Commit b1582025 authored by Tiago Peixoto's avatar Tiago Peixoto
Browse files

Include isomorphism() function in misc module

parent d836b5d0
// 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 (container_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) + 1) * num_edges(m_g) + num_edges(m_g) + 1;
}
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_convertible<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
......@@ -16,7 +16,8 @@ libgraph_tool_misc_la_LDFLAGS = $(MOD_LDFLAGS)
libgraph_tool_misc_la_SOURCES = \
graph_rewiring.cc \
graph_misc.cc
graph_misc.cc \
graph_isomorphism.cc
libgraph_tool_misc_la_include_HEADERS = \
graph_rewiring.hh
// graph-tool -- a general graph modification and manipulation thingy
//
// Copyright (C) 2007 Tiago de Paula Peixoto <tiago@forked.de>
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation; either version 3
// of the License, or (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
#include <boost/lambda/bind.hpp>
#include "graph.hh"
#include "graph_filtering.hh"
#include <boost/graph/isomorphism.hpp>
using namespace graph_tool;
using namespace boost;
using namespace boost::lambda;
struct check_iso
{
template <class Graph1, class Graph2, class IsoMap, class VertexIndexMap>
void operator()(Graph1* g1, Graph2* g2, IsoMap map, VertexIndexMap index1,
VertexIndexMap index2, bool& result) const
{
result = isomorphism(*g1, *g2,isomorphism_map(map).
vertex_index1_map(index1).
vertex_index2_map(index2));
}
};
struct directed_graph_view_pointers:
mpl::transform<graph_tool::detail::always_directed,
mpl::quote1<add_pointer> >::type {};
struct undirected_graph_view_pointers:
mpl::transform<graph_tool::detail::never_directed,
mpl::quote1<add_pointer> >::type {};
typedef property_map_types::apply<integer_types,
GraphInterface::vertex_index_map_t,
mpl::bool_<false> >::type
vertex_props_t;
bool check_isomorphism(GraphInterface& gi1, GraphInterface& gi2,
boost::any iso_map)
{
bool result;
if (gi1.GetDirected() != gi2.GetDirected())
return false;
if (gi1.GetDirected())
{
run_action<graph_tool::detail::always_directed>()
(gi1, bind<void>(check_iso(),
_1, _2, _3, gi1.GetVertexIndex(),
gi2.GetVertexIndex(), var(result)),
directed_graph_view_pointers(), vertex_props_t())
(gi2.GetGraphView(), iso_map);
}
else
{
run_action<graph_tool::detail::never_directed>()
(gi1, bind<void>(check_iso(),
_1, _2, _3, gi1.GetVertexIndex(),
gi2.GetVertexIndex(), var(result)),
undirected_graph_view_pointers(), vertex_props_t())
(gi2.GetGraphView(), iso_map);
}
return result;
}
......@@ -24,8 +24,11 @@ using namespace graph_tool;
void random_rewire(GraphInterface& gi, string strat, bool self_loops,
bool parallel_edges, size_t seed);
bool check_isomorphism(GraphInterface& gi1, GraphInterface& gi2,
boost::any iso_map);
BOOST_PYTHON_MODULE(libgraph_tool_misc)
{
def("random_rewire", &random_rewire);
def("check_isomorphism", &check_isomorphism);
}
......@@ -19,8 +19,9 @@
from .. dl_import import dl_import
dl_import("import libgraph_tool_misc")
from .. core import _prop
import random, sys
__all__ = ["random_rewire"]
__all__ = ["random_rewire", "isomorphism"]
def random_rewire(g, strat="uncorrelated", self_loops = False,
parallel_edges = False, seed = 0):
......@@ -35,3 +36,10 @@ def random_rewire(g, strat="uncorrelated", self_loops = False,
parallel_edges, seed)
if was_reversed:
g.set_reversed(True)
def isomorphism(g1, g2, isomap=None):
if isomap == None:
isomap = g1.new_vertex_property("int32_t")
return libgraph_tool_misc.\