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// Copyright Daniel Trebbien 2010.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or the copy at
// http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP
#define BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP 1
#include <boost/assert.hpp>
#include <set>
#include <vector>
#include <boost/concept_check.hpp>
#include <boost/concept/assert.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/buffer_concepts.hpp>
#include <boost/graph/exception.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/iteration_macros.hpp>
#include <boost/graph/named_function_params.hpp>
#include <boost/graph/detail/d_ary_heap.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/tuple/tuple.hpp>
#include <boost/utility/result_of.hpp>
namespace boost {
namespace detail {
/**
* \brief Performs a phase of the Stoer-Wagner min-cut algorithm
*
* Performs a phase of the Stoer-Wagner min-cut algorithm.
*
* As described by Stoer & Wagner (1997), a phase is simply a maximum adjacency search
* (also called a maximum cardinality search), which results in the selection of two vertices
* \em s and \em t, and, as a side product, a minimum <em>s</em>-<em>t</em> cut of
* the input graph. Here, the input graph is basically \p g, but some vertices are virtually
* assigned to others as a way of viewing \p g as a graph with some sets of
* vertices merged together.
*
* This implementation is a translation of pseudocode by Professor Uri Zwick,
* School of Computer Science, Tel Aviv University.
*
* \pre \p g is a connected, undirected graph
* \param[in] g the input graph
* \param[in] assignments a read/write property map from each vertex to the vertex that it is assigned to
* \param[in] assignedVertices a list of vertices that are assigned to others
* \param[in] weights a readable property map from each edge to its weight (a non-negative value)
* \param[out] pq a keyed, updatable max-priority queue
* \returns a tuple (\em s, \em t, \em w) of the "<em>s</em>" and "<em>t</em>"
* of the minimum <em>s</em>-<em>t</em> cut and the cut weight \em w
* of the minimum <em>s</em>-<em>t</em> cut.
* \see http://www.cs.tau.ac.il/~zwick/grad-algo-08/gmc.pdf
*
* \author Daniel Trebbien
* \date 2010-09-11
*/
template <class UndirectedGraph, class VertexAssignmentMap, class WeightMap, class KeyedUpdatablePriorityQueue>
boost::tuple<typename boost::graph_traits<UndirectedGraph>::vertex_descriptor, typename boost::graph_traits<UndirectedGraph>::vertex_descriptor, typename boost::property_traits<WeightMap>::value_type>
stoer_wagner_phase(const UndirectedGraph& g, VertexAssignmentMap assignments, const std::set<typename boost::graph_traits<UndirectedGraph>::vertex_descriptor>& assignedVertices, WeightMap weights, KeyedUpdatablePriorityQueue& pq) {
typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor;
typedef typename boost::property_traits<WeightMap>::value_type weight_type;
BOOST_ASSERT(pq.empty());
typename KeyedUpdatablePriorityQueue::key_map keys = pq.keys();
BGL_FORALL_VERTICES_T(v, g, UndirectedGraph) {
if (v == get(assignments, v)) { // foreach u \in V do
put(keys, v, weight_type(0));
pq.push(v);
}
}
BOOST_ASSERT(pq.size() >= 2);
vertex_descriptor s = boost::graph_traits<UndirectedGraph>::null_vertex();
vertex_descriptor t = boost::graph_traits<UndirectedGraph>::null_vertex();
weight_type w;
while (!pq.empty()) { // while PQ \neq {} do
const vertex_descriptor u = pq.top(); // u = extractmax(PQ)
w = get(keys, u);
pq.pop();
s = t; t = u;
BGL_FORALL_OUTEDGES_T(u, e, g, UndirectedGraph) { // foreach (u, v) \in E do
const vertex_descriptor v = get(assignments, target(e, g));
if (pq.contains(v)) { // if v \in PQ then
put(keys, v, get(keys, v) + get(weights, e)); // increasekey(PQ, v, wA(v) + w(u, v))
pq.update(v);
}
}
typename std::set<vertex_descriptor>::const_iterator assignedVertexIt, assignedVertexEnd = assignedVertices.end();
for (assignedVertexIt = assignedVertices.begin(); assignedVertexIt != assignedVertexEnd; ++assignedVertexIt) {
const vertex_descriptor uPrime = *assignedVertexIt;
if (get(assignments, uPrime) == u) {
BGL_FORALL_OUTEDGES_T(uPrime, e, g, UndirectedGraph) { // foreach (u, v) \in E do
const vertex_descriptor v = get(assignments, target(e, g));
if (pq.contains(v)) { // if v \in PQ then
put(keys, v, get(keys, v) + get(weights, e)); // increasekey(PQ, v, wA(v) + w(u, v))
pq.update(v);
}
}
}
}
}
return boost::make_tuple(s, t, w);
}
/**
* \brief Computes a min-cut of the input graph
*
* Computes a min-cut of the input graph using the Stoer-Wagner algorithm.
*
* \pre \p g is a connected, undirected graph
* \pre <code>pq.empty()</code>
* \param[in] g the input graph
* \param[in] weights a readable property map from each edge to its weight (a non-negative value)
* \param[out] parities a writable property map from each vertex to a bool type object for
* distinguishing the two vertex sets of the min-cut
* \param[out] assignments a read/write property map from each vertex to a \c vertex_descriptor object. This
* map serves as work space, and no particular meaning should be derived from property values
* after completion of the algorithm.
