boost/graph/strong_components.hpp
//
//=======================================================================
// Copyright 1997, 1998, 1999, 2000 University of Notre Dame.
// Authors: Andrew Lumsdaine, Lie-Quan Lee, Jeremy G. Siek
//
// 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_STRONG_COMPONENTS_HPP
#define BOOST_GRAPH_STRONG_COMPONENTS_HPP
#include <stack>
#include <boost/config.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/type_traits/conversion_traits.hpp>
#include <boost/static_assert.hpp>
#include <boost/graph/overloading.hpp>
#include <boost/concept/assert.hpp>
namespace boost {
//==========================================================================
// This is Tarjan's algorithm for strongly connected components
// from his paper "Depth first search and linear graph algorithms".
// It calculates the components in a single application of DFS.
// We implement the algorithm as a dfs-visitor.
namespace detail {
template <typename ComponentMap, typename RootMap, typename DiscoverTime,
typename Stack>
class tarjan_scc_visitor : public dfs_visitor<>
{
typedef typename property_traits<ComponentMap>::value_type comp_type;
typedef typename property_traits<DiscoverTime>::value_type time_type;
public:
tarjan_scc_visitor(ComponentMap comp_map, RootMap r, DiscoverTime d,
comp_type& c_, Stack& s_)
: c(c_), comp(comp_map), root(r), discover_time(d),
dfs_time(time_type()), s(s_) { }
template <typename Graph>
void discover_vertex(typename graph_traits<Graph>::vertex_descriptor v,
const Graph&) {
put(root, v, v);
put(comp, v, (std::numeric_limits<comp_type>::max)());
put(discover_time, v, dfs_time++);
s.push(v);
}
template <typename Graph>
void finish_vertex(typename graph_traits<Graph>::vertex_descriptor v,
const Graph& g) {
typename graph_traits<Graph>::vertex_descriptor w;
typename graph_traits<Graph>::out_edge_iterator ei, ei_end;
for (boost::tie(ei, ei_end) = out_edges(v, g); ei != ei_end; ++ei) {
w = target(*ei, g);
if (get(comp, w) == (std::numeric_limits<comp_type>::max)())
put(root, v, this->min_discover_time(get(root,v), get(root,w)));
}
if (get(root, v) == v) {
do {
w = s.top(); s.pop();
put(comp, w, c);
put(root, w, v);
} while (w != v);
++c;
}
}
private:
template <typename Vertex>
Vertex min_discover_time(Vertex u, Vertex v) {
return get(discover_time, u) < get(discover_time,v) ? u : v;
}
comp_type& c;
ComponentMap comp;
RootMap root;
DiscoverTime discover_time;
time_type dfs_time;
Stack& s;
};
template <class Graph, class ComponentMap, class RootMap,
class DiscoverTime, class P, class T, class R>
typename property_traits<ComponentMap>::value_type
strong_components_impl
(const Graph& g, // Input
ComponentMap comp, // Output
// Internal record keeping
RootMap root,
DiscoverTime discover_time,
const bgl_named_params<P, T, R>& params)
{
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<ComponentMap, Vertex> ));
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<RootMap, Vertex> ));
typedef typename property_traits<RootMap>::value_type RootV;
BOOST_CONCEPT_ASSERT(( ConvertibleConcept<RootV, Vertex> ));
BOOST_CONCEPT_ASSERT(( ReadWritePropertyMapConcept<DiscoverTime, Vertex> ));
typename property_traits<ComponentMap>::value_type total = 0;
std::stack<Vertex> s;
detail::tarjan_scc_visitor<ComponentMap, RootMap, DiscoverTime,
std::stack<Vertex> >
vis(comp, root, discover_time, total, s);
depth_first_search(g, params.visitor(vis));
return total;
}
//-------------------------------------------------------------------------
// The dispatch functions handle the defaults for the rank and discover
// time property maps.
// dispatch with class specialization to avoid VC++ bug
template <class DiscoverTimeMap>
struct strong_comp_dispatch2 {
template <class Graph, class ComponentMap, class RootMap, class P, class T, class R>
inline static typename property_traits<ComponentMap>::value_type
apply(const Graph& g,
ComponentMap comp,
RootMap r_map,
const bgl_named_params<P, T, R>& params,
DiscoverTimeMap time_map)
{
return strong_components_impl(g, comp, r_map, time_map, params);
}
};
template <>
struct strong_comp_dispatch2<param_not_found> {
template <class Graph, class ComponentMap, class RootMap,
class P, class T, class R>
inline static typename property_traits<ComponentMap>::value_type
apply(const Graph& g,
ComponentMap comp,
RootMap r_map,
const bgl_named_params<P, T, R>& params,
param_not_found)
{
typedef typename graph_traits<Graph>::vertices_size_type size_type;
size_type n = num_vertices(g) > 0 ? num_vertices(g) : 1;
std::vector<size_type> time_vec(n);
return strong_components_impl
(g, comp, r_map,
make_iterator_property_map(time_vec.begin(), choose_const_pmap
(get_param(params, vertex_index),
g, vertex_index), time_vec[0]),
params);
}
};
template <class Graph, class ComponentMap, class RootMap,
class P, class T, class R, class DiscoverTimeMap>
inline typename property_traits<ComponentMap>::value_type
scc_helper2(const Graph& g,
ComponentMap comp,
RootMap r_map,
const bgl_named_params<P, T, R>& params,
DiscoverTimeMap time_map)
{
return strong_comp_dispatch2<DiscoverTimeMap>::apply(g, comp, r_map, params, time_map);
}
template <class RootMap>
struct strong_comp_dispatch1 {
template <class Graph, class ComponentMap, class P, class T, class R>
