boost/graph/core_numbers.hpp
// //======================================================================= // Copyright 2007 Stanford University // Authors: David Gleich // // Distributed under the Boost Software License, Version 1.0. (See // accompanying file LICENSE_1_0.txt or copy at // http://www.boost.org/LICENSE_1_0.txt) //======================================================================= // #ifndef BOOST_GRAPH_CORE_NUMBERS_HPP #define BOOST_GRAPH_CORE_NUMBERS_HPP #include <boost/graph/detail/d_ary_heap.hpp> #include <boost/graph/breadth_first_search.hpp> #include <boost/iterator/reverse_iterator.hpp> #include <boost/concept/assert.hpp> /* * core_numbers * * Requirement: IncidenceGraph */ // History // // 30 July 2007 // Added visitors to the implementation // // 8 February 2008 // Fixed headers and missing typename namespace boost { // A linear time O(m) algorithm to compute the indegree core number // of a graph for unweighted graphs. // // and a O((n+m) log n) algorithm to compute the in-edge-weight core // numbers of a weighted graph. // // The linear algorithm comes from: // Vladimir Batagelj and Matjaz Zaversnik, "An O(m) Algorithm for Cores // Decomposition of Networks." Sept. 1 2002. template <typename Visitor, typename Graph> struct CoreNumbersVisitorConcept { void constraints() { BOOST_CONCEPT_ASSERT(( CopyConstructibleConcept<Visitor> )); vis.examine_vertex(u,g); vis.finish_vertex(u,g); vis.examine_edge(e,g); } Visitor vis; Graph g; typename graph_traits<Graph>::vertex_descriptor u; typename graph_traits<Graph>::edge_descriptor e; }; template <class Visitors = null_visitor> class core_numbers_visitor : public bfs_visitor<Visitors> { public: core_numbers_visitor() {} core_numbers_visitor(Visitors vis) : bfs_visitor<Visitors>(vis) {} private: template <class Vertex, class Graph> void initialize_vertex(Vertex, Graph&) {} template <class Vertex, class Graph> void discover_vertex(Vertex , Graph&) {} template <class Vertex, class Graph> void gray_target(Vertex, Graph&) {} template <class Vertex, class Graph> void black_target(Vertex, Graph&) {} template <class Edge, class Graph> void tree_edge(Edge, Graph&) {} template <class Edge, class Graph> void non_tree_edge(Edge, Graph&) {} }; template <class Visitors> core_numbers_visitor<Visitors> make_core_numbers_visitor(Visitors vis) { return core_numbers_visitor<Visitors>(vis); } typedef core_numbers_visitor<> default_core_numbers_visitor; namespace detail { // implement a constant_property_map to simplify compute_in_degree // for the weighted and unweighted case // this is based on dummy property map template <typename ValueType> class constant_value_property_map : public boost::put_get_helper<ValueType, constant_value_property_map<ValueType> > { public: typedef void key_type; typedef ValueType value_type; typedef const ValueType& reference; typedef boost::readable_property_map_tag category; inline constant_value_property_map(ValueType cc) : c(cc) { } inline constant_value_property_map(const constant_value_property_map<ValueType>& x) : c(x.c) { } template <class Vertex> inline reference operator[](Vertex) const { return c; } protected: ValueType c; }; // the core numbers start as the indegree or inweight. This function // will initialize these values template <typename Graph, typename CoreMap, typename EdgeWeightMap> void compute_in_degree_map(Graph& g, CoreMap d, EdgeWeightMap wm) { typename graph_traits<Graph>::vertex_iterator vi,vi_end; typename graph_traits<Graph>::out_edge_iterator ei,ei_end; for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { put(d,*vi,0); } for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { for (boost::tie(ei,ei_end) = out_edges(*vi,g); ei!