| 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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