[805] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2008 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_MIN_MEAN_CYCLE_H |
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| 20 | #define LEMON_MIN_MEAN_CYCLE_H |
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| 21 | |
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| 22 | /// \ingroup shortest_path |
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| 23 | /// |
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| 24 | /// \file |
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| 25 | /// \brief Howard's algorithm for finding a minimum mean cycle. |
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| 26 | |
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| 27 | #include <vector> |
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| 28 | #include <lemon/core.h> |
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| 29 | #include <lemon/path.h> |
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| 30 | #include <lemon/tolerance.h> |
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| 31 | #include <lemon/connectivity.h> |
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| 32 | |
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| 33 | namespace lemon { |
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| 34 | |
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| 35 | /// \addtogroup shortest_path |
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| 36 | /// @{ |
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| 37 | |
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| 38 | /// \brief Implementation of Howard's algorithm for finding a minimum |
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| 39 | /// mean cycle. |
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| 40 | /// |
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| 41 | /// \ref MinMeanCycle implements Howard's algorithm for finding a |
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| 42 | /// directed cycle of minimum mean length (cost) in a digraph. |
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| 43 | /// |
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| 44 | /// \tparam GR The type of the digraph the algorithm runs on. |
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| 45 | /// \tparam LEN The type of the length map. The default |
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| 46 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
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| 47 | /// |
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| 48 | /// \warning \c LEN::Value must be convertible to \c double. |
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| 49 | #ifdef DOXYGEN |
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| 50 | template <typename GR, typename LEN> |
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| 51 | #else |
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| 52 | template < typename GR, |
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| 53 | typename LEN = typename GR::template ArcMap<int> > |
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| 54 | #endif |
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| 55 | class MinMeanCycle |
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| 56 | { |
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| 57 | public: |
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| 58 | |
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| 59 | /// The type of the digraph the algorithm runs on |
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| 60 | typedef GR Digraph; |
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| 61 | /// The type of the length map |
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| 62 | typedef LEN LengthMap; |
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| 63 | /// The type of the arc lengths |
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| 64 | typedef typename LengthMap::Value Value; |
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| 65 | /// The type of the paths |
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| 66 | typedef lemon::Path<Digraph> Path; |
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| 67 | |
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| 68 | private: |
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| 69 | |
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| 70 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
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| 71 | |
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| 72 | // The digraph the algorithm runs on |
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| 73 | const Digraph &_gr; |
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| 74 | // The length of the arcs |
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| 75 | const LengthMap &_length; |
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| 76 | |
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| 77 | // The total length of the found cycle |
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| 78 | Value _cycle_length; |
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| 79 | // The number of arcs on the found cycle |
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| 80 | int _cycle_size; |
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| 81 | // The found cycle |
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| 82 | Path *_cycle_path; |
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| 83 | |
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| 84 | bool _local_path; |
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| 85 | bool _cycle_found; |
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| 86 | Node _cycle_node; |
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| 87 | |
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| 88 | typename Digraph::template NodeMap<bool> _reached; |
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| 89 | typename Digraph::template NodeMap<double> _dist; |
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| 90 | typename Digraph::template NodeMap<Arc> _policy; |
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| 91 | |
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| 92 | typename Digraph::template NodeMap<int> _comp; |
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| 93 | int _comp_num; |
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| 94 | |
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| 95 | std::vector<Node> _nodes; |
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| 96 | std::vector<Arc> _arcs; |
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| 97 | Tolerance<double> _tol; |
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| 98 | |
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| 99 | public: |
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| 100 | |
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| 101 | /// \brief Constructor. |
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| 102 | /// |
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| 103 | /// The constructor of the class. |
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| 104 | /// |
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| 105 | /// \param digraph The digraph the algorithm runs on. |
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| 106 | /// \param length The lengths (costs) of the arcs. |
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| 107 | MinMeanCycle( const Digraph &digraph, |
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| 108 | const LengthMap &length ) : |
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| 109 | _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1), |
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| 110 | _cycle_path(NULL), _local_path(false), _reached(digraph), |
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| 111 | _dist(digraph), _policy(digraph), _comp(digraph) |
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| 112 | {} |
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| 113 | |
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| 114 | /// Destructor. |
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| 115 | ~MinMeanCycle() { |
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| 116 | if (_local_path) delete _cycle_path; |
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| 117 | } |
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| 118 | |
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| 119 | /// \brief Set the path structure for storing the found cycle. |
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| 120 | /// |
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| 121 | /// This function sets an external path structure for storing the |
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| 122 | /// found cycle. |
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| 123 | /// |
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| 124 | /// If you don't call this function before calling \ref run() or |
