| // 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/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; |
| typedef typename graph_traits<Graph>::edge_descriptor edge_descriptor; |
| |
| 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; |
| 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) |
| random_spanning_tree(g, |
| gen, |
| arg_pack[_root_vertex | *vertices(g).first], |
| arg_pack[_predecessor_map], |
| arg_pack[_weight_map | static_property_map<double>(1.)], |
| boost::detail::make_color_map_from_arg_pack(g, arg_pack)); |
| } |
| } |
| |
| #include <boost/graph/iteration_macros_undef.hpp> |
| |
| #endif // BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP |