582 lines
23 KiB
C++
582 lines
23 KiB
C++
// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// 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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#ifndef BOOST_GRAPH_ISOMORPHISM_HPP
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#define BOOST_GRAPH_ISOMORPHISM_HPP
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#include <utility>
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#include <vector>
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#include <iterator>
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#include <algorithm>
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#include <boost/config.hpp>
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#include <boost/assert.hpp>
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#include <boost/smart_ptr.hpp>
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#include <boost/graph/depth_first_search.hpp>
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#include <boost/detail/algorithm.hpp>
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#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
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#include <boost/concept/assert.hpp>
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#ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
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#define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
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#include <boost/graph/iteration_macros.hpp>
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#endif
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namespace boost {
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namespace detail {
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template <typename Graph1, typename Graph2, typename IsoMapping,
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typename Invariant1, typename Invariant2,
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typename IndexMap1, typename IndexMap2>
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class isomorphism_algo
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{
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typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
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typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
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typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
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typedef typename graph_traits<Graph1>::vertices_size_type size_type;
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typedef typename Invariant1::result_type invar1_value;
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typedef typename Invariant2::result_type invar2_value;
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const Graph1& G1;
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const Graph2& G2;
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IsoMapping f;
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Invariant1 invariant1;
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Invariant2 invariant2;
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std::size_t max_invariant;
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IndexMap1 index_map1;
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IndexMap2 index_map2;
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std::vector<vertex1_t> dfs_vertices;
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typedef typename std::vector<vertex1_t>::iterator vertex_iter;
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std::vector<int> dfs_num_vec;
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typedef safe_iterator_property_map<typename std::vector<int>::iterator,
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IndexMap1
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#ifdef BOOST_NO_STD_ITERATOR_TRAITS
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, int, int&
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#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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> DFSNumMap;
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DFSNumMap dfs_num;
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std::vector<edge1_t> ordered_edges;
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typedef typename std::vector<edge1_t>::iterator edge_iter;
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std::vector<char> in_S_vec;
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typedef safe_iterator_property_map<typename std::vector<char>::iterator,
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IndexMap2
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#ifdef BOOST_NO_STD_ITERATOR_TRAITS
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, char, char&
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#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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> InSMap;
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InSMap in_S;
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int num_edges_on_k;
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friend struct compare_multiplicity;
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struct compare_multiplicity
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{
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compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
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: invariant1(invariant1), multiplicity(multiplicity) { }
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bool operator()(const vertex1_t& x, const vertex1_t& y) const {
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return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
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}
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Invariant1 invariant1;
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size_type* multiplicity;
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};
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struct record_dfs_order : default_dfs_visitor
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{
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record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e)
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: vertices(v), edges(e) { }
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void discover_vertex(vertex1_t v, const Graph1&) const {
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vertices.push_back(v);
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}
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void examine_edge(edge1_t e, const Graph1&) const {
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edges.push_back(e);
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}
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std::vector<vertex1_t>& vertices;
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std::vector<edge1_t>& edges;
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};
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struct edge_cmp {
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edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
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: G1(G1), dfs_num(dfs_num) { }
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bool operator()(const edge1_t& e1, const edge1_t& e2) const {
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using namespace std;
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int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
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int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
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int m1 = (max)(u1, v1);
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int m2 = (max)(u2, v2);
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// lexicographical comparison
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return std::make_pair(m1, std::make_pair(u1, v1))
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< std::make_pair(m2, std::make_pair(u2, v2));
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}
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const Graph1& G1;
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DFSNumMap dfs_num;
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};
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public:
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isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
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Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
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IndexMap1 index_map1, IndexMap2 index_map2)
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: G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
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max_invariant(max_invariant),
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index_map1(index_map1), index_map2(index_map2)
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{
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in_S_vec.resize(num_vertices(G1));