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[806] | 125 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
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[805] | 126 | /// structure. The destuctor deallocates this automatically |
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| 127 | /// allocated object, of course. |
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| 128 | /// |
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| 129 | /// \note The algorithm calls only the \ref lemon::Path::addBack() |
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| 130 | /// "addBack()" function of the given path structure. |
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| 131 | /// |
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| 132 | /// \return <tt>(*this)</tt> |
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| 133 | /// |
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| 134 | /// \sa cycle() |
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| 135 | MinMeanCycle& cyclePath(Path &path) { |
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| 136 | if (_local_path) { |
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| 137 | delete _cycle_path; |
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| 138 | _local_path = false; |
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| 139 | } |
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| 140 | _cycle_path = &path; |
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| 141 | return *this; |
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| 142 | } |
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| 143 | |
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| 144 | /// \name Execution control |
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| 145 | /// The simplest way to execute the algorithm is to call the \ref run() |
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| 146 | /// function.\n |
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[806] | 147 | /// If you only need the minimum mean length, you may call |
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| 148 | /// \ref findMinMean(). |
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[805] | 149 | |
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| 150 | /// @{ |
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| 151 | |
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| 152 | /// \brief Run the algorithm. |
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| 153 | /// |
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| 154 | /// This function runs the algorithm. |
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[806] | 155 | /// It can be called more than once (e.g. if the underlying digraph |
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| 156 | /// and/or the arc lengths have been modified). |
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[805] | 157 | /// |
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| 158 | /// \return \c true if a directed cycle exists in the digraph. |
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| 159 | /// |
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[806] | 160 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
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[805] | 161 | /// \code |
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[806] | 162 | /// return mmc.findMinMean() && mmc.findCycle(); |
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[805] | 163 | /// \endcode |
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| 164 | bool run() { |
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| 165 | return findMinMean() && findCycle(); |
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| 166 | } |
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| 167 | |
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[806] | 168 | /// \brief Find the minimum cycle mean. |
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[805] | 169 | /// |
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[806] | 170 | /// This function finds the minimum mean length of the directed |
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| 171 | /// cycles in the digraph. |
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[805] | 172 | /// |
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[806] | 173 | /// \return \c true if a directed cycle exists in the digraph. |
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| 174 | bool findMinMean() { |
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| 175 | // Initialize |
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[805] | 176 | _tol.epsilon(1e-6); |
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| 177 | if (!_cycle_path) { |
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| 178 | _local_path = true; |
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| 179 | _cycle_path = new Path; |
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| 180 | } |
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[806] | 181 | _cycle_path->clear(); |
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[805] | 182 | _cycle_found = false; |
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[806] | 183 | |
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| 184 | // Find the minimum cycle mean in the components |
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[805] | 185 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
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| 186 | for (int comp = 0; comp < _comp_num; ++comp) { |
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| 187 | if (!initCurrentComponent(comp)) continue; |
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| 188 | while (true) { |
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| 189 | if (!findPolicyCycles()) break; |
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| 190 | contractPolicyGraph(comp); |
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| 191 | if (!computeNodeDistances()) break; |
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| 192 | } |
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| 193 | } |
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| 194 | return _cycle_found; |
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| 195 | } |
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| 196 | |
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| 197 | /// \brief Find a minimum mean directed cycle. |
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| 198 | /// |
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| 199 | /// This function finds a directed cycle of minimum mean length |
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| 200 | /// in the digraph using the data computed by findMinMean(). |
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| 201 | /// |
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| 202 | /// \return \c true if a directed cycle exists in the digraph. |
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| 203 | /// |
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[806] | 204 | /// \pre \ref findMinMean() must be called before using this function. |
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[805] | 205 | bool findCycle() { |
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| 206 | if (!_cycle_found) return false; |
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| 207 | _cycle_path->addBack(_policy[_cycle_node]); |
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| 208 | for ( Node v = _cycle_node; |
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| 209 | (v = _gr.target(_policy[v])) != _cycle_node; ) { |
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| 210 | _cycle_path->addBack(_policy[v]); |
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| 211 | } |
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| 212 | return true; |
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| 213 | } |
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| 214 | |
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| 215 | /// @} |
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| 216 | |
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| 217 | /// \name Query Functions |
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[806] | 218 | /// The results of the algorithm can be obtained using these |
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[805] | 219 | /// functions.\n |
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| 220 | /// The algorithm should be executed before using them. |
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| 221 | |
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| 222 | /// @{ |
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| 223 | |
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| 224 | /// \brief Return the total length of the found cycle. |
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| 225 | /// |
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| 226 | /// This function returns the total length of the found cycle. |
