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341 lines
12 KiB
341 lines
12 KiB
// |
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//======================================================================= |
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// Copyright 1997, 1998, 1999, 2000 University of Notre Dame. |
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// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek |
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// |
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// Distributed under the Boost Software License, Version 1.0. (See |
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// accompanying file LICENSE_1_0.txt or copy at |
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// http://www.boost.org/LICENSE_1_0.txt) |
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//======================================================================= |
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// |
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#ifndef BOOST_GRAPH_STRONG_COMPONENTS_HPP |
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#define BOOST_GRAPH_STRONG_COMPONENTS_HPP |
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#include <stack> |
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#include <boost/config.hpp> |
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#include <boost/graph/depth_first_search.hpp> |
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#include <boost/type_traits/conversion_traits.hpp> |
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#include <boost/static_assert.hpp> |
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#include <boost/graph/overloading.hpp> |
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namespace boost { |
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//========================================================================== |
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// This is Tarjan's algorithm for strongly connected components |
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// from his paper "Depth first search and linear graph algorithms". |
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// It calculates the components in a single application of DFS. |
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// We implement the algorithm as a dfs-visitor. |
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namespace detail { |
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template <typename ComponentMap, typename RootMap, typename DiscoverTime, |
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typename Stack> |
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class tarjan_scc_visitor : public dfs_visitor<> |
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{ |
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typedef typename property_traits<ComponentMap>::value_type comp_type; |
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typedef typename property_traits<DiscoverTime>::value_type time_type; |
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public: |
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tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d, |
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comp_type& c_, Stack& s_) |
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: c(c_), comp(comp_map), root(r), discover_time(d), |
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dfs_time(time_type()), s(s_) { } |
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template <typename Graph> |
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void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v, |
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const Graph&) { |
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put(root, v, v); |
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put(comp, v, (std::numeric_limits<comp_type>::max)()); |
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put(discover_time, v, dfs_time++); |
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s.push(v); |
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} |
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template <typename Graph> |
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void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v, |
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const Graph& g) { |
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typename graph_traits<Graph>::vertex_descriptor w; |
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typename graph_traits<Graph>::out_edge_iterator ei, ei_end; |
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for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) { |
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w = target(*ei, g); |
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if (get(comp, w) == (std::numeric_limits<comp_type>::max)()) |
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put(root, v, this->min_discover_time(get(root,v), get(root,w))); |
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} |
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if (get(root, v) == v) { |
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do { |
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w = s.top(); s.pop(); |
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put(comp, w, c); |
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} while (w != v); |
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++c; |
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} |
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} |
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private: |
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template <typename Vertex> |
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Vertex min_discover_time(Vertex u, Vertex v) { |
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return get(discover_time, u) < get(discover_time,v) ? u : v; |
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} |
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comp_type& c; |
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ComponentMap comp; |
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RootMap root; |
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DiscoverTime discover_time; |
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time_type dfs_time; |
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Stack& s; |
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}; |
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template <class Graph, class ComponentMap, class RootMap, |
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class DiscoverTime, class P, class T, class R> |
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typename property_traits<ComponentMap>::value_type |
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strong_components_impl |
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(const Graph& g, // Input |
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ComponentMap comp, // Output |
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// Internal record keeping |
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RootMap root, |
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DiscoverTime discover_time, |
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const bgl_named_params<P, T, R>& params) |
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{ |
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typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
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function_requires< ReadWritePropertyMapConcept<ComponentMap, Vertex> >(); |
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function_requires< ReadWritePropertyMapConcept<RootMap, Vertex> >(); |
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typedef typename property_traits<RootMap>::value_type RootV; |
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function_requires< ConvertibleConcept<RootV, Vertex> >(); |
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function_requires< ReadWritePropertyMapConcept<DiscoverTime, Vertex> >(); |
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typename property_traits<ComponentMap>::value_type total = 0; |
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std::stack<Vertex> s; |
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detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime, |
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std::stack<Vertex> > |
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vis(comp, root, discover_time, total, s); |
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depth_first_search(g, params.visitor(vis)); |
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return total; |
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} |
