Chris@16: // Copyright (C) 2006-2009 Dmitry Bufistov and Andrey Parfenov
Chris@16: 
Chris@16: // Use, modification and distribution is subject to the Boost Software
Chris@16: // License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
Chris@16: // http://www.boost.org/LICENSE_1_0.txt)
Chris@16: 
Chris@16: #ifndef BOOST_GRAPH_CYCLE_RATIO_HOWARD_HPP
Chris@16: #define BOOST_GRAPH_CYCLE_RATIO_HOWARD_HPP
Chris@16: 
Chris@16: #include <vector>
Chris@16: #include <list>
Chris@16: #include <algorithm>
Chris@16: #include <limits>
Chris@16: 
Chris@16: #include <boost/bind.hpp>
Chris@16: #include <boost/type_traits/is_same.hpp>
Chris@16: #include <boost/type_traits/remove_const.hpp>
Chris@16: #include <boost/concept_check.hpp>
Chris@16: #include <boost/pending/queue.hpp>
Chris@16: #include <boost/property_map/property_map.hpp>
Chris@16: #include <boost/graph/graph_traits.hpp>
Chris@16: #include <boost/graph/graph_concepts.hpp>
Chris@16: #include <boost/concept/assert.hpp>
Chris@16: 
Chris@16: /** @file howard_cycle_ratio.hpp
Chris@16:  * @brief The implementation of the maximum/minimum cycle ratio/mean algorithm.
Chris@16:  * @author Dmitry Bufistov
Chris@16:  * @author Andrey Parfenov
Chris@16:  */
Chris@16: 
Chris@16: namespace boost {
Chris@16: 
Chris@16:   /**
Chris@16:    * The mcr_float is like numeric_limits, but only for floating point types
Chris@16:    * and only defines infinity() and epsilon(). This class is primarily used
Chris@16:    * to encapsulate a less-precise epsilon than natively supported by the
Chris@16:    * floating point type.
Chris@16:    */
Chris@16:   template <typename Float = double> struct mcr_float {
Chris@16:     typedef Float value_type;
Chris@16: 
Chris@16:     static Float infinity()
Chris@16:     { return std::numeric_limits<value_type>::infinity(); }
Chris@16: 
Chris@16:     static Float epsilon()
Chris@16:     { return Float(-0.005); }
Chris@16:   };
Chris@16: 
Chris@16:   namespace detail {
Chris@16: 
Chris@16:     template <typename FloatTraits> struct
Chris@16:     min_comparator_props {
Chris@16:       typedef std::greater<typename FloatTraits::value_type> comparator;
Chris@16:       static const int multiplier = 1;
Chris@16:     };
Chris@16: 
Chris@16:     template <typename FloatTraits> struct
Chris@16:     max_comparator_props {
Chris@16:       typedef std::less<typename FloatTraits::value_type> comparator;
Chris@16:       static const int multiplier = -1;
Chris@16:     };
Chris@16: 
Chris@16:     template <typename FloatTraits, typename ComparatorProps>
Chris@16:     struct float_wrapper {
Chris@16:       typedef typename FloatTraits::value_type value_type;
Chris@16:       typedef ComparatorProps comparator_props_t;
Chris@16:       typedef typename ComparatorProps::comparator comparator;
Chris@16: 
Chris@16:       static value_type infinity()
Chris@16:       { return FloatTraits::infinity() * ComparatorProps::multiplier; }
Chris@16: 
Chris@16:       static value_type epsilon()
Chris@16:       { return FloatTraits::epsilon() * ComparatorProps::multiplier; }
Chris@16: 
Chris@16:     };
Chris@16: 
Chris@16:     /*! @class mcr_howard
Chris@16:      * @brief Calculates optimum (maximum/minimum) cycle ratio of a directed graph.
Chris@16:      * Uses  Howard's iteration policy algorithm. </br>(It is described in the paper
Chris@16:      * "Experimental Analysis of the Fastest Optimum Cycle Ratio and Mean Algorithm"
Chris@16:      * by Ali Dasdan).
