howard_cycle_ratio.hpp

// Copyright (C) 2006-2009 Dmitry Bufistov and Andrey Parfenov

// Use, modification and distribution is subject to 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_CYCLE_RATIO_HOWARD_HPP
#define BOOST_GRAPH_CYCLE_RATIO_HOWARD_HPP

#include <vector>
#include <list>
#include <algorithm>
#include <limits>

#include <boost/bind.hpp>
#include <boost/type_traits/is_same.hpp>
#include <boost/type_traits/remove_const.hpp>
#include <boost/concept_check.hpp>
#include <boost/pending/queue.hpp>
#include <boost/property_map/property_map.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/graph_concepts.hpp>

/** @file howard_cycle_ratio.hpp
 * @brief The implementation of the maximum/minimum cycle ratio/mean algorithm.
 * @author Dmitry Bufistov
 * @author Andrey Parfenov
 */

namespace boost {

  /**
   * The mcr_float is like numeric_limits, but only for floating point types
   * and only defines infinity() and epsilon(). This class is primarily used
   * to encapsulate a less-precise epsilon than natively supported by the
   * floating point type.
   */
  template <typename Float = double> struct mcr_float {
    typedef Float value_type;

    static Float infinity()
    { return std::numeric_limits<value_type>::infinity(); }

    static Float epsilon()
    { return Float(-0.005); }
  };

  namespace detail {

    template <typename FloatTraits> struct
    min_comparator_props {
      typedef std::greater<typename FloatTraits::value_type> comparator;
      static const int multiplier = 1;
    };

    template <typename FloatTraits> struct
    max_comparator_props {
      typedef std::less<typename FloatTraits::value_type> comparator;
      static const int multiplier = -1;
    };

    template <typename FloatTraits, typename ComparatorProps>
    struct float_wrapper {
      typedef typename FloatTraits::value_type value_type;
      typedef ComparatorProps comparator_props_t;
      typedef typename ComparatorProps::comparator comparator;

      static value_type infinity()
      { return FloatTraits::infinity() * ComparatorProps::multiplier; }

      static value_type epsilon()
      { return FloatTraits::epsilon() * ComparatorProps::multiplier; }

    };

    /*! @class mcr_howard
     * @brief Calculates optimum (maximum/minimum) cycle ratio of a directed graph.
     * Uses  Howard's iteration policy algorithm. </br>(It is described in the paper
     * "Experimental Analysis of the Fastest Optimum Cycle Ratio and Mean Algorithm"
     * by Ali Dasdan).
     */
    template <typename FloatTraits,
              typename Graph, typename VertexIndexMap,
              typename EdgeWeight1, typename EdgeWeight2>
    class mcr_howard
    {
    public:
      typedef typename FloatTraits::value_type float_t;
      typedef typename FloatTraits::comparator_props_t cmp_props_t;
      typedef typename FloatTraits::comparator comparator_t;
      typedef enum{ my_white = 0, my_black } my_color_type;
      typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
      typedef typename graph_traits<Graph>::edge_descriptor edge_t;
      typedef typename graph_traits<Graph>::vertices_size_type vn_t;
      typedef std::vector<float_t> vp_t;
      typedef typename boost::iterator_property_map<
        typename vp_t::iterator, VertexIndexMap
      > distance_map_t; //V -> float_t

      typedef typename std::vector<edge_t> ve_t;
      typedef std::vector<my_color_type> vcol_t;
      typedef typename ::boost::iterator_property_map<
        typename ve_t::iterator, VertexIndexMap
      > policy_t; //Vertex -> Edge
      typedef typename ::boost::iterator_property_map<
        typename vcol_t::iterator, VertexIndexMap
      > color_map_t;

      typedef typename std::list<vertex_t> pinel_t;// The in_edges list of the policy graph
      typedef typename std::vector<pinel_t> inedges1_t;
      typedef typename ::boost::iterator_property_map<
        typename inedges1_t::iterator, VertexIndexMap
      > inedges_t;
      typedef typename std::vector<edge_t> critical_cycle_t;