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//------------------------------------------------------------------------- |
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// The dispatch functions handle the defaults for the rank and discover |
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// time property maps. |
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// dispatch with class specialization to avoid VC++ bug |
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template <class DiscoverTimeMap> |
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struct strong_comp_dispatch2 { |
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template <class Graph, class ComponentMap, class RootMap, class P, class T, class R> |
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inline static typename property_traits<ComponentMap>::value_type |
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apply(const Graph& g, |
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ComponentMap comp, |
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RootMap r_map, |
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const bgl_named_params<P, T, R>& params, |
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DiscoverTimeMap time_map) |
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{ |
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return strong_components_impl(g, comp, r_map, time_map, params); |
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} |
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}; |
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template <> |
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struct strong_comp_dispatch2<detail::error_property_not_found> { |
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template <class Graph, class ComponentMap, class RootMap, |
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class P, class T, class R> |
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inline static typename property_traits<ComponentMap>::value_type |
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apply(const Graph& g, |
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ComponentMap comp, |
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RootMap r_map, |
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const bgl_named_params<P, T, R>& params, |
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detail::error_property_not_found) |
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{ |
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typedef typename graph_traits<Graph>::vertices_size_type size_type; |
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size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1; |
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std::vector<size_type> time_vec(n); |
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return strong_components_impl |
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(g, comp, r_map, |
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make_iterator_property_map(time_vec.begin(), choose_const_pmap |
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(get_param(params, vertex_index), |
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g, vertex_index), time_vec[0]), |
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params); |
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} |
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}; |
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template <class Graph, class ComponentMap, class RootMap, |
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class P, class T, class R, class DiscoverTimeMap> |
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inline typename property_traits<ComponentMap>::value_type |
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scc_helper2(const Graph& g, |
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ComponentMap comp, |
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RootMap r_map, |
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const bgl_named_params<P, T, R>& params, |
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DiscoverTimeMap time_map) |
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{ |
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return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map); |
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} |
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template <class RootMap> |
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struct strong_comp_dispatch1 { |
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template <class Graph, class ComponentMap, class P, class T, class R> |
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inline static typename property_traits<ComponentMap>::value_type |
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apply(const Graph& g, |
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ComponentMap comp, |
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const bgl_named_params<P, T, R>& params, |
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RootMap r_map) |
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{ |
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return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time)); |
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} |
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}; |
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template <> |
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struct strong_comp_dispatch1<detail::error_property_not_found> { |
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template <class Graph, class ComponentMap, |
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class P, class T, class R> |
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inline static typename property_traits<ComponentMap>::value_type |
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apply(const Graph& g, |
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ComponentMap comp, |
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const bgl_named_params<P, T, R>& params, |
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detail::error_property_not_found) |
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{ |
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typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
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typename std::vector<Vertex>::size_type |
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n = num_vertices(g) > 0 ? num_vertices(g) : 1; |
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std::vector<Vertex> root_vec(n); |
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return scc_helper2 |
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(g, comp, |
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make_iterator_property_map(root_vec.begin(), choose_const_pmap |
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(get_param(params, vertex_index), |
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g, vertex_index), root_vec[0]), |
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params, |
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get_param(params, vertex_discover_time)); |
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} |
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}; |
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template <class Graph, class ComponentMap, class RootMap, |
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class P, class T, class R> |
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inline typename property_traits<ComponentMap>::value_type |
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scc_helper1(const Graph& g, |
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ComponentMap comp, |
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const bgl_named_params<P, T, R>& params, |
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RootMap r_map) |
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{ |
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return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params, |
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r_map); |
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} |
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} // namespace detail |
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template <class Graph, class ComponentMap, |
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class P, class T, class R> |
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inline typename property_traits<ComponentMap>::value_type |
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strong_components(const Graph& g, ComponentMap comp, |
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const bgl_named_params<P, T, R>& params |
