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Boost-for-Android-Prebuilt/boost-1_72_0/include/boost/graph/isomorphism.hpp

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// 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/assert.hpp>
#include <boost/smart_ptr.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/detail/algorithm.hpp>
#include <boost/pending/indirect_cmp.hpp> // for make_indirect_pmap
#include <boost/concept/assert.hpp>
#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&) 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()
{
// reset isomapping
BGL_FORALL_VERTICES_T(v, G1, Graph1)
f[v] = graph_traits<Graph2>::null_vertex();
{
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.at(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:
struct match_continuation {
enum {pos_G2_vertex_loop, pos_fi_adj_loop, pos_dfs_num} position;
typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
std::pair<vertex_iterator, vertex_iterator> G2_verts;
typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
edge_iter iter;
int dfs_num_k;
};
bool match(edge_iter iter, int dfs_num_k)
{
std::vector<match_continuation> k;
typedef typename graph_traits<Graph2>::vertex_iterator vertex_iterator;
std::pair<vertex_iterator, vertex_iterator> G2_verts(vertices(G2));
typedef typename graph_traits<Graph2>::adjacency_iterator adjacency_iterator;
std::pair<adjacency_iterator, adjacency_iterator> fi_adj;
vertex1_t i, j;
recur:
if (iter != ordered_edges.end()) {
i = source(*iter, G1);
j = target(*iter, G1);
if (dfs_num[i] > dfs_num_k) {
G2_verts = vertices(G2);
while (G2_verts.first != G2_verts.second) {
{
vertex2_t u = *G2_verts.first;
vertex1_t kp1 = dfs_vertices[dfs_num_k + 1];
if (invariant1(kp1) == invariant2(u) && in_S[u] == false) {
{
f[kp1] = u;
in_S[u] = true;
num_edges_on_k = 0;
match_continuation new_k;
new_k.position = match_continuation::pos_G2_vertex_loop;
new_k.G2_verts = G2_verts;
new_k.iter = iter;
new_k.dfs_num_k = dfs_num_k;
k.push_back(new_k);
++dfs_num_k;
goto recur;
}
}
}
G2_loop_k: ++G2_verts.first;
}
}
else if (dfs_num[j] > dfs_num_k) {
{
vertex1_t vk = dfs_vertices[dfs_num_k];
num_edges_on_k -=
count_if(adjacent_vertices(f[vk], 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[vk]);
}
}
if (num_edges_on_k != 0)
goto return_point_false;
fi_adj = adjacent_vertices(f[i], G2);
while (fi_adj.first != fi_adj.second) {
{
vertex2_t v = *fi_adj.first;
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]));
match_continuation new_k;
new_k.position = match_continuation::pos_fi_adj_loop;
new_k.fi_adj = fi_adj;
new_k.iter = iter;
new_k.dfs_num_k = dfs_num_k;
++iter;
dfs_num_k = next_k;
k.push_back(new_k);
goto recur;
}
}
fi_adj_loop_k:++fi_adj.first;
}
}
else {
if (container_contains(adjacent_vertices(f[i], G2), f[j])) {
++num_edges_on_k;
match_continuation new_k;
new_k.position = match_continuation::pos_dfs_num;
k.push_back(new_k);
++iter;
goto recur;
}
}
} else
goto return_point_true;
goto return_point_false;
{
return_point_true: return true;
return_point_false:
if (k.empty()) return false;
const match_continuation& this_k = k.back();
switch (this_k.position) {
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;}
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;}
case match_continuation::pos_dfs_num: {k.pop_back(); goto return_point_false;}
default: {
BOOST_ASSERT(!"Bad position");
#ifdef UNDER_CE
exit(-1);
#else
abort();
#endif
}
}
}
}
};
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_max_vertex_in_degree(0),
m_max_vertex_out_degree(0),
m_g(g) {
BGL_FORALL_VERTICES_T(v, g, Graph) {
m_max_vertex_in_degree =
(std::max)(m_max_vertex_in_degree, get(m_in_degree_map, v));
m_max_vertex_out_degree =
(std::max)(m_max_vertex_out_degree, out_degree(v, g));
}
}
size_type operator()(vertex_t v) const {
return (m_max_vertex_in_degree + 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 (m_max_vertex_in_degree + 1) * (m_max_vertex_out_degree + 1);
}
private:
InDegreeMap m_in_degree_map;
size_type m_max_vertex_in_degree;
size_type m_max_vertex_out_degree;
const Graph& m_g;
};
// Count actual number of vertices, even in filtered graphs.
template <typename Graph>
size_t count_vertices(const Graph& g)
{
size_t n = 0;
BGL_FORALL_VERTICES_T(v, g, Graph) {(void)v; ++n;}
return n;
}
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
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph1> ));
BOOST_CONCEPT_ASSERT(( EdgeListGraphConcept<Graph1> ));
BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<Graph2> ));
//BOOST_CONCEPT_ASSERT(( 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
BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant1,
size_type, vertex1_t> ));
BOOST_CONCEPT_ASSERT(( AdaptableUnaryFunctionConcept<Invariant2,
size_type, vertex2_t> ));
// Property map requirements
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<IsoMapping, vertex1_t> ));
typedef typename property_traits<IsoMapping>::value_type IsoMappingValue;
BOOST_STATIC_ASSERT((is_convertible<IsoMappingValue, vertex2_t>::value));
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap1, vertex1_t> ));
typedef typename property_traits<IndexMap1>::value_type IndexMap1Value;
BOOST_STATIC_ASSERT((is_convertible<IndexMap1Value, size_type>::value));
BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<IndexMap2, vertex2_t> ));
typedef typename property_traits<IndexMap2>::value_type IndexMap2Value;
BOOST_STATIC_ASSERT((is_convertible<IndexMap2Value, size_type>::value));
if (count_vertices(G1) != count_vertices(G2))
return false;
if (count_vertices(G1) == 0 && count_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
);
}
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;
typedef result_type 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