Chris@16:      */
Chris@16:     template <typename FloatTraits,
Chris@16:               typename Graph, typename VertexIndexMap,
Chris@16:               typename EdgeWeight1, typename EdgeWeight2>
Chris@16:     class mcr_howard
Chris@16:     {
Chris@16:     public:
Chris@16:       typedef typename FloatTraits::value_type float_t;
Chris@16:       typedef typename FloatTraits::comparator_props_t cmp_props_t;
Chris@16:       typedef typename FloatTraits::comparator comparator_t;
Chris@16:       typedef enum{ my_white = 0, my_black } my_color_type;
Chris@16:       typedef typename graph_traits<Graph>::vertex_descriptor vertex_t;
Chris@16:       typedef typename graph_traits<Graph>::edge_descriptor edge_t;
Chris@16:       typedef typename graph_traits<Graph>::vertices_size_type vn_t;
Chris@16:       typedef std::vector<float_t> vp_t;
Chris@16:       typedef typename boost::iterator_property_map<
Chris@16:         typename vp_t::iterator, VertexIndexMap
Chris@16:       > distance_map_t; //V -> float_t
Chris@16: 
Chris@16:       typedef typename std::vector<edge_t> ve_t;
Chris@16:       typedef std::vector<my_color_type> vcol_t;
Chris@16:       typedef typename ::boost::iterator_property_map<
Chris@16:         typename ve_t::iterator, VertexIndexMap
Chris@16:       > policy_t; //Vertex -> Edge
Chris@16:       typedef typename ::boost::iterator_property_map<
Chris@16:         typename vcol_t::iterator, VertexIndexMap
Chris@16:       > color_map_t;
Chris@16: 
Chris@16:       typedef typename std::list<vertex_t> pinel_t;// The in_edges list of the policy graph
Chris@16:       typedef typename std::vector<pinel_t> inedges1_t;
Chris@16:       typedef typename ::boost::iterator_property_map<
Chris@16:         typename inedges1_t::iterator, VertexIndexMap
Chris@16:       > inedges_t;
Chris@16:       typedef typename std::vector<edge_t> critical_cycle_t;
Chris@16: 
Chris@16:       //Bad  vertex flag. If true, then the vertex is "bad".
Chris@16:       // Vertex is "bad" if its out_degree is equal to zero.
Chris@16:       typedef typename boost::iterator_property_map<
Chris@16:         std::vector<int>::iterator, VertexIndexMap
Chris@16:       > badv_t;
Chris@16: 
Chris@16:       /*!
Chris@16:        * Constructor
Chris@16:        * \param g = (V, E) - a directed multigraph.
Chris@16:        * \param vim  Vertex Index Map. Read property Map: V -> [0, num_vertices(g)).
Chris@16:        * \param ewm  edge weight map. Read property map: E -> R
Chris@16:        * \param ew2m  edge weight map. Read property map: E -> R+
Chris@16:        * \param infty A big enough value to guaranty that there exist a cycle with
Chris@16:        *  better ratio.
Chris@16:        * \param cmp The compare operator for float_ts.
Chris@16:        */
Chris@16:       mcr_howard(const Graph &g, VertexIndexMap vim,
Chris@16:                   EdgeWeight1 ewm, EdgeWeight2 ew2m) :
Chris@16:         m_g(g), m_vim(vim), m_ew1m(ewm), m_ew2m(ew2m),
Chris@16:         m_bound(mcr_bound()),
Chris@16:         m_cr(m_bound),
Chris@16:         m_V(num_vertices(m_g)),
Chris@16:         m_dis(m_V, 0), m_dm(m_dis.begin(), m_vim),
Chris@16:         m_policyc(m_V), m_policy(m_policyc.begin(), m_vim),
Chris@16:         m_inelc(m_V), m_inel(m_inelc.begin(), m_vim),
Chris@16:         m_badvc(m_V, false), m_badv(m_badvc.begin(), m_vim),
Chris@16:         m_colcv(m_V),
Chris@16:         m_col_bfs(m_V)
Chris@16:       { }
Chris@16: 
Chris@16:       /*!