      //Bad  vertex flag. If true, then the vertex is "bad".
      // Vertex is "bad" if its out_degree is equal to zero.
      typedef typename boost::iterator_property_map<
        std::vector<int>::iterator, VertexIndexMap
      > badv_t;

      /*!
       * Constructor
       * \param g = (V, E) - a directed multigraph.
       * \param vim  Vertex Index Map. Read property Map: V -> [0, num_vertices(g)).
       * \param ewm  edge weight map. Read property map: E -> R
       * \param ew2m  edge weight map. Read property map: E -> R+
       * \param infty A big enough value to guaranty that there exist a cycle with
       *  better ratio.
       * \param cmp The compare operator for float_ts.
       */
      mcr_howard(const Graph &g, VertexIndexMap vim,
                  EdgeWeight1 ewm, EdgeWeight2 ew2m) :
        m_g(g), m_vim(vim), m_ew1m(ewm), m_ew2m(ew2m),
        m_bound(mcr_bound()),
        m_cr(m_bound),
        m_V(num_vertices(m_g)),
        m_dis(m_V, 0), m_dm(m_dis.begin(), m_vim),
        m_policyc(m_V), m_policy(m_policyc.begin(), m_vim),
        m_inelc(m_V), m_inel(m_inelc.begin(), m_vim),
        m_badvc(m_V, false), m_badv(m_badvc.begin(), m_vim),
        m_colcv(m_V),
        m_col_bfs(m_V)
      { }

      /*!
       * \return maximum/minimum_{for all cycles C}
       *         [sum_{e in C} w1(e)] / [sum_{e in C} w2(e)],
       * or FloatTraits::infinity() if graph has no cycles.
       */
      float_t ocr_howard()
      {
        construct_policy_graph();
        int k = 0;
        float_t mcr = 0;
        do
          {
            mcr = policy_mcr();
            ++k;
          }
        while (try_improve_policy(mcr) && k < 100); //To avoid infinite loop

        const float_t eps_ =  -0.00000001 * cmp_props_t::multiplier;
        if (m_cmp(mcr, m_bound + eps_))
          {
            return FloatTraits::infinity();
          }
        else
          {
            return  mcr;
          }
      }
      virtual ~mcr_howard() {}

    protected:
      virtual void store_critical_edge(edge_t, critical_cycle_t &) {}
      virtual void store_critical_cycle(critical_cycle_t &) {}

    private:
      /*!
       * \return lower/upper bound for the maximal/minimal cycle ratio
       */
      float_t mcr_bound()
      {
        typename  graph_traits<Graph>::vertex_iterator  vi, vie;
        typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
        float_t cz = (std::numeric_limits<float_t>::max)(); //Closest to zero value
        float_t s = 0;
        const float_t eps_ = std::numeric_limits<float_t>::epsilon();
        for (tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
          {
            for (tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
              {
                s += std::abs(m_ew1m[*oei]);
                float_t a = std::abs(m_ew2m[*oei]);
                if ( a > eps_ && a < cz)
                {
                  cz = a;
                }
              }
          }
        return  cmp_props_t::multiplier * (s / cz);
      }