inline static typename property_traits<ComponentMap>::value_type
apply(const Graph& g,
ComponentMap comp,
const bgl_named_params<P, T, R>& params,
RootMap r_map)
{
return scc_helper2(g, comp, r_map, params, get_param(params, vertex_discover_time));
}
};
template <>
struct strong_comp_dispatch1<param_not_found> {
template <class Graph, class ComponentMap,
class P, class T, class R>
inline static typename property_traits<ComponentMap>::value_type
apply(const Graph& g,
ComponentMap comp,
const bgl_named_params<P, T, R>& params,
param_not_found)
{
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
typename std::vector<Vertex>::size_type
n = num_vertices(g) > 0 ? num_vertices(g) : 1;
std::vector<Vertex> root_vec(n);
return scc_helper2
(g, comp,
make_iterator_property_map(root_vec.begin(), choose_const_pmap
(get_param(params, vertex_index),
g, vertex_index), root_vec[0]),
params,
get_param(params, vertex_discover_time));
}
};
template <class Graph, class ComponentMap, class RootMap,
class P, class T, class R>
inline typename property_traits<ComponentMap>::value_type
scc_helper1(const Graph& g,
ComponentMap comp,
const bgl_named_params<P, T, R>& params,
RootMap r_map)
{
return detail::strong_comp_dispatch1<RootMap>::apply(g, comp, params,
r_map);
}
} // namespace detail
template <class Graph, class ComponentMap,
class P, class T, class R>
inline typename property_traits<ComponentMap>::value_type
strong_components(const Graph& g, ComponentMap comp,
const bgl_named_params<P, T, R>& params
BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
{
typedef typename graph_traits<Graph>::directed_category DirCat;
BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
return detail::scc_helper1(g, comp, params,
get_param(params, vertex_root_t()));
}
template <class Graph, class ComponentMap>
inline typename property_traits<ComponentMap>::value_type
strong_components(const Graph& g, ComponentMap comp
BOOST_GRAPH_ENABLE_IF_MODELS_PARM(Graph, vertex_list_graph_tag))
{
typedef typename graph_traits<Graph>::directed_category DirCat;
BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
bgl_named_params<int, int> params(0);
return strong_components(g, comp, params);
}
template <typename Graph, typename ComponentMap, typename ComponentLists>
void build_component_lists
(const Graph& g,
typename graph_traits<Graph>::vertices_size_type num_scc,
ComponentMap component_number,
ComponentLists& components)
{
components.resize(num_scc);
typename graph_traits<Graph>::vertex_iterator vi, vi_end;
for (boost::tie(vi, vi_end) = vertices(g); vi != vi_end; ++vi)
components[component_number[*vi]].push_back(*vi);
}
} // namespace boost
#include <queue>
#include <vector>
#include <boost/graph/transpose_graph.hpp>
#include <boost/pending/indirect_cmp.hpp>
#include <boost/graph/connected_components.hpp> // for components_recorder
namespace boost {
//==========================================================================
// This is the version of strongly connected components from
// "Intro. to Algorithms" by Cormen, Leiserson, Rivest, which was
// adapted from "Data Structure and Algorithms" by Aho, Hopcroft,
// and Ullman, who credit the algorithm to S.R. Kosaraju and M. Sharir.
// The algorithm is based on computing DFS forests the graph
// and its transpose.
// This algorithm is slower than Tarjan's by a constant factor, uses
// more memory, and puts more requirements on the graph type.
template <class Graph, class DFSVisitor, class ComponentsMap,
class DiscoverTime, class FinishTime,
class ColorMap>
typename property_traits<ComponentsMap>::value_type
kosaraju_strong_components(Graph& G, ComponentsMap c,
FinishTime finish_time, ColorMap color)
{
BOOST_CONCEPT_ASSERT(( MutableGraphConcept<Graph> ));
// ...
typedef typename graph_traits<Graph>::vertex_descriptor Vertex;
typedef typename property_traits<ColorMap>::value_type ColorValue;
typedef color_traits<ColorValue> Color;
typename property_traits<FinishTime>::value_type time = 0;
depth_first_search
(G, make_dfs_visitor(stamp_times(finish_time, time, on_finish_vertex())),
color);
Graph G_T(num_vertices(G));
transpose_graph(G, G_T);
typedef typename property_traits<ComponentsMap>::value_type count_type;
count_type c_count(0);
detail::components_recorder<ComponentsMap>
vis(c, c_count);
// initialize G_T
typename graph_traits<Graph>::vertex_iterator ui, ui_end;
for (boost::tie(ui, ui_end) = vertices(G_T); ui != ui_end; ++ui)
put(color, *ui, Color::white());
typedef typename property_traits<FinishTime>::value_type D;
typedef indirect_cmp< FinishTime, std::less<D> > Compare;
Compare fl(finish_time);
std::priority_queue<Vertex, std::vector<Vertex>, Compare > Q(fl);
typename graph_traits<Graph>::vertex_iterator i, j, iend, jend;
boost::tie(i, iend) = vertices(G_T);
boost::tie(j, jend) = vertices(G);
for ( ; i != iend; ++i, ++j) {
put(finish_time, *i, get(finish_time, *j));
Q.push(*i);
}
while ( !Q.empty() ) {
Vertex u = Q.top();
Q.pop();
if (get(color, u) == Color::white()) {
depth_first_visit(G_T, u, vis, color);
++c_count;
}
}
return c_count;
}
} // namespace boost
#ifdef BOOST_GRAPH_USE_MPI
# include <boost/graph/distributed/strong_components.hpp>
#endif
#endif // BOOST_GRAPH_STRONG_COMPONENTS_HPP