--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/epoc32/include/stdapis/boost/graph/isomorphism.hpp Tue Mar 16 16:12:26 2010 +0000
@@ -0,0 +1,467 @@
+// Copyright (C) 2001 Jeremy Siek, Douglas Gregor, Brian Osman
+//
+// Distributed under the Boost Software License, Version 1.0. (See
+// accompanying file LICENSE_1_0.txt or copy at
+// http://www.boost.org/LICENSE_1_0.txt)
+#ifndef BOOST_GRAPH_ISOMORPHISM_HPP
+#define BOOST_GRAPH_ISOMORPHISM_HPP
+
+#include <utility>
+#include <vector>
+#include <iterator>
+#include <algorithm>
+#include <boost/config.hpp>
+#include <boost/graph/depth_first_search.hpp>
+#include <boost/utility.hpp>
+#include <boost/detail/algorithm.hpp>
+#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
+
+#ifndef BOOST_GRAPH_ITERATION_MACROS_HPP
+#define BOOST_ISO_INCLUDED_ITER_MACROS // local macro, see bottom of file
+#include <boost/graph/iteration_macros.hpp>
+#endif
+
+namespace boost {
+
+ namespace detail {
+
+ template <typename Graph1, typename Graph2, typename IsoMapping,
+ typename Invariant1, typename Invariant2,
+ typename IndexMap1, typename IndexMap2>
+ class isomorphism_algo
+ {
+ typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
+ typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+ typedef typename graph_traits<Graph1>::edge_descriptor edge1_t;
+ typedef typename graph_traits<Graph1>::vertices_size_type size_type;
+ typedef typename Invariant1::result_type invar1_value;
+ typedef typename Invariant2::result_type invar2_value;
+
+ const Graph1& G1;
+ const Graph2& G2;
+ IsoMapping f;
+ Invariant1 invariant1;
+ Invariant2 invariant2;
+ std::size_t max_invariant;
+ IndexMap1 index_map1;
+ IndexMap2 index_map2;
+
+ std::vector<vertex1_t> dfs_vertices;
+ typedef typename std::vector<vertex1_t>::iterator vertex_iter;
+ std::vector<int> dfs_num_vec;
+ typedef safe_iterator_property_map<typename std::vector<int>::iterator,
+ IndexMap1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+ , int, int&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+ > DFSNumMap;
+ DFSNumMap dfs_num;
+ std::vector<edge1_t> ordered_edges;
+ typedef typename std::vector<edge1_t>::iterator edge_iter;
+
+ std::vector<char> in_S_vec;
+ typedef safe_iterator_property_map<typename std::vector<char>::iterator,
+ IndexMap2
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+ , char, char&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+ > InSMap;
+ InSMap in_S;
+
+ int num_edges_on_k;
+
+ friend struct compare_multiplicity;
+ struct compare_multiplicity
+ {
+ compare_multiplicity(Invariant1 invariant1, size_type* multiplicity)
+ : invariant1(invariant1), multiplicity(multiplicity) { }
+ bool operator()(const vertex1_t& x, const vertex1_t& y) const {
+ return multiplicity[invariant1(x)] < multiplicity[invariant1(y)];
+ }
+ Invariant1 invariant1;
+ size_type* multiplicity;
+ };
+
+ struct record_dfs_order : default_dfs_visitor
+ {
+ record_dfs_order(std::vector<vertex1_t>& v, std::vector<edge1_t>& e)
+ : vertices(v), edges(e) { }
+
+ void discover_vertex(vertex1_t v, const Graph1&) const {
+ vertices.push_back(v);
+ }
+ void examine_edge(edge1_t e, const Graph1& G1) const {
+ edges.push_back(e);
+ }
+ std::vector<vertex1_t>& vertices;
+ std::vector<edge1_t>& edges;
+ };
+
+ struct edge_cmp {
+ edge_cmp(const Graph1& G1, DFSNumMap dfs_num)
+ : G1(G1), dfs_num(dfs_num) { }
+ bool operator()(const edge1_t& e1, const edge1_t& e2) const {