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in_S = make_safe_iterator_property_map
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(in_S_vec.begin(), in_S_vec.size(), index_map2
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#ifdef BOOST_NO_STD_ITERATOR_TRAITS
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, in_S_vec.front()
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#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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);
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}
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bool test_isomorphism()
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{
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// reset isomapping
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BGL_FORALL_VERTICES_T(v, G1, Graph1)
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f[v] = graph_traits<Graph2>::null_vertex();
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{
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std::vector<invar1_value> invar1_array;
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BGL_FORALL_VERTICES_T(v, G1, Graph1)
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invar1_array.push_back(invariant1(v));
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sort(invar1_array);
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std::vector<invar2_value> invar2_array;
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BGL_FORALL_VERTICES_T(v, G2, Graph2)
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invar2_array.push_back(invariant2(v));
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sort(invar2_array);
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if (! equal(invar1_array, invar2_array))
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return false;
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}
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std::vector<vertex1_t> V_mult;
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BGL_FORALL_VERTICES_T(v, G1, Graph1)
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V_mult.push_back(v);
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{
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std::vector<size_type> multiplicity(max_invariant, 0);
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BGL_FORALL_VERTICES_T(v, G1, Graph1)
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++multiplicity.at(invariant1(v));
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sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
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}
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std::vector<default_color_type> color_vec(num_vertices(G1));
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safe_iterator_property_map<std::vector<default_color_type>::iterator,
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IndexMap1
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#ifdef BOOST_NO_STD_ITERATOR_TRAITS
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, default_color_type, default_color_type&
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#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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>
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color_map(color_vec.begin(), color_vec.size(), index_map1);
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record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
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typedef color_traits<default_color_type> Color;
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for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
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if (color_map[*u] == Color::white()) {
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dfs_visitor.start_vertex(*u, G1);
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depth_first_visit(G1, *u, dfs_visitor, color_map);
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}
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}
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// Create the dfs_num array and dfs_num_map
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dfs_num_vec.resize(num_vertices(G1));
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dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
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dfs_num_vec.size(),
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index_map1
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#ifdef BOOST_NO_STD_ITERATOR_TRAITS
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, dfs_num_vec.front()
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#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
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);
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size_type n = 0;
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for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
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dfs_num[*v] = n++;
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sort(ordered_edges, edge_cmp(G1, dfs_num));
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int dfs_num_k = -1;
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return this->match(ordered_edges.begin(), dfs_num_k);
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}
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private:
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struct match_continuation {
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enum {pos_G2_vertex_loop, pos_fi_adj_loop, pos_dfs_num} position;
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typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
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std::pair<vertex_iterator, vertex_iterator> G2_verts;
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typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
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std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
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edge_iter iter;
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int dfs_num_k;
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};
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bool match(edge_iter iter, int dfs_num_k)
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{
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std::vector<match_continuation> k;
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typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
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std::pair<vertex_iterator, vertex_iterator> G2_verts(vertices(G2));
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typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
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std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
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vertex1_t i, j;
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recur:
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if (iter != ordered_edges.end()) {
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i = source(*iter, G1);
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j = target(*iter, G1);
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if (dfs_num[i] > dfs_num_k) {
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G2_verts = vertices(G2);
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while (G2_verts.first != G2_verts.second) {
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{
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vertex2_t u = *G2_verts.first;
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vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
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if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
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{
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f[kp1] = u;
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in_S[u] = true;
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num_edges_on_k = 0;
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match_continuation new_k;
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new_k.position = match_continuation::pos_G2_vertex_loop;
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new_k.G2_verts = G2_verts;
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new_k.iter = iter;
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new_k.dfs_num_k = dfs_num_k;
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k.push_back(new_k);
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++dfs_num_k;
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goto recur;
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}
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}
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}
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G2_loop_k: ++G2_verts.first;
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}
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}
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else if (dfs_num[j] > dfs_num_k) {
