Test file for the min cost flow algorithms.
3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2008
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
19 #ifndef LEMON_MIN_MEAN_CYCLE_H
20 #define LEMON_MIN_MEAN_CYCLE_H
22 /// \ingroup shortest_path
25 /// \brief Howard's algorithm for finding a minimum mean directed cycle.
28 #include <lemon/graph_utils.h>
29 #include <lemon/path.h>
30 #include <lemon/tolerance.h>
31 #include <lemon/topology.h>
35 /// \addtogroup shortest_path
38 /// \brief Implementation of Howard's algorithm for finding a minimum
39 /// mean directed cycle.
41 /// \ref MinMeanCycle implements Howard's algorithm for finding a
42 /// minimum mean directed cycle.
44 /// \tparam Graph The directed graph type the algorithm runs on.
45 /// \tparam LengthMap The type of the length (cost) map.
47 /// \warning \c LengthMap::Value must be convertible to \c double.
49 /// \author Peter Kovacs
51 template < typename Graph,
52 typename LengthMap = typename Graph::template EdgeMap<int> >
55 GRAPH_TYPEDEFS(typename Graph);
57 typedef typename LengthMap::Value Length;
58 typedef Path<Graph> Path;
62 // The directed graph the algorithm runs on
64 // The length of the edges
65 const LengthMap &_length;
67 // The total length of the found cycle
69 // The number of edges on the found cycle
78 typename Graph::template NodeMap<bool> _reached;
79 typename Graph::template NodeMap<double> _dist;
80 typename Graph::template NodeMap<Edge> _policy;
82 typename Graph::template NodeMap<int> _component;
85 std::vector<Node> _nodes;
86 std::vector<Edge> _edges;
87 Tolerance<double> _tolerance;
91 /// \brief The constructor of the class.
93 /// The constructor of the class.
95 /// \param graph The directed graph the algorithm runs on.
96 /// \param length The length (cost) of the edges.
97 MinMeanCycle( const Graph &graph,
98 const LengthMap &length ) :
99 _graph(graph), _length(length), _cycle_length(0), _cycle_size(-1),
100 _cycle_path(NULL), _local_path(false), _reached(graph),
101 _dist(graph), _policy(graph), _component(graph)
104 /// The destructor of the class.
106 if (_local_path) delete _cycle_path;
109 /// \brief Sets the \ref Path "path" structure for storing the found
112 /// Sets an external \ref Path "path" structure for storing the
115 /// If you don't call this function before calling \ref run() or
116 /// \ref init(), it will allocate a local \ref Path "path"
118 /// The destuctor deallocates this automatically allocated map,
121 /// \note The algorithm calls only the \ref lemon::Path::addBack()
122 /// "addBack()" function of the given \ref Path "path" structure.
124 /// \return <tt>(*this)</tt>
127 MinMeanCycle& cyclePath(Path &path) {
136 /// \name Execution control
137 /// The simplest way to execute the algorithm is to call run().
139 /// If you only need the minimum mean value, you may call init()
140 /// and findMinMean().
142 /// If you would like to run the algorithm again (e.g. the
143 /// underlaying graph and/or the edge costs were modified), you may
144 /// not create a new instance of the class, rather call reset(),
145 /// findMinMean(), and findCycle() instead.
149 /// \brief Runs the algorithm.
151 /// Runs the algorithm.
153 /// \return Returns \c true if a directed cycle exists in the graph.
155 /// \note Apart from the return value, <tt>mmc.run()</tt> is just a
156 /// shortcut of the following code.
159 /// mmc.findMinMean();
164 return findMinMean() && findCycle();
167 /// \brief Initializes the internal data structures.
169 /// Initializes the internal data structures.
173 _tolerance.epsilon(1e-6);
176 _cycle_path = new Path;
178 _cycle_found = false;
179 _component_num = stronglyConnectedComponents(_graph, _component);
182 /// \brief Resets the internal data structures.
184 /// Resets the internal data structures so that \ref findMinMean()
185 /// and \ref findCycle() can be called again (e.g. when the
186 /// underlaying graph has been modified).
190 if (_cycle_path) _cycle_path->clear();
191 _cycle_found = false;
192 _component_num = stronglyConnectedComponents(_graph, _component);
195 /// \brief Finds the minimum cycle mean length in the graph.
197 /// Computes all the required data and finds the minimum cycle mean
198 /// length in the graph.
200 /// \return Returns \c true if a directed cycle exists in the graph.
202 /// \pre \ref init() must be called before using this function.
204 // Finding the minimum mean cycle in the components
205 for (int comp = 0; comp < _component_num; ++comp) {
206 if (!initCurrentComponent(comp)) continue;
208 if (!findPolicyCycles()) break;
209 contractPolicyGraph(comp);
210 if (!computeNodeDistances(comp)) break;
216 /// \brief Finds a critical (minimum mean) directed cycle.
218 /// Finds a critical (minimum mean) directed cycle using the data
219 /// computed in the \ref findMinMean() function.
221 /// \return Returns \c true if a directed cycle exists in the graph.
223 /// \pre \ref init() and \ref findMinMean() must be called before
224 /// using this function.
226 if (!_cycle_found) return false;
227 _cycle_path->addBack(_policy[_cycle_node]);
228 for ( Node v = _cycle_node;
229 (v = _graph.target(_policy[v])) != _cycle_node; ) {
230 _cycle_path->addBack(_policy[v]);
237 /// \name Query Functions
238 /// The result of the algorithm can be obtained using these
240 /// \n run() must be called before using them.
244 /// \brief Returns the total length of the found cycle.