=ei_end; ++ei) { put(d,target(*ei,g),get(d,target(*ei,g))+get(wm,*ei)); } } } // the version for weighted graphs is a little different template <typename Graph, typename CoreMap, typename EdgeWeightMap, typename MutableQueue, typename Visitor> typename property_traits<CoreMap>::value_type core_numbers_impl(Graph& g, CoreMap c, EdgeWeightMap wm, MutableQueue& Q, Visitor vis) { typename property_traits<CoreMap>::value_type v_cn = 0; typedef typename graph_traits<Graph>::vertex_descriptor vertex; while (!Q.empty()) { // remove v from the Q, and then decrease the core numbers // of its successors vertex v = Q.top(); vis.examine_vertex(v,g); Q.pop(); v_cn = get(c,v); typename graph_traits<Graph>::out_edge_iterator oi,oi_end; for (boost::tie(oi,oi_end) = out_edges(v,g); oi!=oi_end; ++oi) { vis.examine_edge(*oi,g); vertex u = target(*oi,g); // if c[u] > c[v], then u is still in the graph, if (get(c,u) > v_cn) { // remove the edge put(c,u,get(c,u)-get(wm,*oi)); if (Q.contains(u)) Q.update(u); } } vis.finish_vertex(v,g); } return (v_cn); } template <typename Graph, typename CoreMap, typename EdgeWeightMap, typename IndexMap, typename CoreNumVisitor> typename property_traits<CoreMap>::value_type core_numbers_dispatch(Graph&g, CoreMap c, EdgeWeightMap wm, IndexMap im, CoreNumVisitor vis) { typedef typename property_traits<CoreMap>::value_type D; typedef std::less<D> Cmp; // build the mutable queue typedef typename graph_traits<Graph>::vertex_descriptor vertex; std::vector<std::size_t> index_in_heap_data(num_vertices(g)); typedef iterator_property_map<std::vector<std::size_t>::iterator, IndexMap> index_in_heap_map_type; index_in_heap_map_type index_in_heap_map(index_in_heap_data.begin(), im); typedef d_ary_heap_indirect<vertex, 4, index_in_heap_map_type, CoreMap, Cmp> MutableQueue; MutableQueue Q(c, index_in_heap_map, Cmp()); typename graph_traits<Graph>::vertex_iterator vi,vi_end; for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { Q.push(*vi); } return core_numbers_impl(g, c, wm, Q, vis); } // the version for the unweighted case // for this functions CoreMap must be initialized // with the in degree of each vertex template <typename Graph, typename CoreMap, typename PositionMap, typename Visitor> typename property_traits<CoreMap>::value_type core_numbers_impl(Graph& g, CoreMap c, PositionMap pos, Visitor vis) { typedef typename graph_traits<Graph>::vertices_size_type size_type; typedef typename graph_traits<Graph>::degree_size_type degree_type; typedef typename graph_traits<Graph>::vertex_descriptor vertex; typename graph_traits<Graph>::vertex_iterator vi,vi_end; // store the vertex core numbers typename property_traits<CoreMap>::value_type v_cn = 0; // compute the maximum degree (degrees are in the coremap) typename graph_traits<Graph>::degree_size_type max_deg = 0; for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { max_deg = (std::max<typename graph_traits<Graph>::degree_size_type>)(max_deg, get(c,*vi)); } // store the vertices in bins by their degree // allocate two extra locations to ease boundary cases std::vector<size_type> bin(max_deg+2); for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { ++bin[get(c,*vi)]; } // this loop sets bin[d] to the starting position of vertices // with degree d in the vert array for the bucket sort size_type cur_pos = 0; for (degree_type cur_deg = 0; cur_deg < max_deg+2; ++cur_deg) { degree_type tmp = bin[cur_deg]; bin[cur_deg] = cur_pos; cur_pos += tmp; } // perform the bucket sort with pos and vert so that // pos[0] is the vertex of smallest degree std::vector<vertex> vert(num_vertices(g)); for (boost::tie(vi,vi_end) = vertices(g); vi!