Chris@16:        * \return maximum/minimum_{for all cycles C}
Chris@16:        *         [sum_{e in C} w1(e)] / [sum_{e in C} w2(e)],
Chris@16:        * or FloatTraits::infinity() if graph has no cycles.
Chris@16:        */
Chris@16:       float_t ocr_howard()
Chris@16:       {
Chris@16:         construct_policy_graph();
Chris@16:         int k = 0;
Chris@16:         float_t mcr = 0;
Chris@16:         do
Chris@16:           {
Chris@16:             mcr = policy_mcr();
Chris@16:             ++k;
Chris@16:           }
Chris@16:         while (try_improve_policy(mcr) && k < 100); //To avoid infinite loop
Chris@16: 
Chris@16:         const float_t eps_ =  -0.00000001 * cmp_props_t::multiplier;
Chris@16:         if (m_cmp(mcr, m_bound + eps_))
Chris@16:           {
Chris@16:             return FloatTraits::infinity();
Chris@16:           }
Chris@16:         else
Chris@16:           {
Chris@16:             return  mcr;
Chris@16:           }
Chris@16:       }
Chris@16:       virtual ~mcr_howard() {}
Chris@16: 
Chris@16:     protected:
Chris@16:       virtual void store_critical_edge(edge_t, critical_cycle_t &) {}
Chris@16:       virtual void store_critical_cycle(critical_cycle_t &) {}
Chris@16: 
Chris@16:     private:
Chris@16:       /*!
Chris@16:        * \return lower/upper bound for the maximal/minimal cycle ratio
Chris@16:        */
Chris@16:       float_t mcr_bound()
Chris@16:       {
Chris@16:         typename  graph_traits<Graph>::vertex_iterator  vi, vie;
Chris@16:         typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
Chris@16:         float_t cz = (std::numeric_limits<float_t>::max)(); //Closest to zero value
Chris@16:         float_t s = 0;
Chris@16:         const float_t eps_ = std::numeric_limits<float_t>::epsilon();
Chris@16:         for (boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
Chris@16:           {
Chris@16:             for (boost::tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
Chris@16:               {
Chris@16:                 s += std::abs(m_ew1m[*oei]);
Chris@16:                 float_t a = std::abs(m_ew2m[*oei]);
Chris@16:                 if ( a > eps_ && a < cz)
Chris@16:                 {
Chris@16:                   cz = a;
Chris@16:                 }
Chris@16:               }
Chris@16:           }
Chris@16:         return  cmp_props_t::multiplier * (s / cz);
Chris@16:       }
Chris@16: 
Chris@16: 
Chris@16:       /*!
Chris@16:        *  Constructs an arbitrary policy graph.
Chris@16:        */
Chris@16:       void construct_policy_graph()
Chris@16:       {
Chris@16:         m_sink = graph_traits<Graph>().null_vertex();
Chris@16:         typename  graph_traits<Graph>::vertex_iterator  vi, vie;
Chris@16:         typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
Chris@16:         for ( boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi )
Chris@16:           {
Chris@16:             boost::tie(oei, oeie) = out_edges(*vi, m_g);
Chris@16:             typename graph_traits<Graph>::out_edge_iterator mei =
Chris@16:               std::max_element(oei, oeie,
Chris@16:                                boost::bind(m_cmp,
Chris@16:                                            boost::bind(&EdgeWeight1::operator[], m_ew1m, _1),
Chris@16:                                            boost::bind(&EdgeWeight1::operator[], m_ew1m, _2)
Chris@16:                                           )
Chris@16:                                );
Chris@16:             if (mei == oeie)
Chris@16:               {
Chris@16:                 if (m_sink == graph_traits<Graph>().null_vertex())
Chris@16:                   {
Chris@16:                     m_sink = *vi;
Chris@16:                   }
Chris@16:                 m_badv[*vi] = true;
Chris@16:                 m_inel[m_sink].push_back(*vi);
Chris@16:               }
Chris@16:             else
Chris@16:               {
Chris@16:                 m_inel[target(*mei, m_g)].push_back(*vi);
Chris@16:                 m_policy[*vi] = *mei;
Chris@16:               }
Chris@16:           }
Chris@16:       }
Chris@16:       /*! Sets the distance value for all vertices "v" such that there is
Chris@16:        * a path from "v" to "sv". It does "inverse" breadth first visit of the policy
Chris@16:        * graph, starting from the vertex "sv".