* \param[out] pq a keyed, updatable max-priority queue
* \returns the cut weight of the min-cut
* \see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.114.6687&rep=rep1&type=pdf
* \see http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.31.614&rep=rep1&type=pdf
*
* \author Daniel Trebbien
* \date 2010-09-11
*/
template <class UndirectedGraph, class WeightMap, class ParityMap, class VertexAssignmentMap, class KeyedUpdatablePriorityQueue>
typename boost::property_traits<WeightMap>::value_type
stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights, ParityMap parities, VertexAssignmentMap assignments, KeyedUpdatablePriorityQueue& pq) {
BOOST_CONCEPT_ASSERT((boost::IncidenceGraphConcept<UndirectedGraph>));
BOOST_CONCEPT_ASSERT((boost::VertexListGraphConcept<UndirectedGraph>));
typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor;
typedef typename boost::graph_traits<UndirectedGraph>::vertices_size_type vertices_size_type;
typedef typename boost::graph_traits<UndirectedGraph>::edge_descriptor edge_descriptor;
BOOST_CONCEPT_ASSERT((boost::Convertible<typename boost::graph_traits<UndirectedGraph>::directed_category, boost::undirected_tag>));
BOOST_CONCEPT_ASSERT((boost::ReadablePropertyMapConcept<WeightMap, edge_descriptor>));
typedef typename boost::property_traits<WeightMap>::value_type weight_type;
BOOST_CONCEPT_ASSERT((boost::WritablePropertyMapConcept<ParityMap, vertex_descriptor>));
typedef typename boost::property_traits<ParityMap>::value_type parity_type;
BOOST_CONCEPT_ASSERT((boost::ReadWritePropertyMapConcept<VertexAssignmentMap, vertex_descriptor>));
BOOST_CONCEPT_ASSERT((boost::Convertible<vertex_descriptor, typename boost::property_traits<VertexAssignmentMap>::value_type>));
BOOST_CONCEPT_ASSERT((boost::KeyedUpdatableQueueConcept<KeyedUpdatablePriorityQueue>));
vertices_size_type n = num_vertices(g);
if (n < 2)
throw boost::bad_graph("the input graph must have at least two vertices.");
else if (!pq.empty())
throw std::invalid_argument("the max-priority queue must be empty initially.");
std::set<vertex_descriptor> assignedVertices;
// initialize `assignments` (all vertices are initially assigned to themselves)
BGL_FORALL_VERTICES_T(v, g, UndirectedGraph) {
put(assignments, v, v);
}
vertex_descriptor s, t;
weight_type bestW;
boost::tie(s, t, bestW) = boost::detail::stoer_wagner_phase(g, assignments, assignedVertices, weights, pq);
BOOST_ASSERT(s != t);
BGL_FORALL_VERTICES_T(v, g, UndirectedGraph) {
put(parities, v, parity_type(v == t ? 1 : 0));
}
put(assignments, t, s);
assignedVertices.insert(t);
--n;
for (; n >= 2; --n) {
weight_type w;
boost::tie(s, t, w) = boost::detail::stoer_wagner_phase(g, assignments, assignedVertices, weights, pq);
BOOST_ASSERT(s != t);
if (w < bestW) {
BGL_FORALL_VERTICES_T(v, g, UndirectedGraph) {
put(parities, v, parity_type(get(assignments, v) == t ? 1 : 0));
if (get(assignments, v) == t) // all vertices that were assigned to t are now assigned to s
put(assignments, v, s);
}
bestW = w;
} else {
BGL_FORALL_VERTICES_T(v, g, UndirectedGraph) {
if (get(assignments, v) == t) // all vertices that were assigned to t are now assigned to s
put(assignments, v, s);
}
}
put(assignments, t, s);
assignedVertices.insert(t);
}
BOOST_ASSERT(pq.empty());
return bestW;
}
} // end `namespace detail` within `namespace boost`
template <class UndirectedGraph, class WeightMap, class P, class T, class R>
inline typename boost::property_traits<WeightMap>::value_type
stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights, const boost::bgl_named_params<P, T, R>& params) {
typedef typename boost::graph_traits<UndirectedGraph>::vertex_descriptor vertex_descriptor;
typedef typename std::vector<vertex_descriptor>::size_type heap_container_size_type;
typedef typename boost::property_traits<WeightMap>::value_type weight_type;
typedef boost::bgl_named_params<P, T, R> params_type;
BOOST_GRAPH_DECLARE_CONVERTED_PARAMETERS(params_type, params)
typedef boost::detail::make_priority_queue_from_arg_pack_gen<boost::graph::keywords::tag::max_priority_queue, weight_type, vertex_descriptor, std::greater<weight_type> > gen_type;
gen_type gen(choose_param(get_param(params, boost::distance_zero_t()), weight_type(0)));
typename boost::result_of<gen_type(const UndirectedGraph&, const arg_pack_type&)>::type pq = gen(g, arg_pack);
return boost::detail::stoer_wagner_min_cut(g,
weights,
choose_param(get_param(params, boost::parity_map_t()), boost::dummy_property_map()),
boost::detail::make_property_map_from_arg_pack_gen<boost::graph::keywords::tag::vertex_assignment_map, vertex_descriptor>(vertex_descriptor())(g, arg_pack),
pq
);
}
template <class UndirectedGraph, class WeightMap>
inline typename boost::property_traits<WeightMap>::value_type
stoer_wagner_min_cut(const UndirectedGraph& g, WeightMap weights) {
return boost::stoer_wagner_min_cut(g, weights, boost::vertex_index_map(get(boost::vertex_index, g)));
}
} // end `namespace boost`
#include <boost/graph/iteration_macros_undef.hpp>
#endif // !BOOST_GRAPH_STOER_WAGNER_MIN_CUT_HPP
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