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{
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vertex1_t vk = dfs_vertices[dfs_num_k];
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num_edges_on_k -=
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count_if(adjacent_vertices(f[vk], G2), make_indirect_pmap(in_S));
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for (int jj = 0; jj < dfs_num_k; ++jj) {
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vertex1_t j = dfs_vertices[jj];
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num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[vk]);
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}
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}
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if (num_edges_on_k != 0)
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goto return_point_false;
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fi_adj = adjacent_vertices(f[i], G2);
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while (fi_adj.first != fi_adj.second) {
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{
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vertex2_t v = *fi_adj.first;
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if (invariant2(v) == invariant1(j) && in_S[v] == false) {
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f[j] = v;
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in_S[v] = true;
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num_edges_on_k = 1;
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BOOST_USING_STD_MAX();
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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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match_continuation new_k;
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new_k.position = match_continuation::pos_fi_adj_loop;
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new_k.fi_adj = fi_adj;
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new_k.iter = iter;
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new_k.dfs_num_k = dfs_num_k;
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++iter;
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dfs_num_k = next_k;
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k.push_back(new_k);
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goto recur;
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}
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}
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fi_adj_loop_k:++fi_adj.first;
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}
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}
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else {
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if (container_contains(adjacent_vertices(f[i], G2), f[j])) {
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++num_edges_on_k;
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match_continuation new_k;
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new_k.position = match_continuation::pos_dfs_num;
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k.push_back(new_k);
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++iter;
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goto recur;
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}
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}
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} else
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goto return_point_true;
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goto return_point_false;
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{
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return_point_true: return true;
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return_point_false:
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if (k.empty()) return false;
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const match_continuation& this_k = k.back();
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switch (this_k.position) {
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case match_continuation::pos_G2_vertex_loop: {G2_verts = this_k.G2_verts; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*G2_verts.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto G2_loop_k;}
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case match_continuation::pos_fi_adj_loop: {fi_adj = this_k.fi_adj; iter = this_k.iter; dfs_num_k = this_k.dfs_num_k; k.pop_back(); in_S[*fi_adj.first] = false; i = source(*iter, G1); j = target(*iter, G1); goto fi_adj_loop_k;}
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case match_continuation::pos_dfs_num: {k.pop_back(); goto return_point_false;}
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default: {
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BOOST_ASSERT(!"Bad position");
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#ifdef UNDER_CE
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exit(-1);
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#else
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abort();
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#endif
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}
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}
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}
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}
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};
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template <typename Graph, typename InDegreeMap>
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void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
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{
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BGL_FORALL_VERTICES_T(v, g, Graph)
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put(in_degree_map, v, 0);
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BGL_FORALL_VERTICES_T(u, g, Graph)
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BGL_FORALL_ADJ_T(u, v, g, Graph)
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put(in_degree_map, v, get(in_degree_map, v) + 1);
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}
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} // namespace detail
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template <typename InDegreeMap, typename Graph>
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class degree_vertex_invariant
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{
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typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
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typedef typename graph_traits<Graph>::degree_size_type size_type;
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public:
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typedef vertex_t argument_type;
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typedef size_type result_type;
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degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
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: m_in_degree_map(in_degree_map),
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m_max_vertex_in_degree(0),
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m_max_vertex_out_degree(0),
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m_g(g) {
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BGL_FORALL_VERTICES_T(v, g, Graph) {
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m_max_vertex_in_degree =
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(std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v));
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m_max_vertex_out_degree =
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(std::max)(m_max_vertex_out_degree, out_degree(v, g));
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}
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}
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size_type operator()(vertex_t v) const {
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return (m_max_vertex_in_degree + 1) * out_degree(v, m_g)
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+ get(m_in_degree_map, v);
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}
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// The largest possible vertex invariant number
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size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const {
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return (m_max_vertex_in_degree + 1) * (m_max_vertex_out_degree + 1);
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}
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private:
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InDegreeMap m_in_degree_map;
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size_type m_max_vertex_in_degree;
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size_type m_max_vertex_out_degree;
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const Graph& m_g;
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};
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// Count actual number of vertices, even in filtered graphs.
