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110 lines
4.9 KiB
C++
110 lines
4.9 KiB
C++
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// Copyright 2010 The Trustees of Indiana University.
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// Distributed under the Boost Software License, Version 1.0.
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// (See 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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// Authors: Jeremiah Willcock
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// Andrew Lumsdaine
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#ifndef BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP
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#define BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP
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#include <vector>
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#include <boost/assert.hpp>
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#include <boost/graph/loop_erased_random_walk.hpp>
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#include <boost/graph/random.hpp>
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#include <boost/graph/iteration_macros.hpp>
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#include <boost/property_map/property_map.hpp>
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#include <boost/config.hpp>
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#include <boost/graph/graph_traits.hpp>
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#include <boost/graph/graph_concepts.hpp>
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#include <boost/graph/properties.hpp>
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#include <boost/graph/named_function_params.hpp>
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namespace boost {
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namespace detail {
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// Use Wilson's algorithm (based on loop-free random walks) to generate a
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// random spanning tree. The distribution of edges used is controlled by
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// the next_edge() function, so this version allows either weighted or
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// unweighted selection of trees.
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// Algorithm is from http://en.wikipedia.org/wiki/Uniform_spanning_tree
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template <typename Graph, typename PredMap, typename ColorMap, typename NextEdge>
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void random_spanning_tree_internal(const Graph& g, typename graph_traits<Graph>::vertex_descriptor s, PredMap pred, ColorMap color, NextEdge next_edge) {
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typedef typename graph_traits<Graph>::vertex_descriptor vertex_descriptor;
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BOOST_ASSERT (num_vertices(g) >= 1); // g must also be undirected (or symmetric) and connected
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typedef color_traits<typename property_traits<ColorMap>::value_type> color_gen;
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BGL_FORALL_VERTICES_T(v, g, Graph) put(color, v, color_gen::white());
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std::vector<vertex_descriptor> path;
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put(color, s, color_gen::black());
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put(pred, s, graph_traits<Graph>::null_vertex());
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BGL_FORALL_VERTICES_T(v, g, Graph) {
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if (get(color, v) != color_gen::white()) continue;
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loop_erased_random_walk(g, v, next_edge, color, path);
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for (typename std::vector<vertex_descriptor>::const_reverse_iterator i = path.rbegin();
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boost::next(i) !=
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(typename std::vector<vertex_descriptor>::const_reverse_iterator)path.rend();
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++i) {
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typename std::vector<vertex_descriptor>::const_reverse_iterator j = i;
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++j;
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BOOST_ASSERT (get(color, *j) == color_gen::gray());
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put(color, *j, color_gen::black());
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put(pred, *j, *i);
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}
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}
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}
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}
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// Compute a uniformly-distributed spanning tree on a graph. Use Wilson's algorithm:
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// @inproceedings{wilson96generating,
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// author = {Wilson, David Bruce},
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// title = {Generating random spanning trees more quickly than the cover time},
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// booktitle = {STOC '96: Proceedings of the twenty-eighth annual ACM symposium on Theory of computing},
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// year = {1996},
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// isbn = {0-89791-785-5},
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// pages = {296--303},
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// location = {Philadelphia, Pennsylvania, United States},
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// doi = {http://doi.acm.org/10.1145/237814.237880},
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// publisher = {ACM},
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// address = {New York, NY, USA},
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// }
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//
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template <typename Graph, typename Gen, typename PredMap, typename ColorMap>
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void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits<Graph>::vertex_descriptor root,
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PredMap pred, static_property_map<double>, ColorMap color) {
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unweighted_random_out_edge_gen<Graph, Gen> random_oe(gen);
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detail::random_spanning_tree_internal(g, root, pred, color, random_oe);
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}
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// Compute a weight-distributed spanning tree on a graph.
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template <typename Graph, typename Gen, typename PredMap, typename WeightMap, typename ColorMap>
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void random_spanning_tree(const Graph& g, Gen& gen, typename graph_traits<Graph>::vertex_descriptor root,
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PredMap pred, WeightMap weight, ColorMap color) {
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weighted_random_out_edge_gen<Graph, WeightMap, Gen> random_oe(weight, gen);
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detail::random_spanning_tree_internal(g, root, pred, color, random_oe);
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}
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template <typename Graph, typename Gen, typename P, typename T, typename R>
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void random_spanning_tree(const Graph& g, Gen& gen, const bgl_named_params<P, T, R>& params) {
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using namespace boost::graph::keywords;
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typedef bgl_named_params<P, T, R> params_type;
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BOOST_GRAPH_DECLARE_CONVERTED_PARAMETERS(params_type, params)
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random_spanning_tree(g,
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gen,
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arg_pack[_root_vertex | *vertices(g).first],
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arg_pack[_predecessor_map],
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arg_pack[_weight_map | static_property_map<double>(1.)],
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boost::detail::make_color_map_from_arg_pack(g, arg_pack));
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}
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}
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#include <boost/graph/iteration_macros_undef.hpp>
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#endif // BOOST_GRAPH_RANDOM_SPANNING_TREE_HPP
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