344 lines
13 KiB
C++
344 lines
13 KiB
C++
|
//
|
||
|
|
//=======================================================================
|
||
|
|
// 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
|