1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/lemon/min_mean_cycle.h Mon Aug 03 14:12:55 2009 +0200
1.3 @@ -0,0 +1,462 @@
1.4 +/* -*- C++ -*-
1.5 + *
1.6 + * This file is a part of LEMON, a generic C++ optimization library
1.7 + *
1.8 + * Copyright (C) 2003-2008
1.9 + * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
1.10 + * (Egervary Research Group on Combinatorial Optimization, EGRES).
1.11 + *
1.12 + * Permission to use, modify and distribute this software is granted
1.13 + * provided that this copyright notice appears in all copies. For
1.14 + * precise terms see the accompanying LICENSE file.
1.15 + *
1.16 + * This software is provided "AS IS" with no warranty of any kind,
1.17 + * express or implied, and with no claim as to its suitability for any
1.18 + * purpose.
1.19 + *
1.20 + */
1.21 +
1.22 +#ifndef LEMON_MIN_MEAN_CYCLE_H
1.23 +#define LEMON_MIN_MEAN_CYCLE_H
1.24 +
1.25 +/// \ingroup shortest_path
1.26 +///
1.27 +/// \file
1.28 +/// \brief Howard's algorithm for finding a minimum mean cycle.
1.29 +
1.30 +#include <vector>
1.31 +#include <lemon/core.h>
1.32 +#include <lemon/path.h>
1.33 +#include <lemon/tolerance.h>
1.34 +#include <lemon/connectivity.h>
1.35 +
1.36 +namespace lemon {
1.37 +
1.38 + /// \addtogroup shortest_path
1.39 + /// @{
1.40 +
1.41 + /// \brief Implementation of Howard's algorithm for finding a minimum
1.42 + /// mean cycle.
1.43 + ///
1.44 + /// \ref MinMeanCycle implements Howard's algorithm for finding a
1.45 + /// directed cycle of minimum mean length (cost) in a digraph.
1.46 + ///
1.47 + /// \tparam GR The type of the digraph the algorithm runs on.
1.48 + /// \tparam LEN The type of the length map. The default
1.49 + /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
1.50 + ///
1.51 + /// \warning \c LEN::Value must be convertible to \c double.
1.52 +#ifdef DOXYGEN
1.53 + template <typename GR, typename LEN>
1.54 +#else
1.55 + template < typename GR,
1.56 + typename LEN = typename GR::template ArcMap<int> >
1.57 +#endif
1.58 + class MinMeanCycle
1.59 + {
1.60 + public:
1.61 +
1.62 + /// The type of the digraph the algorithm runs on
1.63 + typedef GR Digraph;
1.64 + /// The type of the length map
1.65 + typedef LEN LengthMap;
1.66 + /// The type of the arc lengths
1.67 + typedef typename LengthMap::Value Value;
1.68 + /// The type of the paths
1.69 + typedef lemon::Path<Digraph> Path;
1.70 +
1.71 + private:
1.72 +
1.73 + TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
1.74 +
1.75 + // The digraph the algorithm runs on
1.76 + const Digraph &_gr;
1.77 + // The length of the arcs
1.78 + const LengthMap &_length;
1.79 +
1.80 + // The total length of the found cycle
1.81 + Value _cycle_length;
1.82 + // The number of arcs on the found cycle
1.83 + int _cycle_size;
1.84 + // The found cycle
1.85 + Path *_cycle_path;
1.86 +
1.87 + bool _local_path;
1.88 + bool _cycle_found;
1.89 + Node _cycle_node;
1.90 +
1.91 + typename Digraph::template NodeMap<bool> _reached;
1.92 + typename Digraph::template NodeMap<double> _dist;
1.93 + typename Digraph::template NodeMap<Arc> _policy;
1.94 +
1.95 + typename Digraph::template NodeMap<int> _comp;
1.96 + int _comp_num;
1.97 +
1.98 + std::vector<Node> _nodes;
1.99 + std::vector<Arc> _arcs;
1.100 + Tolerance<double> _tol;
1.101 +
1.102 + public:
1.103 +
1.104 + /// \brief Constructor.
1.105 + ///
1.106 + /// The constructor of the class.
1.107 + ///
1.108 + /// \param digraph The digraph the algorithm runs on.
1.109 + /// \param length The lengths (costs) of the arcs.
1.110 + MinMeanCycle( const Digraph &digraph,
1.111 + const LengthMap &length ) :
1.112 + _gr(digraph), _length(length), _cycle_length(0), _cycle_size(-1),
1.113 + _cycle_path(NULL), _local_path(false), _reached(digraph),
1.114 + _dist(digraph), _policy(digraph), _comp(digraph)
1.115 + {}
1.116 +
1.117 + /// Destructor.