+ using namespace std;
+ int u1 = dfs_num[source(e1,G1)], v1 = dfs_num[target(e1,G1)];
+ int u2 = dfs_num[source(e2,G1)], v2 = dfs_num[target(e2,G1)];
+ int m1 = (max)(u1, v1);
+ int m2 = (max)(u2, v2);
+ // lexicographical comparison
+ return std::make_pair(m1, std::make_pair(u1, v1))
+ < std::make_pair(m2, std::make_pair(u2, v2));
+ }
+ const Graph1& G1;
+ DFSNumMap dfs_num;
+ };
+
+ public:
+ isomorphism_algo(const Graph1& G1, const Graph2& G2, IsoMapping f,
+ Invariant1 invariant1, Invariant2 invariant2, std::size_t max_invariant,
+ IndexMap1 index_map1, IndexMap2 index_map2)
+ : G1(G1), G2(G2), f(f), invariant1(invariant1), invariant2(invariant2),
+ max_invariant(max_invariant),
+ index_map1(index_map1), index_map2(index_map2)
+ {
+ in_S_vec.resize(num_vertices(G1));
+ in_S = make_safe_iterator_property_map
+ (in_S_vec.begin(), in_S_vec.size(), index_map2
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+ , in_S_vec.front()
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+ );
+ }
+
+ bool test_isomorphism()
+ {
+ {
+ std::vector<invar1_value> invar1_array;
+ BGL_FORALL_VERTICES_T(v, G1, Graph1)
+ invar1_array.push_back(invariant1(v));
+ sort(invar1_array);
+
+ std::vector<invar2_value> invar2_array;
+ BGL_FORALL_VERTICES_T(v, G2, Graph2)
+ invar2_array.push_back(invariant2(v));
+ sort(invar2_array);
+ if (! equal(invar1_array, invar2_array))
+ return false;
+ }
+
+ std::vector<vertex1_t> V_mult;
+ BGL_FORALL_VERTICES_T(v, G1, Graph1)
+ V_mult.push_back(v);
+ {
+ std::vector<size_type> multiplicity(max_invariant, 0);
+ BGL_FORALL_VERTICES_T(v, G1, Graph1)
+ ++multiplicity[invariant1(v)];
+ sort(V_mult, compare_multiplicity(invariant1, &multiplicity[0]));
+ }
+
+ std::vector<default_color_type> color_vec(num_vertices(G1));
+ safe_iterator_property_map<std::vector<default_color_type>::iterator,
+ IndexMap1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+ , default_color_type, default_color_type&
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+ >
+ color_map(color_vec.begin(), color_vec.size(), index_map1);
+ record_dfs_order dfs_visitor(dfs_vertices, ordered_edges);
+ typedef color_traits<default_color_type> Color;
+ for (vertex_iter u = V_mult.begin(); u != V_mult.end(); ++u) {
+ if (color_map[*u] == Color::white()) {
+ dfs_visitor.start_vertex(*u, G1);
+ depth_first_visit(G1, *u, dfs_visitor, color_map);
+ }
+ }
+ // Create the dfs_num array and dfs_num_map
+ dfs_num_vec.resize(num_vertices(G1));
+ dfs_num = make_safe_iterator_property_map(dfs_num_vec.begin(),
+ dfs_num_vec.size(),
+ index_map1
+#ifdef BOOST_NO_STD_ITERATOR_TRAITS
+ , dfs_num_vec.front()
+#endif /* BOOST_NO_STD_ITERATOR_TRAITS */
+ );
+ size_type n = 0;
+ for (vertex_iter v = dfs_vertices.begin(); v != dfs_vertices.end(); ++v)
+ dfs_num[*v] = n++;
+
+ sort(ordered_edges, edge_cmp(G1, dfs_num));
+
+
+ int dfs_num_k = -1;
+ return this->match(ordered_edges.begin(), dfs_num_k);
+ }
+
+ private:
+ bool match(edge_iter iter, int dfs_num_k)
+ {
+ if (iter != ordered_edges.end()) {
+ vertex1_t i = source(*iter, G1), j = target(*iter, G2);
+ if (dfs_num[i] > dfs_num_k) {
+ vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
+ BGL_FORALL_VERTICES_T(u, G2, Graph2) {
+ if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
+ f[kp1] = u;
+ in_S[u] = true;
+ num_edges_on_k = 0;
+
+ if (match(iter, dfs_num_k + 1))
+#if 0
+ // dwa 2003/7/11 -- this *HAS* to be a bug!
