1 | // Copyright 2010 The Trustees of Indiana University. |
2 | |
3 | // Distributed under the Boost Software License, Version 1.0. |
4 | // (See accompanying file LICENSE_1_0.txt or copy at |
5 | // http://www.boost.org/LICENSE_1_0.txt) |
6 | |
7 | // Authors: Jeremiah Willcock |
8 | // Andrew Lumsdaine |
9 | |
10 | #ifndef BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP |
11 | #define BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP |
12 | |
13 | #include <vector> |
14 | #include <boost/assert.hpp> |
15 | #include <boost/graph/loop_erased_random_walk.hpp> |
16 | #include <boost/graph/random.hpp> |
17 | #include <boost/graph/iteration_macros.hpp> |
18 | #include <boost/property_map/property_map.hpp> |
19 | #include <boost/config.hpp> |
20 | #include <boost/graph/graph_traits.hpp> |
21 | #include <boost/graph/graph_concepts.hpp> |
22 | #include <boost/graph/properties.hpp> |
23 | #include <boost/graph/named_function_params.hpp> |
24 | |
25 | namespace boost { |
26 | |
27 | namespace detail { |
28 | // Use Wilson's algorithm (based on loop-free random walks) to generate a |
29 | // random spanning tree. The distribution of edges used is controlled by |
30 | // the next_edge() function, so this version allows either weighted or |
31 | // unweighted selection of trees. |
32 | // Algorithm is from http://en.wikipedia.org/wiki/Uniform_spanning_tree |
33 | template <typename Graph, typename PredMap, typename ColorMap, typename NextEdge> |
34 | void random_spanning_tree_internal(const Graph& g, typename graph_traits<Graph>::vertex_descriptor s, PredMap pred, ColorMap color, NextEdge next_edge) { |
35 | typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor; |
36 | |
37 | BOOST_ASSERT (num_vertices(g) >= 1); // g must also be undirected (or symmetric) and connected |
38 | |
39 | typedef color_traits<typename property_traits<ColorMap>::value_type> color_gen; |
40 | BGL_FORALL_VERTICES_T(v, g, Graph) put(color, v, color_gen::white()); |
41 | |
42 | std::vector<vertex_descriptor> path; |
43 | |
44 | put(color, s, color_gen::black()); |
45 | put(pred, s, graph_traits<Graph>::null_vertex()); |
46 | |
47 | BGL_FORALL_VERTICES_T(v, g, Graph) { |
48 | if (get(color, v) != color_gen::white()) continue; |
49 | loop_erased_random_walk(g, v, next_edge, color, path); |
50 | for (typename std::vector<vertex_descriptor>::const_reverse_iterator i = path.rbegin(); |
51 | boost::next(i) != |
52 | (typename std::vector<vertex_descriptor>::const_reverse_iterator)path.rend(); |
53 | ++i) { |
54 | typename std::vector<vertex_descriptor>::const_reverse_iterator j = i; |
55 | ++j; |
56 | BOOST_ASSERT (get(color, *j) == color_gen::gray()); |
57 | put(color, *j, color_gen::black()); |
58 | put(pred, *j, *i); |
59 | } |
60 | } |
61 | } |
62 | } |
63 | |
64 | // Compute a uniformly-distributed spanning tree on a graph. Use Wilson's algorithm: |
65 | // @inproceedings{wilson96generating, |
66 | // author = {Wilson, David Bruce}, |
67 | // title = {Generating random spanning trees more quickly than the cover time}, |
68 | // booktitle = {STOC '96: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing}, |
69 | // year = {1996}, |
70 | // isbn = {0-89791-785-5}, |
71 | // pages = {296--303}, |
72 | // location = {Philadelphia, Pennsylvania, United States}, |
73 | // doi = {http://doi.acm.org/10.1145/237814.237880}, |
74 | // publisher = {ACM}, |
75 | // address = {New York, NY, USA}, |
76 | // } |
77 | // |
78 | template <typename Graph, typename Gen, typename PredMap, typename ColorMap> |
79 | void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits<Graph>::vertex_descriptor root, |
80 | PredMap pred, static_property_map<double>, ColorMap color) { |
81 | unweighted_random_out_edge_gen<Graph, Gen> random_oe(gen); |
82 | detail::random_spanning_tree_internal(g, root, pred, color, random_oe); |
83 | } |
84 | |
85 | // Compute a weight-distributed spanning tree on a graph. |
86 | template <typename Graph, typename Gen, typename PredMap, typename WeightMap, typename ColorMap> |
87 | void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits<Graph>::vertex_descriptor root, |
88 | PredMap pred, WeightMap weight, ColorMap color) { |
89 | weighted_random_out_edge_gen<Graph, WeightMap, Gen> random_oe(weight, gen); |
90 | detail::random_spanning_tree_internal(g, root, pred, color, random_oe); |
91 | } |
92 | |
93 | template <typename Graph, typename Gen, typename P, typename T, typename R> |
94 | void random_spanning_tree(const Graph& g, Gen& gen, const bgl_named_params<P, T, R>& params) { |
95 | using namespace boost::graph::keywords; |
96 | typedef bgl_named_params<P, T, R> params_type; |
97 | BOOST_GRAPH_DECLARE_CONVERTED_PARAMETERS(params_type, params) |
98 | random_spanning_tree(g, |
99 | gen, |
100 | arg_pack[_root_vertex | *vertices(g).first], |
101 | arg_pack[_predecessor_map], |
102 | arg_pack[_weight_map | static_property_map<double>(1.)], |
103 | boost::detail::make_color_map_from_arg_pack(g, arg_pack)); |
104 | } |
105 | } |
106 | |
107 | #include <boost/graph/iteration_macros_undef.hpp> |
108 | |
109 | #endif // BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP |
110 | |