1.118 + ~MinMeanCycle() {
1.119 + if (_local_path) delete _cycle_path;
1.120 + }
1.121 +
1.122 + /// \brief Set the path structure for storing the found cycle.
1.123 + ///
1.124 + /// This function sets an external path structure for storing the
1.125 + /// found cycle.
1.126 + ///
1.127 + /// If you don't call this function before calling \ref run() or
1.128 + /// \ref init(), it will allocate a local \ref Path "path"
1.129 + /// structure. The destuctor deallocates this automatically
1.130 + /// allocated object, of course.
1.131 + ///
1.132 + /// \note The algorithm calls only the \ref lemon::Path::addBack()
1.133 + /// "addBack()" function of the given path structure.
1.134 + ///
1.135 + /// \return <tt>(*this)</tt>
1.136 + ///
1.137 + /// \sa cycle()
1.138 + MinMeanCycle& cyclePath(Path &path) {
1.139 + if (_local_path) {
1.140 + delete _cycle_path;
1.141 + _local_path = false;
1.142 + }
1.143 + _cycle_path = &path;
1.144 + return *this;
1.145 + }
1.146 +
1.147 + /// \name Execution control
1.148 + /// The simplest way to execute the algorithm is to call the \ref run()
1.149 + /// function.\n
1.150 + /// If you only need the minimum mean length, you may call \ref init()
1.151 + /// and \ref findMinMean().
1.152 + /// If you would like to run the algorithm again (e.g. the underlying
1.153 + /// digraph and/or the arc lengths has been modified), you may not
1.154 + /// create a new instance of the class, rather call \ref reset(),
1.155 + /// \ref findMinMean() and \ref findCycle() instead.
1.156 +
1.157 + /// @{
1.158 +
1.159 + /// \brief Run the algorithm.
1.160 + ///
1.161 + /// This function runs the algorithm.
1.162 + ///
1.163 + /// \return \c true if a directed cycle exists in the digraph.
1.164 + ///
1.165 + /// \note Apart from the return value, <tt>mmc.run()</tt> is just a
1.166 + /// shortcut of the following code.
1.167 + /// \code
1.168 + /// mmc.init();
1.169 + /// mmc.findMinMean();
1.170 + /// mmc.findCycle();
1.171 + /// \endcode
1.172 + bool run() {
1.173 + init();
1.174 + return findMinMean() && findCycle();
1.175 + }
1.176 +
1.177 + /// \brief Initialize the internal data structures.
1.178 + ///
1.179 + /// This function initializes the internal data structures.
1.180 + ///
1.181 + /// \sa reset()
1.182 + void init() {
1.183 + _tol.epsilon(1e-6);
1.184 + if (!_cycle_path) {
1.185 + _local_path = true;
1.186 + _cycle_path = new Path;
1.187 + }
1.188 + _cycle_found = false;
1.189 + _comp_num = stronglyConnectedComponents(_gr, _comp);
1.190 + }
1.191 +
1.192 + /// \brief Reset the internal data structures.
1.193 + ///
1.194 + /// This function resets the internal data structures so that
1.195 + /// findMinMean() and findCycle() can be called again (e.g. when the
1.196 + /// underlying digraph and/or the arc lengths has been modified).
1.197 + ///
1.198 + /// \sa init()
1.199 + void reset() {
1.200 + if (_cycle_path) _cycle_path->clear();
1.201 + _cycle_found = false;
1.202 + _comp_num = stronglyConnectedComponents(_gr, _comp);
1.203 + }
1.204 +
1.205 + /// \brief Find the minimum cycle mean.
1.206 + ///
1.207 + /// This function computes all the required data and finds the
1.208 + /// minimum mean length of the directed cycles in the digraph.
1.209 + ///
1.210 + /// \return \c true if a directed cycle exists in the digraph.
1.211 + ///
1.212 + /// \pre \ref init() must be called before using this function.
1.213 + bool findMinMean() {
1.214 + // Find the minimum cycle mean in the components
1.215 + for (int comp = 0; comp < _comp_num; ++comp) {
1.216 + if (!initCurrentComponent(comp)) continue;
1.217 + while (true) {
1.218 + if (!findPolicyCycles()) break;
1.219 + contractPolicyGraph(comp);
1.220 + if (!computeNodeDistances()) break;
1.221 + }
1.222 + }
1.223 + return _cycle_found;
1.224 + }
1.225 +
1.226 + /// \brief Find a minimum mean directed cycle.
1.227 + ///
1.228 + /// This function finds a directed cycle of minimum mean length
1.229 + /// in the digraph using the data computed by findMinMean().
1.230 + ///
1.231 + /// \return \c true if a directed cycle exists in the digraph.
1.232 + ///
1.233 + /// \pre \ref init() and \ref findMinMean() must be called before
1.234 + /// using this function.
