1 | // Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
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2 | //
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3 | // Permission to copy, use, sell and distribute this software is granted
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4 | // provided this copyright notice appears in all copies.
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5 | // Permission to modify the code and to distribute modified code is granted
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6 | // provided this copyright notice appears in all copies, and a notice
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7 | // that the code was modified is included with the copyright notice.
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8 | //
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9 | // This software is provided "as is" without express or implied warranty,
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10 | // and with no claim as to its suitability for any purpose.
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11 | #ifndef BOOST_GRAPH_ISOMORPHISM_HPP
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12 | #define BOOST_GRAPH_ISOMORPHISM_HPP
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13 |
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14 | #include <utility>
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15 | #include <vector>
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16 | #include <iterator>
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17 | #include <algorithm>
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18 | #include <boost/config.hpp>
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19 | #include <boost/graph/depth_first_search.hpp>
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20 | #include <boost/utility.hpp>
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21 | #include <boost/detail/algorithm.hpp>
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22 | #include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
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23 |
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24 | #ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
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25 | #define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
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26 | #include <boost/graph/iteration_macros.hpp>
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27 | #endif
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28 |
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29 | namespace boost {
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30 |
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31 | namespace detail {
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32 |
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33 | template <typename Graph1, typename Graph2, typename IsoMapping,
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34 | typename Invariant1, typename Invariant2,
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35 | typename IndexMap1, typename IndexMap2>
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36 | class isomorphism_algo
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37 | {
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38 | typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
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39 | typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
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40 | typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
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41 | typedef typename graph_traits<Graph1>::vertices_size_type size_type;
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42 | typedef typename Invariant1::result_type invar1_value;
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43 | typedef typename Invariant2::result_type invar2_value;
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44 |
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45 | const Graph1& G1;
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46 | const Graph2& G2;
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47 | IsoMapping f;
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48 | Invariant1 invariant1;
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49 | Invariant2 invariant2;
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50 | std::size_t max_invariant;
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51 | IndexMap1 index_map1;
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52 | IndexMap2 index_map2;
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53 |
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54 | std::vector<vertex1_t> dfs_vertices;
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55 | typedef typename std::vector<vertex1_t>::iterator vertex_iter;
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56 | std::vector<int> dfs_num_vec;
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57 | typedef safe_iterator_property_map<typename std::vector<int>::iterator,
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58 | IndexMap1
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59 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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60 | , int, int&
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61 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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62 | > DFSNumMap;
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63 | DFSNumMap dfs_num;
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64 | std::vector<edge1_t> ordered_edges;
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65 | typedef typename std::vector<edge1_t>::iterator edge_iter;
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66 |
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67 | std::vector<char> in_S_vec;
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68 | typedef safe_iterator_property_map<typename std::vector<char>::iterator,
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69 | IndexMap2
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70 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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71 | , char, char&
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72 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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73 | > InSMap;
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74 | InSMap in_S;
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75 |
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76 | int num_edges_on_k;
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77 |
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78 | friend struct compare_multiplicity;
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79 | struct compare_multiplicity
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80 | {
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81 | compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
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82 | : invariant1(invariant1), multiplicity(multiplicity) { }
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83 | bool operator()(const vertex1_t& x, const vertex1_t& y) const {
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84 | return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
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85 | }
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86 | Invariant1 invariant1;
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87 | size_type* multiplicity;
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88 | };
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89 |
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90 | struct record_dfs_order : default_dfs_visitor
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91 | {
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92 | record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e)
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93 | : vertices(v), edges(e) { }
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94 |
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95 | void discover_vertex(vertex1_t v, const Graph1&) const {
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96 | vertices.push_back(v);
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97 | }
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98 | void examine_edge(edge1_t e, const Graph1& G1) const {
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99 | edges.push_back(e);
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100 | }
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101 | std::vector<vertex1_t>& vertices;
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102 | std::vector<edge1_t>& edges;
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103 | };
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104 |
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105 | struct edge_cmp {
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106 | edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
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107 | : G1(G1), dfs_num(dfs_num) { }
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108 | bool operator()(const edge1_t& e1, const edge1_t& e2) const {
