710 lines
26 KiB
C++
710 lines
26 KiB
C++
|
// 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
|