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BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag)) |
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{ |
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typedef typename graph_traits<Graph>::directed_category DirCat; |
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BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true)); |
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return detail::scc_helper1(g, comp, params, |
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get_param(params, vertex_root_t())); |
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} |
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template <class Graph, class ComponentMap> |
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inline typename property_traits<ComponentMap>::value_type |
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strong_components(const Graph& g, ComponentMap comp |
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BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag)) |
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{ |
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typedef typename graph_traits<Graph>::directed_category DirCat; |
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BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true)); |
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bgl_named_params<int, int> params(0); |
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return strong_components(g, comp, params); |
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} |
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template <typename Graph, typename ComponentMap, typename ComponentLists> |
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void build_component_lists |
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(const Graph& g, |
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typename graph_traits<Graph>::vertices_size_type num_scc, |
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ComponentMap component_number, |
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ComponentLists& components) |
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{ |
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components.resize(num_scc); |
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typename graph_traits<Graph>::vertex_iterator vi, vi_end; |
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for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi) |
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components[component_number[*vi]].push_back(*vi); |
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} |
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} // namespace boost |
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#include <queue> |
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#include <vector> |
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#include <boost/graph/transpose_graph.hpp> |
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#include <boost/pending/indirect_cmp.hpp> |
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#include <boost/graph/connected_components.hpp> // for components_recorder |
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namespace boost { |
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//========================================================================== |
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// This is the version of strongly connected components from |
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// "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was |
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// adapted from "Data Structure and Algorithms" by Aho, Hopcroft, |
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// and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir. |
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// The algorithm is based on computing DFS forests the graph |
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// and its transpose. |
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// This algorithm is slower than Tarjan's by a constant factor, uses |
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// more memory, and puts more requirements on the graph type. |
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template <class Graph, class DFSVisitor, class ComponentsMap, |
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class DiscoverTime, class FinishTime, |
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class ColorMap> |
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typename property_traits<ComponentsMap>::value_type |
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kosaraju_strong_components(Graph& G, ComponentsMap c, |
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FinishTime finish_time, ColorMap color) |
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{ |
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function_requires< MutableGraphConcept<Graph> >(); |
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// ... |
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typedef typename graph_traits<Graph>::vertex_descriptor Vertex; |
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typedef typename property_traits<ColorMap>::value_type ColorValue; |
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typedef color_traits<ColorValue> Color; |
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typename property_traits<FinishTime>::value_type time = 0; |
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depth_first_search |
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(G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())), |
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color); |
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Graph G_T(num_vertices(G)); |
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transpose_graph(G, G_T); |
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typedef typename property_traits<ComponentsMap>::value_type count_type; |
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count_type c_count(0); |
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detail::components_recorder<ComponentsMap> |
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vis(c, c_count); |
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// initialize G_T |
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typename graph_traits<Graph>::vertex_iterator ui, ui_end; |
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for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui) |
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put(color, *ui, Color::white()); |
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typedef typename property_traits<FinishTime>::value_type D; |
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typedef indirect_cmp< FinishTime, std::less<D> > Compare; |
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Compare fl(finish_time); |
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std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl); |
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typename graph_traits<Graph>::vertex_iterator i, j, iend, jend; |
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boost::tie(i, iend) = vertices(G_T); |
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boost::tie(j, jend) = vertices(G); |
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for ( ; i != iend; ++i, ++j) { |
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put(finish_time, *i, get(finish_time, *j)); |
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Q.push(*i); |
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} |
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while ( !Q.empty() ) { |
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Vertex u = Q.top(); |
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Q.pop(); |
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if (get(color, u) == Color::white()) { |
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depth_first_visit(G_T, u, vis, color); |
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++c_count; |
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} |
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} |
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return c_count; |
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} |
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} // namespace boost |
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#ifdef BOOST_GRAPH_USE_MPI |
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# include <boost/graph/distributed/strong_components.hpp> |
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#endif |
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#endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP
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