=vi_end; ++vi) { vertex v=*vi; size_type p=bin[get(c,v)]; put(pos,v,p); vert[p]=v; ++bin[get(c,v)]; } // we ``abused'' bin while placing the vertices, now, // we need to restore it std::copy(boost::make_reverse_iterator(bin.end()-2), boost::make_reverse_iterator(bin.begin()), boost::make_reverse_iterator(bin.end()-1)); // now simulate removing the vertices for (size_type i=0; i < num_vertices(g); ++i) { vertex v = vert[i]; vis.examine_vertex(v,g); v_cn = get(c,v); typename graph_traits<Graph>::out_edge_iterator oi,oi_end; for (boost::tie(oi,oi_end) = out_edges(v,g); oi!=oi_end; ++oi) { vis.examine_edge(*oi,g); vertex u = target(*oi,g); // if c[u] > c[v], then u is still in the graph, if (get(c,u) > v_cn) { degree_type deg_u = get(c,u); degree_type pos_u = get(pos,u); // w is the first vertex with the same degree as u // (this is the resort operation!) degree_type pos_w = bin[deg_u]; vertex w = vert[pos_w]; if (u!=v) { // swap u and w put(pos,u,pos_w); put(pos,w,pos_u); vert[pos_w] = u; vert[pos_u] = w; } // now, the vertices array is sorted assuming // we perform the following step // start the set of vertices with degree of u // one into the future (this now points at vertex // w which we swapped with u). ++bin[deg_u]; // we are removing v from the graph, so u's degree // decreases put(c,u,get(c,u)-1); } } vis.finish_vertex(v,g); } return v_cn; } } // namespace detail // non-named parameter version for the unweighted case template <typename Graph, typename CoreMap, typename CoreNumVisitor> typename property_traits<CoreMap>::value_type core_numbers(Graph& g, CoreMap c, CoreNumVisitor vis) { typedef typename graph_traits<Graph>::vertices_size_type size_type; detail::compute_in_degree_map(g,c, detail::constant_value_property_map< typename property_traits<CoreMap>::value_type>(1) ); return detail::core_numbers_impl(g,c, make_iterator_property_map( std::vector<size_type>(num_vertices(g)).begin(),get(vertex_index, g)), vis ); } // non-named paramter version for the unweighted case template <typename Graph, typename CoreMap> typename property_traits<CoreMap>::value_type core_numbers(Graph& g, CoreMap c) { return core_numbers(g, c, make_core_numbers_visitor(null_visitor())); } // non-named parameter version for the weighted case template <typename Graph, typename CoreMap, typename EdgeWeightMap, typename VertexIndexMap, typename CoreNumVisitor> typename property_traits<CoreMap>::value_type core_numbers(Graph& g, CoreMap c, EdgeWeightMap wm, VertexIndexMap vim, CoreNumVisitor vis) { detail::compute_in_degree_map(g,c,wm); return detail::core_numbers_dispatch(g,c,wm,vim,vis); } // non-named parameter version for the weighted case // template <typename Graph, typename CoreMap, typename EdgeWeightMap> // typename property_traits<CoreMap>::value_type // core_numbers(Graph& g, CoreMap c, EdgeWeightMap wm) // { // typedef typename graph_traits<Graph>::vertices_size_type size_type; // detail::compute_in_degree_map(g,c,wm); // return detail::core_numbers_dispatch(g,c,wm,get(vertex_index,g), // make_core_numbers_visitor(null_visitor())); // } template <typename Graph, typename CoreMap> typename property_traits<CoreMap>::value_type weighted_core_numbers(Graph& g, CoreMap c) { return weighted_core_numbers( g,c, make_core_numbers_visitor(null_visitor()) ); } template <typename Graph, typename CoreMap, typename CoreNumVisitor> typename property_traits<CoreMap>::value_type weighted_core_numbers(Graph& g, CoreMap c, CoreNumVisitor vis) { return core_numbers(g,c,get(edge_weight,g),get(vertex_index,g),vis); } } // namespace boost #endif // BOOST_GRAPH_CORE_NUMBERS_HPP