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| 227 | /// |
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| 228 | /// \pre \ref run() or \ref findCycle() must be called before |
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| 229 | /// using this function. |
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| 230 | Value cycleLength() const { |
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| 231 | return _cycle_length; |
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| 232 | } |
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| 233 | |
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| 234 | /// \brief Return the number of arcs on the found cycle. |
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| 235 | /// |
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| 236 | /// This function returns the number of arcs on the found cycle. |
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| 237 | /// |
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| 238 | /// \pre \ref run() or \ref findCycle() must be called before |
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| 239 | /// using this function. |
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| 240 | int cycleArcNum() const { |
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| 241 | return _cycle_size; |
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| 242 | } |
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| 243 | |
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| 244 | /// \brief Return the mean length of the found cycle. |
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| 245 | /// |
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| 246 | /// This function returns the mean length of the found cycle. |
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| 247 | /// |
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| 248 | /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the |
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| 249 | /// following code. |
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| 250 | /// \code |
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| 251 | /// return double(mmc.cycleLength()) / mmc.cycleArcNum(); |
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| 252 | /// \endcode |
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| 253 | /// |
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| 254 | /// \pre \ref run() or \ref findMinMean() must be called before |
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| 255 | /// using this function. |
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| 256 | double cycleMean() const { |
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| 257 | return double(_cycle_length) / _cycle_size; |
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| 258 | } |
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| 259 | |
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| 260 | /// \brief Return the found cycle. |
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| 261 | /// |
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| 262 | /// This function returns a const reference to the path structure |
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| 263 | /// storing the found cycle. |
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| 264 | /// |
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| 265 | /// \pre \ref run() or \ref findCycle() must be called before using |
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| 266 | /// this function. |
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| 267 | /// |
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| 268 | /// \sa cyclePath() |
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| 269 | const Path& cycle() const { |
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| 270 | return *_cycle_path; |
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| 271 | } |
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| 272 | |
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| 273 | ///@} |
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| 274 | |
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| 275 | private: |
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| 276 | |
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| 277 | // Initialize the internal data structures for the current strongly |
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| 278 | // connected component and create the policy graph. |
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| 279 | // The policy graph can be represented by the _policy map because |
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| 280 | // the out-degree of every node is 1. |
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| 281 | bool initCurrentComponent(int comp) { |
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| 282 | // Find the nodes of the current component |
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| 283 | _nodes.clear(); |
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| 284 | for (NodeIt n(_gr); n != INVALID; ++n) { |
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| 285 | if (_comp[n] == comp) _nodes.push_back(n); |
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| 286 | } |
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| 287 | if (_nodes.size() <= 1) return false; |
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| 288 | // Find the arcs of the current component |
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| 289 | _arcs.clear(); |
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| 290 | for (ArcIt e(_gr); e != INVALID; ++e) { |
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| 291 | if ( _comp[_gr.source(e)] == comp && |
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| 292 | _comp[_gr.target(e)] == comp ) |
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| 293 | _arcs.push_back(e); |
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| 294 | } |
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| 295 | // Initialize _reached, _dist, _policy maps |
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| 296 | for (int i = 0; i < int(_nodes.size()); ++i) { |
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| 297 | _reached[_nodes[i]] = false; |
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| 298 | _policy[_nodes[i]] = INVALID; |
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| 299 | } |
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| 300 | Node u; Arc e; |
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| 301 | for (int j = 0; j < int(_arcs.size()); ++j) { |
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| 302 | e = _arcs[j]; |
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| 303 | u = _gr.source(e); |
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| 304 | if (!_reached[u] || _length[e] < _dist[u]) { |
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| 305 | _dist[u] = _length[e]; |
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| 306 | _policy[u] = e; |
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| 307 | _reached[u] = true; |
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| 308 | } |
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| 309 | } |
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| 310 | return true; |
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| 311 | } |
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| 312 | |
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| 313 | // Find all cycles in the policy graph. |
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| 314 | // Set _cycle_found to true if a cycle is found and set |
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| 315 | // _cycle_length, _cycle_size, _cycle_node to represent the minimum |
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| 316 | // mean cycle in the policy graph. |
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| 317 | bool findPolicyCycles() { |
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| 318 | typename Digraph::template NodeMap<int> level(_gr, -1); |
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| 319 | bool curr_cycle_found = false; |
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| 320 | Value clength; |
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| 321 | int csize; |
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| 322 | int path_cnt = 0; |
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| 323 | Node u, v; |
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| 324 | // Searching for cycles |
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| 325 | for (int i = 0; i < int(_nodes.size()); ++i) { |
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| 326 | if (level[_nodes[i]] < 0) { |
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| 327 | u = _nodes[i]; |
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| 328 | level[u] = path_cnt; |
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| 329 | while (level[u = _gr.target(_policy[u])] < 0) |
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| 330 | level[u] = path_cnt; |