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109 | using namespace std;
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110 | int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
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111 | int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
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112 | int m1 = (max)(u1, v1);
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113 | int m2 = (max)(u2, v2);
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114 | // lexicographical comparison
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115 | return std::make_pair(m1, std::make_pair(u1, v1))
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116 | < std::make_pair(m2, std::make_pair(u2, v2));
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117 | }
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118 | const Graph1& G1;
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119 | DFSNumMap dfs_num;
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120 | };
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121 |
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122 | public:
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123 | isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
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124 | Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
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125 | IndexMap1 index_map1, IndexMap2 index_map2)
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126 | : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
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127 | max_invariant(max_invariant),
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128 | index_map1(index_map1), index_map2(index_map2)
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129 | {
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130 | in_S_vec.resize(num_vertices(G1));
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131 | in_S = make_safe_iterator_property_map
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132 | (in_S_vec.begin(), in_S_vec.size(), index_map2
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133 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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134 | , in_S_vec.front()
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135 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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136 | );
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137 | }
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138 |
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139 | bool test_isomorphism()
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140 | {
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141 | {
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142 | std::vector<invar1_value> invar1_array;
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143 | BGL_FORALL_VERTICES_T(v, G1, Graph1)
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144 | invar1_array.push_back(invariant1(v));
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145 | sort(invar1_array);
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146 |
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147 | std::vector<invar2_value> invar2_array;
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148 | BGL_FORALL_VERTICES_T(v, G2, Graph2)
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149 | invar2_array.push_back(invariant2(v));
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150 | sort(invar2_array);
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151 | if (! equal(invar1_array, invar2_array))
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152 | return false;
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153 | }
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154 |
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155 | std::vector<vertex1_t> V_mult;
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156 | BGL_FORALL_VERTICES_T(v, G1, Graph1)
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157 | V_mult.push_back(v);
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158 | {
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159 | std::vector<size_type> multiplicity(max_invariant, 0);
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160 | BGL_FORALL_VERTICES_T(v, G1, Graph1)
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161 | ++multiplicity[invariant1(v)];
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162 | sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
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163 | }
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164 |
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165 | std::vector<default_color_type> color_vec(num_vertices(G1));
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166 | safe_iterator_property_map<std::vector<default_color_type>::iterator,
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167 | IndexMap1
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168 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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169 | , default_color_type, default_color_type&
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170 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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171 | >
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172 | color_map(color_vec.begin(), color_vec.size(), index_map1);
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173 | record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
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174 | typedef color_traits<default_color_type> Color;
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175 | for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
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176 | if (color_map[*u] == Color::white()) {
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177 | dfs_visitor.start_vertex(*u, G1);
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178 | depth_first_visit(G1, *u, dfs_visitor, color_map);
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179 | }
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180 | }
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181 | // Create the dfs_num array and dfs_num_map
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182 | dfs_num_vec.resize(num_vertices(G1));
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183 | dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
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184 | dfs_num_vec.size(),
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185 | index_map1
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186 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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187 | , dfs_num_vec.front()
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188 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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189 | );
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190 | size_type n = 0;
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191 | for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
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192 | dfs_num[*v] = n++;
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193 |
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194 | sort(ordered_edges, edge_cmp(G1, dfs_num));
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195 |
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196 |
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197 | int dfs_num_k = -1;
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198 | return this->match(ordered_edges.begin(), dfs_num_k);
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199 | }
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200 |
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201 | private:
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202 | bool match(edge_iter iter, int dfs_num_k)
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203 | {
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204 | if (iter != ordered_edges.end()) {
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205 | vertex1_t i = source(*iter, G1), j = target(*iter, G2);
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206 | if (dfs_num[i] > dfs_num_k) {
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207 | vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
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208 | BGL_FORALL_VERTICES_T(u, G2, Graph2) {
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209 | if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
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210 | f[kp1] = u;
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211 | in_S[u] = true;
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212 | num_edges_on_k = 0;
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213 |
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214 | if (match(iter, dfs_num_k + 1))
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215 | #if 0
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216 | // dwa 2003/7/11 -- this *HAS* to be a bug!