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template <typename Graph>
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size_t count_vertices(const Graph& g)
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{
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size_t n = 0;
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BGL_FORALL_VERTICES_T(v, g, Graph) {(void)v; ++n;}
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return n;
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}
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template <typename Graph1, typename Graph2, typename IsoMapping,
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typename Invariant1, typename Invariant2,
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typename IndexMap1, typename IndexMap2>
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bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f,
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Invariant1 invariant1, Invariant2 invariant2,
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std::size_t max_invariant,
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IndexMap1 index_map1, IndexMap2 index_map2)
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{
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// Graph requirements
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BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph1> ));
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BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph1> ));
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BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph2> ));
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//BOOST_CONCEPT_ASSERT(( BidirectionalGraphConcept<Graph2> ));
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typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
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typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
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typedef typename graph_traits<Graph1>::vertices_size_type size_type;
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// Vertex invariant requirement
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BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant1,
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size_type, vertex1_t> ));
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BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant2,
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size_type, vertex2_t> ));
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// Property map requirements
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BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<IsoMapping, vertex1_t> ));
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typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
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BOOST_STATIC_ASSERT((is_convertible<IsoMappingValue, vertex2_t>::value));
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BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap1, vertex1_t> ));
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typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
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BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
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BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap2, vertex2_t> ));
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typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
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BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
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if (count_vertices(G1) != count_vertices(G2))
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return false;
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if (count_vertices(G1) == 0 && count_vertices(G2) == 0)
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return true;
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detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
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Invariant2, IndexMap1, IndexMap2>
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algo(G1, G2, f, invariant1, invariant2, max_invariant,
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index_map1, index_map2);
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return algo.test_isomorphism();
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}
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namespace detail {
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template <typename Graph1, typename Graph2,
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typename IsoMapping,
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typename IndexMap1, typename IndexMap2,
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typename P, typename T, typename R>
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bool isomorphism_impl(const Graph1& G1, const Graph2& G2,
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IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
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|
