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/usr/include/boost/graph/random_spanning_tree.hpp
(5775B)
// Copyright 2010 The Trustees of Indiana University. // 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) // Authors: Jeremiah Willcock // Andrew Lumsdaine #ifndef BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP #define BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP #include <vector> #include <boost/assert.hpp> #include <boost/graph/loop_erased_random_walk.hpp> #include <boost/graph/random.hpp> #include <boost/graph/iteration_macros.hpp> #include <boost/property_map/property_map.hpp> #include <boost/config.hpp> #include <boost/graph/graph_traits.hpp> #include <boost/graph/graph_concepts.hpp> #include <boost/graph/properties.hpp> #include <boost/graph/named_function_params.hpp> namespace boost { namespace detail { // Use Wilson's algorithm (based on loop-free random walks) to generate a // random spanning tree. The distribution of edges used is controlled by // the next_edge() function, so this version allows either weighted or // unweighted selection of trees. // Algorithm is from http://en.wikipedia.org/wiki/Uniform_spanning_tree template < typename Graph, typename PredMap, typename ColorMap, typename NextEdge > void random_spanning_tree_internal(const Graph& g, typename graph_traits< Graph >::vertex_descriptor s, PredMap pred, ColorMap color, NextEdge next_edge) { typedef typename graph_traits< Graph >::vertex_descriptor vertex_descriptor; BOOST_ASSERT(num_vertices(g) >= 1); // g must also be undirected (or symmetric) and connected typedef color_traits< typename property_traits< ColorMap >::value_type > color_gen; BGL_FORALL_VERTICES_T(v, g, Graph) put(color, v, color_gen::white()); std::vector< vertex_descriptor > path; put(color, s, color_gen::black()); put(pred, s, graph_traits< Graph >::null_vertex()); BGL_FORALL_VERTICES_T(v, g, Graph) { if (get(color, v) != color_gen::white()) continue; loop_erased_random_walk(g, v, next_edge, color, path); for (typename std::vector< vertex_descriptor >::const_reverse_iterator i = path.rbegin(); boost::next(i) != (typename std::vector< vertex_descriptor >::const_reverse_iterator)path.rend(); ++i) { typename std::vector< vertex_descriptor >::const_reverse_iterator j = i; ++j; BOOST_ASSERT(get(color, *j) == color_gen::gray()); put(color, *j, color_gen::black()); put(pred, *j, *i); } } } } // Compute a uniformly-distributed spanning tree on a graph. Use Wilson's // algorithm: // @inproceedings{wilson96generating, // author = {Wilson, David Bruce}, // title = {Generating random spanning trees more quickly than the cover // time}, booktitle = {STOC '96: Proceedings of the twenty-eighth annual ACM // symposium on Theory of computing}, year = {1996}, isbn = {0-89791-785-5}, // pages = {296--303}, // location = {Philadelphia, Pennsylvania, United States}, // doi = {http://doi.acm.org/10.1145/237814.237880}, // publisher = {ACM}, // address = {New York, NY, USA}, // } // template < typename Graph, typename Gen, typename PredMap, typename ColorMap > void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits< Graph >::vertex_descriptor root, PredMap pred, static_property_map< double >, ColorMap color) { unweighted_random_out_edge_gen< Graph, Gen > random_oe(gen); detail::random_spanning_tree_internal(g, root, pred, color, random_oe); } // Compute a weight-distributed spanning tree on a graph. template < typename Graph, typename Gen, typename PredMap, typename WeightMap, typename ColorMap > void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits< Graph >::vertex_descriptor root, PredMap pred, WeightMap weight, ColorMap color) { weighted_random_out_edge_gen< Graph, WeightMap, Gen > random_oe( weight, gen); detail::random_spanning_tree_internal(g, root, pred, color, random_oe); } template < typename Graph, typename Gen, typename P, typename T, typename R > void random_spanning_tree( const Graph& g, Gen& gen, const bgl_named_params< P, T, R >& params) { using namespace boost::graph::keywords; typedef bgl_named_params< P, T, R > params_type; BOOST_GRAPH_DECLARE_CONVERTED_PARAMETERS(params_type, params) typedef typename graph_traits< Graph >::vertex_descriptor vertex_descriptor; vertex_descriptor default_vertex = *vertices(g).first; vertex_descriptor start_vertex = arg_pack[_root_vertex | default_vertex]; typename boost::parameter::binding< arg_pack_type, boost::graph::keywords::tag::predecessor_map >::type pred_map = arg_pack[_predecessor_map]; static_property_map< double > default_weight_map(1.); typename boost::parameter::value_type< arg_pack_type, boost::graph::keywords::tag::weight_map, static_property_map< double > >::type e_w_map = arg_pack[_weight_map | default_weight_map]; typename boost::detail::map_maker< Graph, arg_pack_type, boost::graph::keywords::tag::color_map, boost::default_color_type >::map_type c_map = boost::detail::make_color_map_from_arg_pack(g, arg_pack); random_spanning_tree(g, gen, start_vertex, pred_map, e_w_map, c_map); } } #include <boost/graph/iteration_macros_undef.hpp> #endif // BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP
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