Chris@16:        */
Chris@16:       void mcr_bfv(vertex_t sv, float_t cr, color_map_t c)
Chris@16:       {
Chris@16:         boost::queue<vertex_t> Q;
Chris@16:         c[sv] = my_black;
Chris@16:         Q.push(sv);
Chris@16:         while (!Q.empty())
Chris@16:           {
Chris@16:             vertex_t v = Q.top(); Q.pop();
Chris@16:             for (typename pinel_t::const_iterator itr = m_inel[v].begin();
Chris@16:                  itr != m_inel[v].end(); ++itr)
Chris@16:               //For all in_edges of the policy graph
Chris@16:               {
Chris@16:                 if (*itr != sv)
Chris@16:                   {
Chris@16:                     if (m_badv[*itr])
Chris@16:                       {
Chris@16:                         m_dm[*itr] = m_dm[v] + m_bound - cr;
Chris@16:                       }
Chris@16:                     else
Chris@16:                       {
Chris@16:                         m_dm[*itr] = m_dm[v] + m_ew1m[m_policy[*itr]] -
Chris@16:                           m_ew2m[m_policy[*itr]] * cr;
Chris@16:                       }
Chris@16:                     c[*itr] = my_black;
Chris@16:                     Q.push(*itr);
Chris@16:                   }
Chris@16:               }
Chris@16:           }
Chris@16:       }
Chris@16: 
Chris@16:       /*!
Chris@16:        * \param sv an arbitrary (undiscovered) vertex of the policy graph.
Chris@16:        * \return a vertex in the policy graph that belongs to a cycle.
Chris@16:        * Performs a depth first visit until a cycle edge is found.
Chris@16:        */
Chris@16:       vertex_t find_cycle_vertex(vertex_t sv)
Chris@16:       {
Chris@16:         vertex_t gv = sv;
Chris@16:         std::fill(m_colcv.begin(), m_colcv.end(), my_white);
Chris@16:         color_map_t cm(m_colcv.begin(), m_vim);
Chris@16:         do
Chris@16:           {
Chris@16:             cm[gv] = my_black;
Chris@16:             if (! m_badv[gv])
Chris@16:               {
Chris@16:                 gv = target(m_policy[gv], m_g);
Chris@16:               }
Chris@16:             else
Chris@16:               {
Chris@16:                 gv = m_sink;
Chris@16:               }
Chris@16:           }
Chris@16:         while (cm[gv] != my_black);
Chris@16:         return gv;
Chris@16:       }
Chris@16: 
Chris@16:       /*!
Chris@16:        * \param sv - vertex that belongs to a cycle in the policy graph.