      /*!
       *  Constructs an arbitrary policy graph.
       */
      void construct_policy_graph()
      {
        m_sink = graph_traits<Graph>().null_vertex();
        typename  graph_traits<Graph>::vertex_iterator  vi, vie;
        typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
        for ( tie(vi, vie) = vertices(m_g); vi != vie; ++vi )
          {
            tie(oei, oeie) = out_edges(*vi, m_g);
            typename graph_traits<Graph>::out_edge_iterator mei =
              std::max_element(oei, oeie,
                               boost::bind(m_cmp,
                                           boost::bind(&EdgeWeight1::operator[], m_ew1m, _1),
                                           boost::bind(&EdgeWeight1::operator[], m_ew1m, _2)
                                          )
                               );
            if (mei == oeie)
              {
                if (m_sink == graph_traits<Graph>().null_vertex())
                  {
                    m_sink = *vi;
                  }
                m_badv[*vi] = true;
                m_inel[m_sink].push_back(*vi);
              }
            else
              {
                m_inel[target(*mei, m_g)].push_back(*vi);
                m_policy[*vi] = *mei;
              }
          }
      }
      /*! Sets the distance value for all vertices "v" such that there is
       * a path from "v" to "sv". It does "inverse" breadth first visit of the policy
       * graph, starting from the vertex "sv".
       */
      void mcr_bfv(vertex_t sv, float_t cr, color_map_t c)
      {
        boost::queue<vertex_t> Q;
        c[sv] = my_black;
        Q.push(sv);
        while (!Q.empty())
          {
            vertex_t v = Q.top(); Q.pop();
            for (typename pinel_t::const_iterator itr = m_inel[v].begin();
                 itr != m_inel[v].end(); ++itr)
              //For all in_edges of the policy graph
              {
                if (*itr != sv)
                  {
                    if (m_badv[*itr])
                      {
                        m_dm[*itr] = m_dm[v] + m_bound - cr;
                      }
                    else
                      {
                        m_dm[*itr] = m_dm[v] + m_ew1m[m_policy[*itr]] -
                          m_ew2m[m_policy[*itr]] * cr;
                      }
                    c[*itr] = my_black;
                    Q.push(*itr);
                  }
              }
          }
      }

      /*!
       * \param sv an arbitrary (undiscovered) vertex of the policy graph.
       * \return a vertex in the policy graph that belongs to a cycle.
       * Performs a depth first visit until a cycle edge is found.
       */
      vertex_t find_cycle_vertex(vertex_t sv)
      {
        vertex_t gv = sv;
        std::fill(m_colcv.begin(), m_colcv.end(), my_white);
        color_map_t cm(m_colcv.begin(), m_vim);
        do
          {
            cm[gv] = my_black;
            if (! m_badv[gv])
              {
                gv = target(m_policy[gv], m_g);
              }
            else
              {
                gv = m_sink;
              }
          }
        while (cm[gv] != my_black);
        return gv;
      }

      /*!
       * \param sv - vertex that belongs to a cycle in the policy graph.
       */
      float_t cycle_ratio(vertex_t sv)
      {
        if (sv == m_sink) return m_bound;
        std::pair<float_t, float_t> sums_(float_t(0), float_t(0));
        vertex_t v = sv;
        critical_cycle_t cc;
        do
          {
            store_critical_edge(m_policy[v], cc);
            sums_.first += m_ew1m[m_policy[v]];
            sums_.second += m_ew2m[m_policy[v]];
            v = target(m_policy[v], m_g);
          }
        while (v != sv);
        float_t cr = sums_.first / sums_.second;
        if ( m_cmp(m_cr, cr) )
          {
            m_cr = cr;
            store_critical_cycle(cc);
          }
        return cr;
      }

      /*!
       *  Finds the optimal cycle ratio of the policy graph
       */
      float_t policy_mcr()
      {
        std::fill(m_col_bfs.begin(), m_col_bfs.end(), my_white);
        color_map_t vcm_ = color_map_t(m_col_bfs.begin(), m_vim);
        typename graph_traits<Graph>::vertex_iterator uv_itr, vie;
        tie(uv_itr, vie) = vertices(m_g);
        float_t mcr = m_bound;
        while ( (uv_itr = std::find_if(uv_itr, vie,
                                       boost::bind(std::equal_to<my_color_type>(),
                                                   my_white,
                                                   boost::bind(&color_map_t::operator[], vcm_, _1)
                                                   )
                                       )
                 ) != vie )
          ///While there are undiscovered vertices
          {
            vertex_t gv = find_cycle_vertex(*uv_itr);
            float_t cr = cycle_ratio(gv) ;
            mcr_bfv(gv, cr, vcm_);
            if ( m_cmp(mcr, cr) )  mcr = cr;
            ++uv_itr;
          }
        return mcr;
      }

      /*!
       * Changes the edge m_policy[s] to the new_edge.
       */
      void improve_policy(vertex_t s, edge_t new_edge)
      {
        vertex_t t = target(m_policy[s], m_g);
        typename property_traits<VertexIndexMap>::value_type ti = m_vim[t];
        m_inelc[ti].erase( std::find(m_inelc[ti].begin(), m_inelc[ti].end(), s));
        m_policy[s] = new_edge;
        t = target(new_edge, m_g);
        m_inel[t].push_back(s); ///Maintain in_edge list
      }