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217 | ;
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218 | #endif
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219 | return true;
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220 |
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221 | in_S[u] = false;
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222 | }
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223 | }
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224 |
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225 | }
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226 | else if (dfs_num[j] > dfs_num_k) {
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227 | vertex1_t k = dfs_vertices[dfs_num_k];
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228 | num_edges_on_k -=
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229 | count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));
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230 |
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231 | for (int jj = 0; jj < dfs_num_k; ++jj) {
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232 | vertex1_t j = dfs_vertices[jj];
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233 | num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);
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234 | }
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235 |
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236 | if (num_edges_on_k != 0)
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237 | return false;
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238 | BGL_FORALL_ADJ_T(f[i], v, G2, Graph2)
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239 | if (invariant2(v) == invariant1(j) && in_S[v] == false) {
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240 | f[j] = v;
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241 | in_S[v] = true;
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242 | num_edges_on_k = 1;
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243 | BOOST_USING_STD_MAX();
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244 | int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));
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245 | if (match(next(iter), next_k))
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246 | return true;
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247 | in_S[v] = false;
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248 | }
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249 |
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250 |
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251 | }
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252 | else {
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253 | if (contains(adjacent_vertices(f[i], G2), f[j])) {
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254 | ++num_edges_on_k;
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255 | if (match(next(iter), dfs_num_k))
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256 | return true;
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257 | }
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258 |
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259 | }
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260 | } else
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261 | return true;
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262 | return false;
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263 | }
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264 |
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265 | };
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266 |
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267 |
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268 | template <typename Graph, typename InDegreeMap>
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269 | void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
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270 | {
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271 | BGL_FORALL_VERTICES_T(v, g, Graph)
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272 | put(in_degree_map, v, 0);
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273 |
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274 | BGL_FORALL_VERTICES_T(u, g, Graph)
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275 | BGL_FORALL_ADJ_T(u, v, g, Graph)
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276 | put(in_degree_map, v, get(in_degree_map, v) + 1);
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277 | }
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278 |
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279 | } // namespace detail
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280 |
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281 |
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282 | template <typename InDegreeMap, typename Graph>
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283 | class degree_vertex_invariant
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284 | {
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285 | typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
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286 | typedef typename graph_traits<Graph>::degree_size_type size_type;
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287 | public:
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288 | typedef vertex_t argument_type;
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289 | typedef size_type result_type;
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290 |
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291 | degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
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292 | : m_in_degree_map(in_degree_map), m_g(g) { }
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293 |
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294 | size_type operator()(vertex_t v) const {
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295 | return (num_vertices(m_g) + 1) * out_degree(v, m_g)
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296 | + get(m_in_degree_map, v);
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297 | }
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298 | // The largest possible vertex invariant number
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299 | size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const {
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300 | return num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g);
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301 | }
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302 | private:
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303 | InDegreeMap m_in_degree_map;
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304 | const Graph& m_g;
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305 | };
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306 |
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307 |
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308 | template <typename Graph1, typename Graph2, typename IsoMapping,
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309 | typename Invariant1, typename Invariant2,
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310 | typename IndexMap1, typename IndexMap2>
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311 | bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f,
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312 | Invariant1 invariant1, Invariant2 invariant2,
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313 | std::size_t max_invariant,
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314 | IndexMap1 index_map1, IndexMap2 index_map2)
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315 |
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316 | {
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317 | // Graph requirements
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318 | function_requires< VertexListGraphConcept<Graph1> >();
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319 | function_requires< EdgeListGraphConcept<Graph1> >();
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320 | function_requires< VertexListGraphConcept<Graph2> >();
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321 | function_requires< BidirectionalGraphConcept<Graph2> >();
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322 |
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323 | typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
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324 | typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
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325 | typedef typename graph_traits<Graph1>::vertices_size_type size_type;
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326 |
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327 | // Vertex invariant requirement
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328 | function_requires< AdaptableUnaryFunctionConcept<Invariant1,
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329 | size_type, vertex1_t> >();
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330 | function_requires< AdaptableUnaryFunctionConcept<Invariant2,
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331 | size_type, vertex2_t> >();
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332 |
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333 | // Property map requirements
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334 | function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >();
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335 | typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
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336 | BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value));
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337 |
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338 | function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >();
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339 | typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
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340 | BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
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341 |
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342 | function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >();
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343 | typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
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344 | BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
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345 |
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346 | if (num_vertices(G1) != num_vertices(G2))
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347 | return false;
