor vis;
        Graph g;
        Clique k;
    };
} /* namespace concepts */
using concepts::CliqueVisitorConcept;
} /* namespace boost */
#include <boost/concept/detail/concept_undef.hpp>

namespace boost
{
// The algorithm implemented in this paper is based on the so-called
// Algorithm 457, published as:
//
//     @article{362367,
//         author = {Coen Bron and Joep Kerbosch},
//         title = {Algorithm 457: finding all cliques of an undirected graph},
//         journal = {Communications of the ACM},
//         volume = {16},
//         number = {9},
//         year = {1973},
//         issn = {0001-0782},
//         pages = {575--577},
//         doi = {http://doi.acm.org/10.1145/362342.362367},
//             publisher = {ACM Press},
//             address = {New York, NY, USA},
//         }
//
// Sort of. This implementation is adapted from the 1st version of the
// algorithm and does not implement the candidate selection optimization
// described as published - it could, it just doesn't yet.
//
// The algorithm is given as proportional to (3.14)^(n/3) power. This is
// not the same as O(...), but based on time measures and approximation.
//
// Unfortunately, this implementation may be less efficient on non-
// AdjacencyMatrix modeled graphs due to the non-constant implementation
// of the edge(u,v,g) functions.
//
// TODO: It might be worthwhile to provide functionality for passing
// a connectivity matrix to improve the efficiency of those lookups
// when needed. This could simply be passed as a BooleanMatrix
// s.t. edge(u,v,B) returns true or false. This could easily be
// abstracted for adjacency matricies.
//
// The following paper is interesting for a number of reasons. First,
// it lists a number of other such algorithms and second, it describes
// a new algorithm (that does not appear to require the edge(u,v,g)
// function and appears fairly efficient. It is probably worth investigating.
//
//      @article{DBLP:journals/tcs/TomitaTT06,
//          author = {Etsuji Tomita and Akira Tanaka and Haruhisa Takahashi},
//          title = {The worst-case time complexity for generating all maximal
//          cliques and computational experiments}, journal = {Theor. Comput.
//          Sci.}, volume = {363}, number = {1}, year = {2006}, pages = {28-42}
//          ee = {https://doi.org/10.1016/j.tcs.2006.06.015}
//      }

/**
 * The default clique_visitor supplies an empty visitation function.
 */
struct clique_visitor
{
    template < typename VertexSet, typename Graph >
    void clique(const VertexSet&, Graph&)
    {
    }
};

/**
 * The max_clique_visitor records the size of the maximum clique (but not the
 * clique itself).
 */
struct max_clique_visitor
{
    max_clique_visitor(std::size_t& max) : maximum(max) {}

template < typename Clique, typename Graph >
    inline void clique(const Clique& p, const Graph& g)
    {
        BOOST_USING_STD_MAX();
        maximum = max BOOST_PREVENT_MACRO_SUBSTITUTION(maximum, p.size());
    }
    std::size_t& maximum;
};

inline max_clique_visitor find_max_clique(std::size_t& max)
{
    return max_clique_visitor(max);
}

namespace detail
{
    template < typename Graph >
    inline bool is_connected_to_clique(const Graph& g,
        typename graph_traits< Graph >::vertex_descriptor u,
        typename graph_traits< Graph >::vertex_descriptor v,
        typename graph_traits< Graph >::undirected_category)
    {
        return lookup_edge(u, v, g).second;
    }

template < typename Graph >
    inline bool is_connected_to_clique(const Graph& g,
        typename graph_traits< Graph >::vertex_descriptor u,
        typename graph_traits< Graph >::vertex_descriptor v,
        typename graph_traits< Graph >::directed_category)
    {
        // Note that this could alternate between using an || to determine
        // full connectivity. I believe that this should produce strongly
        // connected components. Note that using && instead of || will
        // change the results to a fully connected subgraph (i.e., symmetric
        // edges between all vertices s.t., if a->b, then b->a.
        return lookup_edge(u, v, g).second && lookup_edge(v, u, g).second;
    }

template < typename Graph, typename Container >
    inline void filter_unconnected_vertices(const Graph& g,
        typename graph_traits< Graph >::vertex_descriptor v,
        const Container& in, Container& out)
    {
        BOOST_CONCEPT_ASSERT((GraphConcept< Graph >));

typename graph_traits< Graph >::directed_category cat;
        typename Container::const_iterator i, end = in.end();
        for (i = in.begin(); i != end; ++i)
        {
            if (is_connected_to_clique(g, v, *i, cat))
            {
                out.push_back(*i);
            }
        }
    }

template < typename Graph,
        typename Clique, // compsub type
        typename Container, // candidates/not type
        typename Visitor >
    void extend_clique(const Graph& g, Clique& clique, Container& cands,
        Container& nots, Visitor vis, std::size_t min)
    {
        BOOST_CONCEPT_ASSERT((GraphConcept< Graph >));
        BOOST_CONCEPT_ASSERT((CliqueVisitorConcept< Visitor, Clique, Graph >));
        typedef typename graph_traits< Graph >::vertex_descriptor Vertex;