      /*!
       * A negative cycle detector.
       */
      bool try_improve_policy(float_t cr)
      {
        bool improved = false;
        typename  graph_traits<Graph>::vertex_iterator  vi, vie;
        typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
        const float_t eps_ =  FloatTraits::epsilon();
        for (tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
          {
            if (!m_badv[*vi])
              {
                for (tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
                  {
                    vertex_t t = target(*oei, m_g);
                    //Current distance from *vi to some vertex
                    float_t dis_ = m_ew1m[*oei] - m_ew2m[*oei] * cr + m_dm[t];
                    if ( m_cmp(m_dm[*vi] + eps_, dis_) )
                      {
                        improve_policy(*vi, *oei);
                        m_dm[*vi] = dis_;
                        improved = true;
                      }
                  }
              }
            else
              {
                float_t dis_ = m_bound - cr + m_dm[m_sink];
                if ( m_cmp(m_dm[*vi] + eps_, dis_) )
                  {
                    m_dm[*vi] = dis_;
                  }
              }
          }
        return improved;
      }
    private:
      const Graph &m_g;
      VertexIndexMap m_vim;
      EdgeWeight1 m_ew1m;
      EdgeWeight2 m_ew2m;
      comparator_t m_cmp;
      float_t m_bound; //> The lower/upper bound to the maximal/minimal cycle ratio
      float_t m_cr; //>The best cycle ratio that has been found so far

      vn_t m_V; //>The number of the vertices in the graph
      vp_t m_dis; //>Container for the distance map
      distance_map_t m_dm; //>Distance map

      ve_t m_policyc; //>Container for the policy graph
      policy_t m_policy; //>The interface for the policy graph

      inedges1_t m_inelc; //>Container fot in edges list
      inedges_t m_inel; //>Policy graph, input edges list

      std::vector<int> m_badvc;
      badv_t m_badv; //Marks "bad" vertices

      vcol_t m_colcv, m_col_bfs; //Color maps
      vertex_t m_sink; //To convert any graph to "good"
    };

    /*! \class mcr_howard1
  * \brief Finds optimum cycle raio and a critical cycle
     */
    template <typename FloatTraits,
              typename Graph, typename VertexIndexMap,
              typename EdgeWeight1, typename EdgeWeight2>
    class mcr_howard1  : public
    mcr_howard<FloatTraits, Graph, VertexIndexMap,
               EdgeWeight1, EdgeWeight2>
    {
    public:
      typedef mcr_howard<FloatTraits, Graph, VertexIndexMap,
        EdgeWeight1, EdgeWeight2> inhr_t;
      mcr_howard1(const Graph &g, VertexIndexMap vim,
        EdgeWeight1 ewm, EdgeWeight2 ew2m) :
        inhr_t(g, vim, ewm, ew2m)
      { }

      void get_critical_cycle(typename inhr_t::critical_cycle_t &cc)
      { return cc.swap(m_cc); }

    protected:
      void store_critical_edge(typename inhr_t::edge_t ed,
        typename inhr_t::critical_cycle_t &cc)
      { cc.push_back(ed); }

      void store_critical_cycle(typename inhr_t::critical_cycle_t &cc)
      { m_cc.swap(cc); }

    private:
      typename inhr_t::critical_cycle_t m_cc; //Critical cycle
    };

    /*!
     * \param g a directed multigraph.
     * \param vim Vertex Index Map. A map V->[0, num_vertices(g))
     * \param ewm Edge weight1 map.
     * \param ew2m Edge weight2 map.
     * \param pcc  pointer to the critical edges list.
     * \return Optimum cycle ratio of g or FloatTraits::infinity() if g has no cycles.
     */
    template <typename FT,
              typename TG, typename TVIM,
              typename TEW1, typename TEW2,
              typename EV>
    typename FT::value_type
 optimum_cycle_ratio(const TG &g, TVIM vim, TEW1 ewm, TEW2 ew2m, EV* pcc)
    {
      typedef typename graph_traits<TG>::directed_category DirCat;
      BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
      function_requires< IncidenceGraphConcept<TG> >();
      function_requires< VertexListGraphConcept<TG> >();
      typedef typename graph_traits<TG>::vertex_descriptor Vertex;
      function_requires< ReadablePropertyMapConcept<TVIM, Vertex> >();
      typedef typename graph_traits<TG>::edge_descriptor Edge;
      function_requires< ReadablePropertyMapConcept<TEW1, Edge> >();
      function_requires< ReadablePropertyMapConcept<TEW2, Edge> >();