Chris@16:        */
Chris@16:       float_t cycle_ratio(vertex_t sv)
Chris@16:       {
Chris@16:         if (sv == m_sink) return m_bound;
Chris@16:         std::pair<float_t, float_t> sums_(float_t(0), float_t(0));
Chris@16:         vertex_t v = sv;
Chris@16:         critical_cycle_t cc;
Chris@16:         do
Chris@16:           {
Chris@16:             store_critical_edge(m_policy[v], cc);
Chris@16:             sums_.first += m_ew1m[m_policy[v]];
Chris@16:             sums_.second += m_ew2m[m_policy[v]];
Chris@16:             v = target(m_policy[v], m_g);
Chris@16:           }
Chris@16:         while (v != sv);
Chris@16:         float_t cr = sums_.first / sums_.second;
Chris@16:         if ( m_cmp(m_cr, cr) )
Chris@16:           {
Chris@16:             m_cr = cr;
Chris@16:             store_critical_cycle(cc);
Chris@16:           }
Chris@16:         return cr;
Chris@16:       }
Chris@16: 
Chris@16:       /*!
Chris@16:        *  Finds the optimal cycle ratio of the policy graph
Chris@16:        */
Chris@16:       float_t policy_mcr()
Chris@16:       {
Chris@16:         std::fill(m_col_bfs.begin(), m_col_bfs.end(), my_white);
Chris@16:         color_map_t vcm_ = color_map_t(m_col_bfs.begin(), m_vim);
Chris@16:         typename graph_traits<Graph>::vertex_iterator uv_itr, vie;
Chris@16:         boost::tie(uv_itr, vie) = vertices(m_g);
Chris@16:         float_t mcr = m_bound;
Chris@16:         while ( (uv_itr = std::find_if(uv_itr, vie,
Chris@16:                                        boost::bind(std::equal_to<my_color_type>(),
Chris@16:                                                    my_white,
Chris@16:                                                    boost::bind(&color_map_t::operator[], vcm_, _1)
Chris@16:                                                    )
Chris@16:                                        )
Chris@16:                  ) != vie )
Chris@16:           ///While there are undiscovered vertices
Chris@16:           {
Chris@16:             vertex_t gv = find_cycle_vertex(*uv_itr);
Chris@16:             float_t cr = cycle_ratio(gv) ;
Chris@16:             mcr_bfv(gv, cr, vcm_);
Chris@16:             if ( m_cmp(mcr, cr) )  mcr = cr;
Chris@16:             ++uv_itr;
Chris@16:           }
Chris@16:         return mcr;
Chris@16:       }
Chris@16: 
Chris@16:       /*!
Chris@16:        * Changes the edge m_policy[s] to the new_edge.
Chris@16:        */
Chris@16:       void improve_policy(vertex_t s, edge_t new_edge)
Chris@16:       {
Chris@16:         vertex_t t = target(m_policy[s], m_g);
Chris@16:         typename property_traits<VertexIndexMap>::value_type ti = m_vim[t];
Chris@16:         m_inelc[ti].erase( std::find(m_inelc[ti].begin(), m_inelc[ti].end(), s));
Chris@16:         m_policy[s] = new_edge;
Chris@16:         t = target(new_edge, m_g);
Chris@16:         m_inel[t].push_back(s); ///Maintain in_edge list
Chris@16:       }
Chris@16: 
Chris@16:       /*!
Chris@16:        * A negative cycle detector.
