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