// Is there vertex in nots that is connected to all vertices
        // in the candidate set? If so, no clique can ever be found.
        // This could be broken out into a separate function.
        {
            typename Container::iterator ni, nend = nots.end();
            typename Container::iterator ci, cend = cands.end();
            for (ni = nots.begin(); ni != nend; ++ni)
            {
                for (ci = cands.begin(); ci != cend; ++ci)
                {
                    // if we don't find an edge, then we're okay.
                    if (!lookup_edge(*ni, *ci, g).second)
                        break;
                }
                // if we iterated all the way to the end, then *ni
                // is connected to all *ci
                if (ci == cend)
                    break;
            }
            // if we broke early, we found *ni connected to all *ci
            if (ni != nend)
                return;
        }

// TODO: the original algorithm 457 describes an alternative
        // (albeit really complicated) mechanism for selecting candidates.
        // The given optimizaiton seeks to bring about the above
        // condition sooner (i.e., there is a vertex in the not set
        // that is connected to all candidates). unfortunately, the
        // method they give for doing this is fairly unclear.

// basically, for every vertex in not, we should know how many
        // vertices it is disconnected from in the candidate set. if
        // we fix some vertex in the not set, then we want to keep
        // choosing vertices that are not connected to that fixed vertex.
        // apparently, by selecting fix point with the minimum number
        // of disconnections (i.e., the maximum number of connections
        // within the candidate set), then the previous condition wil
        // be reached sooner.

// there's some other stuff about using the number of disconnects
        // as a counter, but i'm jot really sure i followed it.

// TODO: If we min-sized cliques to visit, then theoretically, we
        // should be able to stop recursing if the clique falls below that
        // size - maybe?

// otherwise, iterate over candidates and and test
        // for maxmimal cliquiness.
        typename Container::iterator i, j;
        for (i = cands.begin(); i != cands.end();)
        {
            Vertex candidate = *i;

// add the candidate to the clique (keeping the iterator!)
            // typename Clique::iterator ci = clique.insert(clique.end(),
            // candidate);
            clique.push_back(candidate);

// remove it from the candidate set
            i = cands.erase(i);

// build new candidate and not sets by removing all vertices
            // that are not connected to the current candidate vertex.
            // these actually invert the operation, adding them to the new
            // sets if the vertices are connected. its semantically the same.
            Container new_cands, new_nots;
            filter_unconnected_vertices(g, candidate, cands, new_cands);
            filter_unconnected_vertices(g, candidate, nots, new_nots);

if (new_cands.empty() && new_nots.empty())
            {
                // our current clique is maximal since there's nothing
                // that's connected that we haven't already visited. If
                // the clique is below our radar, then we won't visit it.
                if (clique.size() >= min)
                {
                    vis.clique(clique, g);
                }
            }
            else
            {
                // recurse to explore the new candidates
                extend_clique(g, clique, new_cands, new_nots, vis, min);
            }

// we're done with this vertex, so we need to move it
            // to the nots, and remove the candidate from the clique.
            nots.push_back(candidate);
            clique.pop_back();
        }
    }
} /* namespace detail */

template < typename Graph, typename Visitor >
inline void bron_kerbosch_all_cliques(
    const Graph& g, Visitor vis, std::size_t min)
{
    BOOST_CONCEPT_ASSERT((IncidenceGraphConcept< Graph >));
    BOOST_CONCEPT_ASSERT((VertexListGraphConcept< Graph >));
    BOOST_CONCEPT_ASSERT(
        (AdjacencyMatrixConcept< Graph >)); // Structural requirement only
    typedef typename graph_traits< Graph >::vertex_descriptor Vertex;
    typedef typename graph_traits< Graph >::vertex_iterator VertexIterator;
    typedef std::vector< Vertex > VertexSet;
    typedef std::deque< Vertex > Clique;
    BOOST_CONCEPT_ASSERT((CliqueVisitorConcept< Visitor, Clique, Graph >));

// NOTE: We're using a deque to implement the clique, because it provides
    // constant inserts and removals at the end and also a constant size.

VertexIterator i, end;
    boost::tie(i, end) = vertices(g);
    VertexSet cands(i, end); // start with all vertices as candidates
    VertexSet nots; // start with no vertices visited

Clique clique; // the first clique is an empty vertex set
    detail::extend_clique(g, clique, cands, nots, vis, min);
}

// NOTE: By default the minimum number of vertices per clique is set at 2
// because singleton cliques aren't really very interesting.
template < typename Graph, typename Visitor >
inline void bron_kerbosch_all_cliques(const Graph& g, Visitor vis)
{
    bron_kerbosch_all_cliques(g, vis, 2);
}

template < typename Graph >
inline std::size_t bron_kerbosch_clique_number(const Graph& g)
{
    std::size_t ret = 0;
    bron_kerbosch_all_cliques(g, find_max_clique(ret));
    return ret;
}

} /* namespace boost */

#endif

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