Chris@16:        */
Chris@16:       bool try_improve_policy(float_t cr)
Chris@16:       {
Chris@16:         bool improved = false;
Chris@16:         typename  graph_traits<Graph>::vertex_iterator  vi, vie;
Chris@16:         typename  graph_traits<Graph>::out_edge_iterator  oei, oeie;
Chris@16:         const float_t eps_ =  FloatTraits::epsilon();
Chris@16:         for (boost::tie(vi, vie) = vertices(m_g); vi != vie; ++vi)
Chris@16:           {
Chris@16:             if (!m_badv[*vi])
Chris@16:               {
Chris@16:                 for (boost::tie(oei, oeie) = out_edges(*vi, m_g); oei != oeie; ++oei)
Chris@16:                   {
Chris@16:                     vertex_t t = target(*oei, m_g);
Chris@16:                     //Current distance from *vi to some vertex
Chris@16:                     float_t dis_ = m_ew1m[*oei] - m_ew2m[*oei] * cr + m_dm[t];
Chris@16:                     if ( m_cmp(m_dm[*vi] + eps_, dis_) )
Chris@16:                       {
Chris@16:                         improve_policy(*vi, *oei);
Chris@16:                         m_dm[*vi] = dis_;
Chris@16:                         improved = true;
Chris@16:                       }
Chris@16:                   }
Chris@16:               }
Chris@16:             else
Chris@16:               {
Chris@16:                 float_t dis_ = m_bound - cr + m_dm[m_sink];
Chris@16:                 if ( m_cmp(m_dm[*vi] + eps_, dis_) )
Chris@16:                   {
Chris@16:                     m_dm[*vi] = dis_;
Chris@16:                   }
Chris@16:               }
Chris@16:           }
Chris@16:         return improved;
Chris@16:       }
Chris@16:     private:
Chris@16:       const Graph &m_g;
Chris@16:       VertexIndexMap m_vim;
Chris@16:       EdgeWeight1 m_ew1m;
Chris@16:       EdgeWeight2 m_ew2m;
Chris@16:       comparator_t m_cmp;
Chris@16:       float_t m_bound; //> The lower/upper bound to the maximal/minimal cycle ratio
Chris@16:       float_t m_cr; //>The best cycle ratio that has been found so far
Chris@16: 
Chris@16:       vn_t m_V; //>The number of the vertices in the graph
Chris@16:       vp_t m_dis; //>Container for the distance map
Chris@16:       distance_map_t m_dm; //>Distance map
Chris@16: 
Chris@16:       ve_t m_policyc; //>Container for the policy graph
Chris@16:       policy_t m_policy; //>The interface for the policy graph
Chris@16: 
Chris@16:       inedges1_t m_inelc; //>Container fot in edges list
Chris@16:       inedges_t m_inel; //>Policy graph, input edges list
Chris@16: 
Chris@16:       std::vector<int> m_badvc;
Chris@16:       badv_t m_badv; //Marks "bad" vertices
Chris@16: 
Chris@16:       vcol_t m_colcv, m_col_bfs; //Color maps
Chris@16:       vertex_t m_sink; //To convert any graph to "good"
Chris@16:     };
Chris@16: 
Chris@16:     /*! \class mcr_howard1
Chris@16:   * \brief Finds optimum cycle raio and a critical cycle
Chris@16:      */
Chris@16:     template <typename FloatTraits,
Chris@16:               typename Graph, typename VertexIndexMap,
Chris@16:               typename EdgeWeight1, typename EdgeWeight2>
Chris@16:     class mcr_howard1  : public
Chris@16:     mcr_howard<FloatTraits, Graph, VertexIndexMap,
Chris@16:                EdgeWeight1, EdgeWeight2>
Chris@16:     {
Chris@16:     public:
Chris@16:       typedef mcr_howard<FloatTraits, Graph, VertexIndexMap,
Chris@16:         EdgeWeight1, EdgeWeight2> inhr_t;
Chris@16:       mcr_howard1(const Graph &g, VertexIndexMap vim,
Chris@16:         EdgeWeight1 ewm, EdgeWeight2 ew2m) :
Chris@16:         inhr_t(g, vim, ewm, ew2m)
Chris@16:       { }
Chris@16: 
Chris@16:       void get_critical_cycle(typename inhr_t::critical_cycle_t &cc)
Chris@16:       { return cc.swap(m_cc); }
Chris@16: 
Chris@16:     protected:
Chris@16:       void store_critical_edge(typename inhr_t::edge_t ed,
Chris@16:         typename inhr_t::critical_cycle_t &cc)
Chris@16:       { cc.push_back(ed); }
Chris@16: 
Chris@16:       void store_critical_cycle(typename inhr_t::critical_cycle_t &cc)
Chris@16:       { m_cc.swap(cc); }
Chris@16: 
Chris@16:     private:
Chris@16:       typename inhr_t::critical_cycle_t m_cc; //Critical cycle
Chris@16:     };
Chris@16: 
Chris@16:     /*!