1.235 + bool findCycle() {
1.236 + if (!_cycle_found) return false;
1.237 + _cycle_path->addBack(_policy[_cycle_node]);
1.238 + for ( Node v = _cycle_node;
1.239 + (v = _gr.target(_policy[v])) != _cycle_node; ) {
1.240 + _cycle_path->addBack(_policy[v]);
1.241 + }
1.242 + return true;
1.243 + }
1.244 +
1.245 + /// @}
1.246 +
1.247 + /// \name Query Functions
1.248 + /// The result of the algorithm can be obtained using these
1.249 + /// functions.\n
1.250 + /// The algorithm should be executed before using them.
1.251 +
1.252 + /// @{
1.253 +
1.254 + /// \brief Return the total length of the found cycle.
1.255 + ///
1.256 + /// This function returns the total length of the found cycle.
1.257 + ///
1.258 + /// \pre \ref run() or \ref findCycle() must be called before
1.259 + /// using this function.
1.260 + Value cycleLength() const {
1.261 + return _cycle_length;
1.262 + }
1.263 +
1.264 + /// \brief Return the number of arcs on the found cycle.
1.265 + ///
1.266 + /// This function returns the number of arcs on the found cycle.
1.267 + ///
1.268 + /// \pre \ref run() or \ref findCycle() must be called before
1.269 + /// using this function.
1.270 + int cycleArcNum() const {
1.271 + return _cycle_size;
1.272 + }
1.273 +
1.274 + /// \brief Return the mean length of the found cycle.
1.275 + ///
1.276 + /// This function returns the mean length of the found cycle.
1.277 + ///
1.278 + /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
1.279 + /// following code.
1.280 + /// \code
1.281 + /// return double(mmc.cycleLength()) / mmc.cycleArcNum();
1.282 + /// \endcode
1.283 + ///
1.284 + /// \pre \ref run() or \ref findMinMean() must be called before
1.285 + /// using this function.
1.286 + double cycleMean() const {
1.287 + return double(_cycle_length) / _cycle_size;
1.288 + }
1.289 +
1.290 + /// \brief Return the found cycle.
1.291 + ///
1.292 + /// This function returns a const reference to the path structure
1.293 + /// storing the found cycle.
1.294 + ///
1.295 + /// \pre \ref run() or \ref findCycle() must be called before using
1.296 + /// this function.
1.297 + ///
1.298 + /// \sa cyclePath()
1.299 + const Path& cycle() const {
1.300 + return *_cycle_path;
1.301 + }
1.302 +
1.303 + ///@}
1.304 +
1.305 + private:
1.306 +
1.307 + // Initialize the internal data structures for the current strongly
1.308 + // connected component and create the policy graph.
1.309 + // The policy graph can be represented by the _policy map because
1.310 + // the out-degree of every node is 1.
1.311 + bool initCurrentComponent(int comp) {
1.312 + // Find the nodes of the current component
1.313 + _nodes.clear();
1.314 + for (NodeIt n(_gr); n != INVALID; ++n) {
1.315 + if (_comp[n] == comp) _nodes.push_back(n);
1.316 + }
1.317 + if (_nodes.size() <= 1) return false;
1.318 + // Find the arcs of the current component
1.319 + _arcs.clear();
1.320 + for (ArcIt e(_gr); e != INVALID; ++e) {
1.321 + if ( _comp[_gr.source(e)] == comp &&
1.322 + _comp[_gr.target(e)] == comp )
1.323 + _arcs.push_back(e);
1.324 + }
1.325 + // Initialize _reached, _dist, _policy maps
1.326 + for (int i = 0; i < int(_nodes.size()); ++i) {
1.327 + _reached[_nodes[i]] = false;
1.328 + _policy[_nodes[i]] = INVALID;
1.329 + }
1.330 + Node u; Arc e;
1.331 + for (int j = 0; j < int(_arcs.size()); ++j) {
1.332 + e = _arcs[j];
1.333 + u = _gr.source(e);
1.334 + if (!_reached[u] || _length[e] < _dist[u]) {
1.335 + _dist[u] = _length[e];
1.336 + _policy[u] = e;
1.337 + _reached[u] = true;
1.338 + }
1.339 + }
1.340 + return true;
1.341 + }
1.342 +
1.343 + // Find all cycles in the policy graph.
1.344 + // Set _cycle_found to true if a cycle is found and set
1.345 + // _cycle_length, _cycle_size, _cycle_node to represent the minimum
1.346 + // mean cycle in the policy graph.