+ ;
+#endif
+ return true;
+
+ in_S[u] = false;
+ }
+ }
+
+ }
+ else if (dfs_num[j] > dfs_num_k) {
+ vertex1_t k = dfs_vertices[dfs_num_k];
+ num_edges_on_k -=
+ count_if(adjacent_vertices(f[k], G2), make_indirect_pmap(in_S));
+
+ for (int jj = 0; jj < dfs_num_k; ++jj) {
+ vertex1_t j = dfs_vertices[jj];
+ num_edges_on_k -= count(adjacent_vertices(f[j], G2), f[k]);
+ }
+
+ if (num_edges_on_k != 0)
+ return false;
+ BGL_FORALL_ADJ_T(f[i], v, G2, Graph2)
+ if (invariant2(v) == invariant1(j) && in_S[v] == false) {
+ f[j] = v;
+ in_S[v] = true;
+ num_edges_on_k = 1;
+ BOOST_USING_STD_MAX();
+ int next_k = max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num_k, max BOOST_PREVENT_MACRO_SUBSTITUTION(dfs_num[i], dfs_num[j]));
+ if (match(next(iter), next_k))
+ return true;
+ in_S[v] = false;
+ }
+
+
+ }
+ else {
+ if (contains(adjacent_vertices(f[i], G2), f[j])) {
+ ++num_edges_on_k;
+ if (match(next(iter), dfs_num_k))
+ return true;
+ }
+
+ }
+ } else
+ return true;
+ return false;
+ }
+
+ };
+
+
+ template <typename Graph, typename InDegreeMap>
+ void compute_in_degree(const Graph& g, InDegreeMap in_degree_map)
+ {
+ BGL_FORALL_VERTICES_T(v, g, Graph)
+ put(in_degree_map, v, 0);
+
+ BGL_FORALL_VERTICES_T(u, g, Graph)
+ BGL_FORALL_ADJ_T(u, v, g, Graph)
+ put(in_degree_map, v, get(in_degree_map, v) + 1);
+ }
+
+ } // namespace detail
+
+
+ template <typename InDegreeMap, typename Graph>
+ class degree_vertex_invariant
+ {
+ typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
+ typedef typename graph_traits<Graph>::degree_size_type size_type;
+ public:
+ typedef vertex_t argument_type;
+ typedef size_type result_type;
+
+ degree_vertex_invariant(const InDegreeMap& in_degree_map, const Graph& g)
+ : m_in_degree_map(in_degree_map), m_g(g) { }
+
+ size_type operator()(vertex_t v) const {
+ return (num_vertices(m_g) + 1) * out_degree(v, m_g)
+ + get(m_in_degree_map, v);
+ }
+ // The largest possible vertex invariant number
+ size_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const {
+ return num_vertices(m_g) * num_vertices(m_g) + num_vertices(m_g);
+ }
+ private:
+ InDegreeMap m_in_degree_map;
+ const Graph& m_g;
+ };
+
+
+ template <typename Graph1, typename Graph2, typename IsoMapping,
+ typename Invariant1, typename Invariant2,
+ typename IndexMap1, typename IndexMap2>
+ bool isomorphism(const Graph1& G1, const Graph2& G2, IsoMapping f,
+ Invariant1 invariant1, Invariant2 invariant2,
+ std::size_t max_invariant,
+ IndexMap1 index_map1, IndexMap2 index_map2)
+
+ {
+ // Graph requirements
+ function_requires< VertexListGraphConcept<Graph1> >();
+ function_requires< EdgeListGraphConcept<Graph1> >();
+ function_requires< VertexListGraphConcept<Graph2> >();
+ function_requires< BidirectionalGraphConcept<Graph2> >();
+
+ typedef typename graph_traits<Graph1>::vertex_descriptor vertex1_t;
+ typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+ typedef typename graph_traits<Graph1>::vertices_size_type size_type;
+