      if(pcc == 0) {
          return detail::mcr_howard<FT,TG, TVIM, TEW1, TEW2>(
            g, vim, ewm, ew2m
          ).ocr_howard();
      }

      detail::mcr_howard1<FT, TG, TVIM, TEW1, TEW2> obj(g, vim, ewm, ew2m);
      double ocr = obj.ocr_howard();
      obj.get_critical_cycle(*pcc);
      return ocr;
    }
  } // namespace detail

// Algorithms
// Maximum Cycle Ratio

template <
    typename FloatTraits,
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeight1Map,
    typename EdgeWeight2Map>
inline typename FloatTraits::value_type
maximum_cycle_ratio(const Graph &g, VertexIndexMap vim, EdgeWeight1Map ew1m,
                    EdgeWeight2Map ew2m,
                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
                    FloatTraits = FloatTraits())
{
    typedef detail::float_wrapper<
        FloatTraits, detail::max_comparator_props<FloatTraits>
    > Traits;
    return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
}

template <
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeight1Map,
    typename EdgeWeight2Map>
inline double
maximum_cycle_ratio(const Graph &g, VertexIndexMap vim,
                    EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return maximum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }

// Minimum Cycle Ratio

template <
    typename FloatTraits,
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeight1Map,
    typename EdgeWeight2Map>
typename FloatTraits::value_type
minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
                    EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
                    std::vector<typename graph_traits<Graph>::edge_descriptor> *pcc = 0,
                    FloatTraits = FloatTraits())
{
    typedef detail::float_wrapper<
        FloatTraits, detail::min_comparator_props<FloatTraits>
    > Traits;
    return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
}

template <
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeight1Map,
    typename EdgeWeight2Map>
inline double
minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
                    EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return minimum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }

// Maximum Cycle Mean

template <
    typename FloatTraits,
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeightMap,
    typename EdgeIndexMap>
inline typename FloatTraits::value_type
maximum_cycle_mean(const Graph &g, VertexIndexMap vim,
                   EdgeWeightMap ewm, EdgeIndexMap eim,
                   std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
                   FloatTraits ft = FloatTraits())
{
    typedef typename remove_const<
        typename property_traits<EdgeWeightMap>::value_type
    >::type Weight;
    typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
    return maximum_cycle_ratio(g, vim, ewm,
                               make_iterator_property_map(ed_w2.begin(), eim),
                               pcc, ft);
}

template <
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeightMap,
    typename EdgeIndexMap>
inline double
maximum_cycle_mean(const Graph& g, VertexIndexMap vim,
                   EdgeWeightMap ewm, EdgeIndexMap eim,
                   std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return maximum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }

// Minimum Cycle Mean

template <
    typename FloatTraits,
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeightMap,
    typename EdgeIndexMap>
inline typename FloatTraits::value_type
minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
                   EdgeWeightMap ewm, EdgeIndexMap eim,
                   std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
                   FloatTraits ft = FloatTraits())
{
    typedef typename remove_const<
        typename property_traits<EdgeWeightMap>::value_type
    >::type Weight;
    typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
    return minimum_cycle_ratio(g, vim, ewm,
                               make_iterator_property_map(ed_w2.begin(), eim),
                               pcc, ft);
}

template <
    typename Graph,
    typename VertexIndexMap,
    typename EdgeWeightMap,
    typename EdgeIndexMap>
inline double
minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
                   EdgeWeightMap ewm, EdgeIndexMap eim,
                   std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
{ return minimum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }

} //namespace boost

#endif