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| 331 | if (level[u] == path_cnt) { |
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| 332 | // A cycle is found |
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| 333 | curr_cycle_found = true; |
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| 334 | clength = _length[_policy[u]]; |
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| 335 | csize = 1; |
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| 336 | for (v = u; (v = _gr.target(_policy[v])) != u; ) { |
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| 337 | clength += _length[_policy[v]]; |
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| 338 | ++csize; |
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| 339 | } |
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| 340 | if ( !_cycle_found || |
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| 341 | clength * _cycle_size < _cycle_length * csize ) { |
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| 342 | _cycle_found = true; |
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| 343 | _cycle_length = clength; |
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| 344 | _cycle_size = csize; |
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| 345 | _cycle_node = u; |
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| 346 | } |
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| 347 | } |
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| 348 | ++path_cnt; |
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| 349 | } |
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| 350 | } |
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| 351 | return curr_cycle_found; |
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| 352 | } |
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| 353 | |
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| 354 | // Contract the policy graph to be connected by cutting all cycles |
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| 355 | // except for the main cycle (i.e. the minimum mean cycle). |
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| 356 | void contractPolicyGraph(int comp) { |
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| 357 | // Find the component of the main cycle using reverse BFS search |
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| 358 | typename Digraph::template NodeMap<int> found(_gr, false); |
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| 359 | std::deque<Node> queue; |
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| 360 | queue.push_back(_cycle_node); |
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| 361 | found[_cycle_node] = true; |
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| 362 | Node u, v; |
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| 363 | while (!queue.empty()) { |
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| 364 | v = queue.front(); queue.pop_front(); |
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| 365 | for (InArcIt e(_gr, v); e != INVALID; ++e) { |
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| 366 | u = _gr.source(e); |
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| 367 | if (_policy[u] == e && !found[u]) { |
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| 368 | found[u] = true; |
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| 369 | queue.push_back(u); |
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| 370 | } |
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| 371 | } |
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| 372 | } |
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| 373 | // Connect all other nodes to this component using reverse BFS search |
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| 374 | queue.clear(); |
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| 375 | for (int i = 0; i < int(_nodes.size()); ++i) |
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| 376 | if (found[_nodes[i]]) queue.push_back(_nodes[i]); |
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| 377 | int found_cnt = queue.size(); |
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| 378 | while (found_cnt < int(_nodes.size())) { |
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| 379 | v = queue.front(); queue.pop_front(); |
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| 380 | for (InArcIt e(_gr, v); e != INVALID; ++e) { |
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| 381 | u = _gr.source(e); |
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| 382 | if (_comp[u] == comp && !found[u]) { |
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| 383 | found[u] = true; |
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| 384 | ++found_cnt; |
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| 385 | _policy[u] = e; |
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| 386 | queue.push_back(u); |
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| 387 | } |
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| 388 | } |
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| 389 | } |
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| 390 | } |
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| 391 | |
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| 392 | // Compute node distances in the policy graph and update the |
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| 393 | // policy graph if the node distances can be improved. |
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| 394 | bool computeNodeDistances() { |
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| 395 | // Compute node distances using reverse BFS search |
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| 396 | double cycle_mean = double(_cycle_length) / _cycle_size; |
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| 397 | typename Digraph::template NodeMap<int> found(_gr, false); |
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| 398 | std::deque<Node> queue; |
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| 399 | queue.push_back(_cycle_node); |
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| 400 | found[_cycle_node] = true; |
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| 401 | _dist[_cycle_node] = 0; |
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| 402 | Node u, v; |
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| 403 | while (!queue.empty()) { |
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| 404 | v = queue.front(); queue.pop_front(); |
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| 405 | for (InArcIt e(_gr, v); e != INVALID; ++e) { |
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| 406 | u = _gr.source(e); |
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| 407 | if (_policy[u] == e && !found[u]) { |
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| 408 | found[u] = true; |
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| 409 | _dist[u] = _dist[v] + _length[e] - cycle_mean; |
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| 410 | queue.push_back(u); |
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| 411 | } |
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| 412 | } |
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| 413 | } |
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| 414 | // Improving node distances |
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| 415 | bool improved = false; |
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| 416 | for (int j = 0; j < int(_arcs.size()); ++j) { |
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| 417 | Arc e = _arcs[j]; |
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| 418 | u = _gr.source(e); v = _gr.target(e); |
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| 419 | double delta = _dist[v] + _length[e] - cycle_mean; |
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| 420 | if (_tol.less(delta, _dist[u])) { |
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| 421 | improved = true; |
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| 422 | _dist[u] = delta; |
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| 423 | _policy[u] = e; |
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| 424 | } |
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| 425 | } |
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| 426 | return improved; |
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| 427 | } |
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| 428 | |
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| 429 | }; //class MinMeanCycle |
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| 430 | |
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| 431 | ///@} |
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| 432 | |
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| 433 | } //namespace lemon |
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| 434 | |
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| 435 | #endif //LEMON_MIN_MEAN_CYCLE_H |
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