// 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; | |
typedef typename graph_traits<Graph>::edge_descriptor edge_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) | |
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 |