+ // Vertex invariant requirement
+ function_requires< AdaptableUnaryFunctionConcept<Invariant1,
+ size_type, vertex1_t> >();
+ function_requires< AdaptableUnaryFunctionConcept<Invariant2,
+ size_type, vertex2_t> >();
+
+ // Property map requirements
+ function_requires< ReadWritePropertyMapConcept<IsoMapping, vertex1_t> >();
+ typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
+ BOOST_STATIC_ASSERT((is_same<IsoMappingValue, vertex2_t>::value));
+
+ function_requires< ReadablePropertyMapConcept<IndexMap1, vertex1_t> >();
+ typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
+ BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
+
+ function_requires< ReadablePropertyMapConcept<IndexMap2, vertex2_t> >();
+ typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
+ BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
+
+ if (num_vertices(G1) != num_vertices(G2))
+ return false;
+ if (num_vertices(G1) == 0 && num_vertices(G2) == 0)
+ return true;
+
+ detail::isomorphism_algo<Graph1, Graph2, IsoMapping, Invariant1,
+ Invariant2, IndexMap1, IndexMap2>
+ algo(G1, G2, f, invariant1, invariant2, max_invariant,
+ index_map1, index_map2);
+ return algo.test_isomorphism();
+ }
+
+
+ namespace detail {
+
+ template <typename Graph1, typename Graph2,
+ typename IsoMapping,
+ typename IndexMap1, typename IndexMap2,
+ typename P, typename T, typename R>
+ bool isomorphism_impl(const Graph1& G1, const Graph2& G2,
+ IsoMapping f, IndexMap1 index_map1, IndexMap2 index_map2,
+ 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
+ );
+ }
+
+ } // namespace detail
+
+
+ // Named parameter interface
+ template <typename Graph1, typename Graph2, class P, class T, class R>
+ bool isomorphism(const Graph1& g1,
+ const Graph2& g2,
+ const bgl_named_params<P,T,R>& params)
+ {
+ typedef typename graph_traits<Graph2>::vertex_descriptor vertex2_t;
+ typename std::vector<vertex2_t>::size_type n = num_vertices(g1);
+ std::vector<vertex2_t> f(n);
+ return detail::isomorphism_impl
+ (g1, g2,
+ choose_param(get_param(params, vertex_isomorphism_t()),
+ make_safe_iterator_property_map(f.begin(), f.size(),
+ choose_const_pmap(get_param(params, vertex_index1),
+ g1, vertex_index), vertex2_t())),
+ choose_const_pmap(get_param(params, vertex_index1), g1, vertex_index),
+ choose_const_pmap(get_param(params, vertex_index2), g2, vertex_index),
+ params
+ );
+ }
+
+ // All defaults interface
+ template <typename Graph1, typename Graph2>
+ bool isomorphism(const Graph1& g1, const Graph2& g2)
+ {
+ return isomorphism(g1, g2,
+ bgl_named_params<int, buffer_param_t>(0));// bogus named param
+ }
+
+
+ // 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
+
+ for (typename graph_traits<Graph1>::edge_iterator e1 = edges(g1).first;
+ e1 != edges(g1).second; ++e1) {
+ bool found_edge = false;
+ for (typename graph_traits<Graph2>::edge_iterator e2 = edges(g2).first;
+ e2 != edges(g2).second && !found_edge; ++e2) {
+ 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