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348 | if (num_vertices(G1) == 0 && num_vertices(G2) == 0)
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349 | return true;
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350 |
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351 | detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
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352 | Invariant2, IndexMap1, IndexMap2>
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353 | algo(G1, G2, f, invariant1, invariant2, max_invariant,
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354 | index_map1, index_map2);
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355 | return algo.test_isomorphism();
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356 | }
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357 |
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358 |
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359 | namespace detail {
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360 |
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361 | template <typename Graph1, typename Graph2,
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362 | typename IsoMapping,
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363 | typename IndexMap1, typename IndexMap2,
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364 | typename P, typename T, typename R>
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365 | bool isomorphism_impl(const Graph1& G1, const Graph2& G2,
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366 | IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
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367 | const bgl_named_params<P,T,R>& params)
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368 | {
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369 | std::vector<std::size_t> in_degree1_vec(num_vertices(G1));
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370 | typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
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371 | IndexMap1
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372 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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373 | , std::size_t, std::size_t&
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374 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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375 | > InDeg1;
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376 | InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
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377 | compute_in_degree(G1, in_degree1);
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378 |
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379 | std::vector<std::size_t> in_degree2_vec(num_vertices(G2));
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380 | typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
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381 | IndexMap2
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382 | #ifdef BOOST_NO_STD_ITERATOR_TRAITS
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383 | , std::size_t, std::size_t&
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384 | #endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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385 | > InDeg2;
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386 | InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
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387 | compute_in_degree(G2, in_degree2);
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388 |
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389 | degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);
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390 | degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);
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391 |
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392 | return isomorphism(G1, G2, f,
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393 | choose_param(get_param(params, vertex_invariant1_t()), invariant1),
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394 | choose_param(get_param(params, vertex_invariant2_t()), invariant2),
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395 | choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),
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396 | index_map1, index_map2
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397 | );
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398 | }
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399 |
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400 | } // namespace detail
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401 |
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402 |
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403 | // Named parameter interface
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404 | template <typename Graph1, typename Graph2, class P, class T, class R>
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405 | bool isomorphism(const Graph1& g1,
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406 | const Graph2& g2,
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407 | const bgl_named_params<P,T,R>& params)
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408 | {
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409 | typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
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410 | typename std::vector<vertex2_t>::size_type n = num_vertices(g1);
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411 | std::vector<vertex2_t> f(n);
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412 | return detail::isomorphism_impl
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413 | (g1, g2,
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414 | choose_param(get_param(params, vertex_isomorphism_t()),
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415 | make_safe_iterator_property_map(f.begin(), f.size(),
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416 | choose_const_pmap(get_param(params, vertex_index1),
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417 | g1, vertex_index), vertex2_t())),
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418 | choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index),
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419 | choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index),
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420 | params
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421 | );
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422 | }
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423 |
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424 | // All defaults interface
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425 | template <typename Graph1, typename Graph2>
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426 | bool isomorphism(const Graph1& g1, const Graph2& g2)
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427 | {
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428 | return isomorphism(g1, g2,
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429 | bgl_named_params<int, buffer_param_t>(0));// bogus named param
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430 | }
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431 |
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432 |
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433 | // Verify that the given mapping iso_map from the vertices of g1 to the
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434 | // vertices of g2 describes an isomorphism.
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435 | // Note: this could be made much faster by specializing based on the graph
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436 | // concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
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437 | // O(n^4) won't hurt us.
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438 | template<typename Graph1, typename Graph2, typename IsoMap>
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439 | inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)
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440 | {
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441 | #if 0
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442 | // problematic for filtered_graph!
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443 | if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
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444 | return false;
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445 | #endif
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446 |
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447 | for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first;
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448 | e1 != edges(g1).second; ++e1) {
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449 | bool found_edge = false;
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450 | for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first;
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451 | e2 != edges(g2).second && !found_edge; ++e2) {
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452 | if (source(*e2, g2) == get(iso_map, source(*e1, g1)) &&
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453 | target(*e2, g2) == get(iso_map, target(*e1, g1))) {
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454 | found_edge = true;
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455 | }
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456 | }
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457 |
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458 | if (!found_edge)
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459 | return false;
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460 | }
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461 |
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462 | return true;
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463 | }
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464 |
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465 | } // namespace boost
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466 |
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467 | #ifdef BOOST_ISO_INCLUDED_ITER_MACROS
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468 | #undef BOOST_ISO_INCLUDED_ITER_MACROS
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469 | #include <boost/graph/iteration_macros_undef.hpp>
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470 | #endif
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471 |
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472 | #endif // BOOST_GRAPH_ISOMORPHISM_HPP
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