stoer_wagner_min_cut.hpp 11.3 KB
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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/typeof/typeof.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 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)
    
    BOOST_AUTO(pq, (boost::detail::make_priority_queue_from_arg_pack_gen<boost::graph::keywords::tag::max_priority_queue, weight_type, vertex_descriptor, std::greater<weight_type> >(choose_param(get_param(params, boost::distance_zero_t()), weight_type(0)))(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