Chris@16:      * \param g a directed multigraph.
Chris@16:      * \param vim Vertex Index Map. A map V->[0, num_vertices(g))
Chris@16:      * \param ewm Edge weight1 map.
Chris@16:      * \param ew2m Edge weight2 map.
Chris@16:      * \param pcc  pointer to the critical edges list.
Chris@16:      * \return Optimum cycle ratio of g or FloatTraits::infinity() if g has no cycles.
Chris@16:      */
Chris@16:     template <typename FT,
Chris@16:               typename TG, typename TVIM,
Chris@16:               typename TEW1, typename TEW2,
Chris@16:               typename EV>
Chris@16:     typename FT::value_type
Chris@16:  optimum_cycle_ratio(const TG &g, TVIM vim, TEW1 ewm, TEW2 ew2m, EV* pcc)
Chris@16:     {
Chris@16:       typedef typename graph_traits<TG>::directed_category DirCat;
Chris@16:       BOOST_STATIC_ASSERT((is_convertible<DirCat*, directed_tag*>::value == true));
Chris@16:       BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept<TG> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( VertexListGraphConcept<TG> ));
Chris@16:       typedef typename graph_traits<TG>::vertex_descriptor Vertex;
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TVIM, Vertex> ));
Chris@16:       typedef typename graph_traits<TG>::edge_descriptor Edge;
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TEW1, Edge> ));
Chris@16:       BOOST_CONCEPT_ASSERT(( ReadablePropertyMapConcept<TEW2, Edge> ));
Chris@16: 
Chris@16:       if(pcc == 0) {
Chris@16:           return detail::mcr_howard<FT,TG, TVIM, TEW1, TEW2>(
Chris@16:             g, vim, ewm, ew2m
Chris@16:           ).ocr_howard();
Chris@16:       }
Chris@16: 
Chris@16:       detail::mcr_howard1<FT, TG, TVIM, TEW1, TEW2> obj(g, vim, ewm, ew2m);
Chris@16:       double ocr = obj.ocr_howard();
Chris@16:       obj.get_critical_cycle(*pcc);
Chris@16:       return ocr;
Chris@16:     }
Chris@16:   } // namespace detail
Chris@16: 
Chris@16: // Algorithms
Chris@16: // Maximum Cycle Ratio
Chris@16: 
Chris@16: template <
Chris@16:     typename FloatTraits,
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeight1Map,
Chris@16:     typename EdgeWeight2Map>
Chris@16: inline typename FloatTraits::value_type
Chris@16: maximum_cycle_ratio(const Graph &g, VertexIndexMap vim, EdgeWeight1Map ew1m,
Chris@16:                     EdgeWeight2Map ew2m,
Chris@16:                     std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
Chris@16:                     FloatTraits = FloatTraits())
Chris@16: {
Chris@16:     typedef detail::float_wrapper<
Chris@16:         FloatTraits, detail::max_comparator_props<FloatTraits>
Chris@16:     > Traits;
Chris@16:     return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
Chris@16: }
Chris@16: 
Chris@16: template <
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeight1Map,
Chris@16:     typename EdgeWeight2Map>
Chris@16: inline double
Chris@16: maximum_cycle_ratio(const Graph &g, VertexIndexMap vim,
Chris@16:                     EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
Chris@16:                     std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
Chris@16: { return maximum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }
Chris@16: 
Chris@16: // Minimum Cycle Ratio
Chris@16: 
Chris@16: template <
Chris@16:     typename FloatTraits,
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeight1Map,
Chris@16:     typename EdgeWeight2Map>
Chris@16: typename FloatTraits::value_type
Chris@16: minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
Chris@16:                     EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
Chris@16:                     std::vector<typename graph_traits<Graph>::edge_descriptor> *pcc = 0,