246 /// Returns the total length of the found cycle.
248 /// \pre \ref run() or \ref findMinMean() must be called before
249 /// using this function.
250 Length cycleLength() const {
251 return _cycle_length;
254 /// \brief Returns the number of edges on the found cycle.
256 /// Returns the number of edges on the found cycle.
258 /// \pre \ref run() or \ref findMinMean() must be called before
259 /// using this function.
260 int cycleEdgeNum() const {
264 /// \brief Returns the mean length of the found cycle.
266 /// Returns the mean length of the found cycle.
268 /// \pre \ref run() or \ref findMinMean() must be called before
269 /// using this function.
271 /// \note <tt>mmc.cycleMean()</tt> is just a shortcut of the
274 /// return double(mmc.cycleLength()) / mmc.cycleEdgeNum();
276 double cycleMean() const {
277 return double(_cycle_length) / _cycle_size;
280 /// \brief Returns a const reference to the \ref Path "path"
281 /// structure storing the found cycle.
283 /// Returns a const reference to the \ref Path "path"
284 /// structure storing the found cycle.
286 /// \pre \ref run() or \ref findCycle() must be called before using
290 const Path& cycle() const {
298 // Initializes the internal data structures for the current strongly
299 // connected component and creating the policy graph.
300 // The policy graph can be represented by the _policy map because
301 // the out degree of every node is 1.
302 bool initCurrentComponent(int comp) {
303 // Finding the nodes of the current component
305 for (NodeIt n(_graph); n != INVALID; ++n) {
306 if (_component[n] == comp) _nodes.push_back(n);
308 if (_nodes.size() <= 1) return false;
309 // Finding the edges of the current component
311 for (EdgeIt e(_graph); e != INVALID; ++e) {
312 if ( _component[_graph.source(e)] == comp &&
313 _component[_graph.target(e)] == comp )
316 // Initializing _reached, _dist, _policy maps
317 for (int i = 0; i < int(_nodes.size()); ++i) {
318 _reached[_nodes[i]] = false;
319 _policy[_nodes[i]] = INVALID;
322 for (int j = 0; j < int(_edges.size()); ++j) {
324 u = _graph.source(e);
325 if (!_reached[u] || _length[e] < _dist[u]) {
326 _dist[u] = _length[e];
334 // Finds all cycles in the policy graph.
335 // Sets _cycle_found to true if a cycle is found and sets
336 // _cycle_length, _cycle_size, _cycle_node to represent the minimum
337 // mean cycle in the policy graph.
338 bool findPolicyCycles() {
339 typename Graph::template NodeMap<int> level(_graph, -1);
340 bool curr_cycle_found = false;
345 // Searching for cycles
346 for (int i = 0; i < int(_nodes.size()); ++i) {
347 if (level[_nodes[i]] < 0) {
350 while (level[u = _graph.target(_policy[u])] < 0)
352 if (level[u] == path_cnt) {
354 curr_cycle_found = true;
355 clength = _length[_policy[u]];
357 for (v = u; (v = _graph.target(_policy[v])) != u; ) {
358 clength += _length[_policy[v]];
361 if ( !_cycle_found ||
362 clength * _cycle_size < _cycle_length * csize ) {
364 _cycle_length = clength;
372 return curr_cycle_found;
375 // Contracts the policy graph to be connected by cutting all cycles
376 // except for the main cycle (i.e. the minimum mean cycle).
377 void contractPolicyGraph(int comp) {
378 // Finding the component of the main cycle using
379 // reverse BFS search
380 typename Graph::template NodeMap<int> found(_graph, false);
381 std::deque<Node> queue;
382 queue.push_back(_cycle_node);
383 found[_cycle_node] = true;
385 while (!queue.empty()) {
386 v = queue.front(); queue.pop_front();
387 for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
388 u = _graph.source(e);
389 if (_component[u] == comp && !found[u] && _policy[u] == e) {
395 // Connecting all other nodes to this component using
396 // reverse BFS search
398 for (int i = 0; i < int(_nodes.size()); ++i)
399 if (found[_nodes[i]]) queue.push_back(_nodes[i]);
400 int found_cnt = queue.size();
401 while (found_cnt < int(_nodes.size()) && !queue.empty()) {
402 v = queue.front(); queue.pop_front();
403 for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
404 u = _graph.source(e);
405 if (_component[u] == comp && !found[u]) {
415 // Computes node distances in the policy graph and updates the
416 // policy graph if the node distances can be improved.
417 bool computeNodeDistances(int comp) {
418 // Computing node distances using reverse BFS search
419 double cycle_mean = double(_cycle_length) / _cycle_size;
420 typename Graph::template NodeMap<int> found(_graph, false);
421 std::deque<Node> queue;
422 queue.push_back(_cycle_node);
423 found[_cycle_node] = true;
424 _dist[_cycle_node] = 0;
426 while (!queue.empty()) {
427 v = queue.front(); queue.pop_front();
428 for (InEdgeIt e(_graph, v); e != INVALID; ++e) {
429 u = _graph.source(e);
430 if (_component[u] == comp && !found[u] && _policy[u] == e) {
432 _dist[u] = _dist[v] + _length[e] - cycle_mean;
437 // Improving node distances
438 bool improved = false;
439 for (int j = 0; j < int(_edges.size()); ++j) {
441 u = _graph.source(e); v = _graph.target(e);
442 double delta = _dist[v] + _length[e] - cycle_mean;
443 if (_tolerance.less(delta, _dist[u])) {
452 }; //class MinMeanCycle
458 #endif //LEMON_MIN_MEAN_CYCLE_H