1.347 + bool findPolicyCycles() {
1.348 + typename Digraph::template NodeMap<int> level(_gr, -1);
1.349 + bool curr_cycle_found = false;
1.350 + Value clength;
1.351 + int csize;
1.352 + int path_cnt = 0;
1.353 + Node u, v;
1.354 + // Searching for cycles
1.355 + for (int i = 0; i < int(_nodes.size()); ++i) {
1.356 + if (level[_nodes[i]] < 0) {
1.357 + u = _nodes[i];
1.358 + level[u] = path_cnt;
1.359 + while (level[u = _gr.target(_policy[u])] < 0)
1.360 + level[u] = path_cnt;
1.361 + if (level[u] == path_cnt) {
1.362 + // A cycle is found
1.363 + curr_cycle_found = true;
1.364 + clength = _length[_policy[u]];
1.365 + csize = 1;
1.366 + for (v = u; (v = _gr.target(_policy[v])) != u; ) {
1.367 + clength += _length[_policy[v]];
1.368 + ++csize;
1.369 + }
1.370 + if ( !_cycle_found ||
1.371 + clength * _cycle_size < _cycle_length * csize ) {
1.372 + _cycle_found = true;
1.373 + _cycle_length = clength;
1.374 + _cycle_size = csize;
1.375 + _cycle_node = u;
1.376 + }
1.377 + }
1.378 + ++path_cnt;
1.379 + }
1.380 + }
1.381 + return curr_cycle_found;
1.382 + }
1.383 +
1.384 + // Contract the policy graph to be connected by cutting all cycles
1.385 + // except for the main cycle (i.e. the minimum mean cycle).
1.386 + void contractPolicyGraph(int comp) {
1.387 + // Find the component of the main cycle using reverse BFS search
1.388 + typename Digraph::template NodeMap<int> found(_gr, false);
1.389 + std::deque<Node> queue;
1.390 + queue.push_back(_cycle_node);
1.391 + found[_cycle_node] = true;
1.392 + Node u, v;
1.393 + while (!queue.empty()) {
1.394 + v = queue.front(); queue.pop_front();
1.395 + for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.396 + u = _gr.source(e);
1.397 + if (_policy[u] == e && !found[u]) {
1.398 + found[u] = true;
1.399 + queue.push_back(u);
1.400 + }
1.401 + }
1.402 + }
1.403 + // Connect all other nodes to this component using reverse BFS search
1.404 + queue.clear();
1.405 + for (int i = 0; i < int(_nodes.size()); ++i)
1.406 + if (found[_nodes[i]]) queue.push_back(_nodes[i]);
1.407 + int found_cnt = queue.size();
1.408 + while (found_cnt < int(_nodes.size())) {
1.409 + v = queue.front(); queue.pop_front();
1.410 + for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.411 + u = _gr.source(e);
1.412 + if (_comp[u] == comp && !found[u]) {
1.413 + found[u] = true;
1.414 + ++found_cnt;
1.415 + _policy[u] = e;
1.416 + queue.push_back(u);
1.417 + }
1.418 + }
1.419 + }
1.420 + }
1.421 +
1.422 + // Compute node distances in the policy graph and update the
1.423 + // policy graph if the node distances can be improved.
1.424 + bool computeNodeDistances() {
1.425 + // Compute node distances using reverse BFS search
1.426 + double cycle_mean = double(_cycle_length) / _cycle_size;
1.427 + typename Digraph::template NodeMap<int> found(_gr, false);
1.428 + std::deque<Node> queue;
1.429 + queue.push_back(_cycle_node);
1.430 + found[_cycle_node] = true;
1.431 + _dist[_cycle_node] = 0;
1.432 + Node u, v;
1.433 + while (!queue.empty()) {
1.434 + v = queue.front(); queue.pop_front();
1.435 + for (InArcIt e(_gr, v); e != INVALID; ++e) {
1.436 + u = _gr.source(e);
1.437 + if (_policy[u] == e && !found[u]) {
1.438 + found[u] = true;
1.439 + _dist[u] = _dist[v] + _length[e] - cycle_mean;
1.440 + queue.push_back(u);
1.441 + }
1.442 + }
1.443 + }
1.444 + // Improving node distances
1.445 + bool improved = false;
1.446 + for (int j = 0; j < int(_arcs.size()); ++j) {
1.447 + Arc e = _arcs[j];
1.448 + u = _gr.source(e); v = _gr.target(e);
1.449 + double delta = _dist[v] + _length[e] - cycle_mean;
1.450 + if (_tol.less(delta, _dist[u])) {
1.451 + improved = true;
1.452 + _dist[u] = delta;
1.453 + _policy[u] = e;
1.454 + }
1.455 + }
1.456 + return improved;
1.457 + }
1.458 +
1.459 + }; //class MinMeanCycle
1.460 +
1.461 + ///@}
1.462 +
1.463 +} //namespace lemon
1.464 +
1.465 +#endif //LEMON_MIN_MEAN_CYCLE_H