Chris@16:                     FloatTraits = FloatTraits())
Chris@16: {
Chris@16:     typedef detail::float_wrapper<
Chris@16:         FloatTraits, detail::min_comparator_props<FloatTraits>
Chris@16:     > Traits;
Chris@16:     return detail::optimum_cycle_ratio<Traits>(g, vim, ew1m, ew2m, pcc);
Chris@16: }
Chris@16: 
Chris@16: template <
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeight1Map,
Chris@16:     typename EdgeWeight2Map>
Chris@16: inline double
Chris@16: minimum_cycle_ratio(const Graph &g, VertexIndexMap vim,
Chris@16:                     EdgeWeight1Map ew1m, EdgeWeight2Map ew2m,
Chris@16:                     std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
Chris@16: { return minimum_cycle_ratio(g, vim, ew1m, ew2m, pcc, mcr_float<>()); }
Chris@16: 
Chris@16: // Maximum Cycle Mean
Chris@16: 
Chris@16: template <
Chris@16:     typename FloatTraits,
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeightMap,
Chris@16:     typename EdgeIndexMap>
Chris@16: inline typename FloatTraits::value_type
Chris@16: maximum_cycle_mean(const Graph &g, VertexIndexMap vim,
Chris@16:                    EdgeWeightMap ewm, EdgeIndexMap eim,
Chris@16:                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
Chris@16:                    FloatTraits ft = FloatTraits())
Chris@16: {
Chris@16:     typedef typename remove_const<
Chris@16:         typename property_traits<EdgeWeightMap>::value_type
Chris@16:     >::type Weight;
Chris@16:     typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
Chris@16:     return maximum_cycle_ratio(g, vim, ewm,
Chris@16:                                make_iterator_property_map(ed_w2.begin(), eim),
Chris@16:                                pcc, ft);
Chris@16: }
Chris@16: 
Chris@16: template <
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeightMap,
Chris@16:     typename EdgeIndexMap>
Chris@16: inline double
Chris@16: maximum_cycle_mean(const Graph& g, VertexIndexMap vim,
Chris@16:                    EdgeWeightMap ewm, EdgeIndexMap eim,
Chris@16:                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
Chris@16: { return maximum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }
Chris@16: 
Chris@16: // Minimum Cycle Mean
Chris@16: 
Chris@16: template <
Chris@16:     typename FloatTraits,
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeightMap,
Chris@16:     typename EdgeIndexMap>
Chris@16: inline typename FloatTraits::value_type
Chris@16: minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
Chris@16:                    EdgeWeightMap ewm, EdgeIndexMap eim,
Chris@16:                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0,
Chris@16:                    FloatTraits ft = FloatTraits())
Chris@16: {
Chris@16:     typedef typename remove_const<
Chris@16:         typename property_traits<EdgeWeightMap>::value_type
Chris@16:     >::type Weight;
Chris@16:     typename std::vector<Weight> ed_w2(boost::num_edges(g), 1);
Chris@16:     return minimum_cycle_ratio(g, vim, ewm,
Chris@16:                                make_iterator_property_map(ed_w2.begin(), eim),
Chris@16:                                pcc, ft);
Chris@16: }
Chris@16: 
Chris@16: template <
Chris@16:     typename Graph,
Chris@16:     typename VertexIndexMap,
Chris@16:     typename EdgeWeightMap,
Chris@16:     typename EdgeIndexMap>
Chris@16: inline double
Chris@16: minimum_cycle_mean(const Graph &g, VertexIndexMap vim,
Chris@16:                    EdgeWeightMap ewm, EdgeIndexMap eim,
Chris@16:                    std::vector<typename graph_traits<Graph>::edge_descriptor>* pcc = 0)
Chris@16: { return minimum_cycle_mean(g, vim, ewm, eim, pcc, mcr_float<>()); }
Chris@16: 
Chris@16: } //namespace boost
Chris@16: 
Chris@16: #endif