const bgl_named_params<P,T,R>& params)
|
|
{
|
|
std::vector<std::size_t> in_degree1_vec(num_vertices(G1));
|
|
typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
|
|
IndexMap1
|
|
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
|
|
, std::size_t, std::size_t&
|
|
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
|
|
> InDeg1;
|
|
InDeg1 in_degree1(in_degree1_vec.begin(), in_degree1_vec.size(), index_map1);
|
|
compute_in_degree(G1, in_degree1);
|
|
|
|
std::vector<std::size_t> in_degree2_vec(num_vertices(G2));
|
|
typedef safe_iterator_property_map<std::vector<std::size_t>::iterator,
|
|
IndexMap2
|
|
#ifdef BOOST_NO_STD_ITERATOR_TRAITS
|
|
, std::size_t, std::size_t&
|
|
#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
|
|
> InDeg2;
|
|
InDeg2 in_degree2(in_degree2_vec.begin(), in_degree2_vec.size(), index_map2);
|
|
compute_in_degree(G2, in_degree2);
|
|
|
|
degree_vertex_invariant<InDeg1, Graph1> invariant1(in_degree1, G1);
|
|
degree_vertex_invariant<InDeg2, Graph2> invariant2(in_degree2, G2);
|
|
|
|
return isomorphism(G1, G2, f,
|
|
choose_param(get_param(params, vertex_invariant1_t()), invariant1),
|
|
choose_param(get_param(params, vertex_invariant2_t()), invariant2),
|
|
choose_param(get_param(params, vertex_max_invariant_t()), (invariant2.max)()),
|
|
index_map1, index_map2
|
|
);
|
|
}
|
|
|
|
template <typename G, typename Index>
|
|
struct make_degree_invariant {
|
|
const G& g;
|
|
const Index& index;
|
|
make_degree_invariant(const G& g, const Index& index): g(g), index(index) {}
|
|
typedef typename boost::graph_traits<G>::degree_size_type degree_size_type;
|
|
typedef shared_array_property_map<degree_size_type, Index> prop_map_type;
|
|
typedef degree_vertex_invariant<prop_map_type, G> result_type;
|
|
result_type operator()() const {
|
|
prop_map_type pm = make_shared_array_property_map(num_vertices(g), degree_size_type(), index);
|
|
compute_in_degree(g, pm);
|
|
return result_type(pm, g);
|
|
}
|
|
};
|
|
|
|
} // namespace detail
|
|
|
|
namespace graph {
|
|
namespace detail {
|
|
template <typename Graph1, typename Graph2>
|
|
struct isomorphism_impl {
|
|
typedef bool result_type;
|
|
template <typename ArgPack>
|
|
bool operator()(const Graph1& g1, const Graph2& g2, const ArgPack& arg_pack) const {
|
|
using namespace boost::graph::keywords;
|
|
typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index1_map, boost::vertex_index_t, Graph1>::type index1_map_type;
|
|
typedef typename boost::detail::override_const_property_result<ArgPack, tag::vertex_index2_map, boost::vertex_index_t, Graph2>::type index2_map_type;
|
|
index1_map_type index1_map = boost::detail::override_const_property(arg_pack, _vertex_index1_map, g1, boost::vertex_index);
|
|
index2_map_type index2_map = boost::detail::override_const_property(arg_pack, _vertex_index2_map, g2, boost::vertex_index);
|
|
typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
|
|
typename std::vector<vertex2_t>::size_type n = (typename std::vector<vertex2_t>::size_type)num_vertices(g1);
|
|
std::vector<vertex2_t> f(n);
|
|
typename boost::parameter::lazy_binding<
|
|
ArgPack,
|
|
tag::vertex_invariant1,
|
|
boost::detail::make_degree_invariant<Graph1, index1_map_type> >::type
|
|
invariant1 =
|
|
arg_pack[_vertex_invariant1 || boost::detail::make_degree_invariant<Graph1, index1_map_type>(g1, index1_map)];
|
|
typename boost::parameter::lazy_binding<
|
|
ArgPack,
|
|
tag::vertex_invariant2,
|
|
boost::detail::make_degree_invariant<Graph2, index2_map_type> >::type
|
|
invariant2 =
|
|
arg_pack[_vertex_invariant2 || boost::detail::make_degree_invariant<Graph2, index2_map_type>(g2, index2_map)];
|
|
return boost::isomorphism
|
|
(g1, g2,
|
|
choose_param(arg_pack[_isomorphism_map | boost::param_not_found()],
|
|
make_shared_array_property_map(num_vertices(g1), vertex2_t(), index1_map)),
|
|
invariant1,
|
|
invariant2,
|
|
arg_pack[_vertex_max_invariant | (invariant2.max)()],
|
|
index1_map,
|
|
index2_map);
|
|
}
|
|
};
|
|
}
|
|
BOOST_GRAPH_MAKE_FORWARDING_FUNCTION(isomorphism, 2, 6)
|
|
}
|
|
|
|
// Named parameter interface
|
|
BOOST_GRAPH_MAKE_OLD_STYLE_PARAMETER_FUNCTION(isomorphism, 2)
|
|
|
|
// Verify that the given mapping iso_map from the vertices of g1 to the
|
|
// vertices of g2 describes an isomorphism.
|
|
// Note: this could be made much faster by specializing based on the graph
|
|
// concepts modeled, but since we're verifying an O(n^(lg n)) algorithm,
|
|
// O(n^4) won't hurt us.
|
|
template<typename Graph1, typename Graph2, typename IsoMap>
|
|
inline bool verify_isomorphism(const Graph1& g1, const Graph2& g2, IsoMap iso_map)
|
|
{
|
|
#if 0
|
|
// problematic for filtered_graph!
|
|
if (num_vertices(g1) != num_vertices(g2) || num_edges(g1) != num_edges(g2))
|
|
return false;
|
|
#endif
|
|
|
|
BGL_FORALL_EDGES_T(e1, g1, Graph1) {
|
|
bool found_edge = false;
|
|
BGL_FORALL_EDGES_T(e2, g2, Graph2) {
|
|
if (source(e2, g2) == get(iso_map, source(e1, g1)) &&
|
|
target(e2, g2) == get(iso_map, target(e1, g1))) {
|
|
found_edge = true;
|
|
}
|
|
}
|
|
|
|
if (!found_edge)
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
} // namespace boost
|
|
|
|
#ifdef BOOST_ISO_INCLUDED_ITER_MACROS
|
|
#undef BOOST_ISO_INCLUDED_ITER_MACROS
|
|
#include <boost/graph/iteration_macros_undef.hpp>
|
|
#endif
|
|
|
|
#endif // BOOST_GRAPH_ISOMORPHISM_HPP
|