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_HARTMANN_ORLIN_H
20 #define LEMON_HARTMANN_ORLIN_H
22 /// \ingroup shortest_path
25 /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle.
29 #include <lemon/core.h>
30 #include <lemon/path.h>
31 #include <lemon/tolerance.h>
32 #include <lemon/connectivity.h>
36 /// \brief Default traits class of HartmannOrlin algorithm.
38 /// Default traits class of HartmannOrlin algorithm.
39 /// \tparam GR The type of the digraph.
40 /// \tparam LEN The type of the length map.
41 /// It must conform to the \ref concepts::Rea_data "Rea_data" concept.
43 template <typename GR, typename LEN>
45 template <typename GR, typename LEN,
46 bool integer = std::numeric_limits<typename LEN::Value>::is_integer>
48 struct HartmannOrlinDefaultTraits
50 /// The type of the digraph
52 /// The type of the length map
53 typedef LEN LengthMap;
54 /// The type of the arc lengths
55 typedef typename LengthMap::Value Value;
57 /// \brief The large value type used for internal computations
59 /// The large value type used for internal computations.
60 /// It is \c long \c long if the \c Value type is integer,
61 /// otherwise it is \c double.
62 /// \c Value must be convertible to \c LargeValue.
63 typedef double LargeValue;
65 /// The tolerance type used for internal computations
66 typedef lemon::Tolerance<LargeValue> Tolerance;
68 /// \brief The path type of the found cycles
70 /// The path type of the found cycles.
71 /// It must conform to the \ref lemon::concepts::Path "Path" concept
72 /// and it must have an \c addBack() function.
73 typedef lemon::Path<Digraph> Path;
76 // Default traits class for integer value types
77 template <typename GR, typename LEN>
78 struct HartmannOrlinDefaultTraits<GR, LEN, true>
81 typedef LEN LengthMap;
82 typedef typename LengthMap::Value Value;
83 #ifdef LEMON_HAVE_LONG_LONG
84 typedef long long LargeValue;
86 typedef long LargeValue;
88 typedef lemon::Tolerance<LargeValue> Tolerance;
89 typedef lemon::Path<Digraph> Path;
93 /// \addtogroup shortest_path
96 /// \brief Implementation of the Hartmann-Orlin algorithm for finding
97 /// a minimum mean cycle.
99 /// This class implements the Hartmann-Orlin algorithm for finding
100 /// a directed cycle of minimum mean length (cost) in a digraph.
101 /// It is an improved version of \ref Karp "Karp's original algorithm",
102 /// it applies an efficient early termination scheme.
104 /// \tparam GR The type of the digraph the algorithm runs on.
105 /// \tparam LEN The type of the length map. The default
106 /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>".
108 template <typename GR, typename LEN, typename TR>
110 template < typename GR,
111 typename LEN = typename GR::template ArcMap<int>,
112 typename TR = HartmannOrlinDefaultTraits<GR, LEN> >
118 /// The type of the digraph
119 typedef typename TR::Digraph Digraph;
120 /// The type of the length map
121 typedef typename TR::LengthMap LengthMap;
122 /// The type of the arc lengths
123 typedef typename TR::Value Value;
125 /// \brief The large value type
127 /// The large value type used for internal computations.
128 /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
129 /// it is \c long \c long if the \c Value type is integer,
130 /// otherwise it is \c double.
131 typedef typename TR::LargeValue LargeValue;
133 /// The tolerance type
134 typedef typename TR::Tolerance Tolerance;
136 /// \brief The path type of the found cycles
138 /// The path type of the found cycles.
139 /// Using the \ref HartmannOrlinDefaultTraits "default traits class",
140 /// it is \ref lemon::Path "Path<Digraph>".
141 typedef typename TR::Path Path;
143 /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm
148 TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
150 // Data sturcture for path data
156 PathData(bool f = false, LargeValue d = 0, Arc p = INVALID) :
157 found(f), dist(d), pred(p) {}
160 typedef typename Digraph::template NodeMap<std::vector<PathData> >
165 // The digraph the algorithm runs on
167 // The length of the arcs
168 const LengthMap &_length;
170 // Data for storing the strongly connected components
172 typename Digraph::template NodeMap<int> _comp;
173 std::vector<std::vector<Node> > _comp_nodes;
174 std::vector<Node>* _nodes;
175 typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs;
177 // Data for the found cycles
178 bool _curr_found, _best_found;
179 LargeValue _curr_length, _best_length;
180 int _curr_size, _best_size;
181 Node _curr_node, _best_node;
182 int _curr_level, _best_level;
187 // Node map for storing path data
188 PathDataNodeMap _data;
189 // The processed nodes in the last round
190 std::vector<Node> _process;
192 Tolerance _tolerance;
196 /// \name Named Template Parameters
199 template <typename T>
200 struct SetLargeValueTraits : public Traits {
201 typedef T LargeValue;
202 typedef lemon::Tolerance<T> Tolerance;
205 /// \brief \ref named-templ-param "Named parameter" for setting
206 /// \c LargeValue type.
208 /// \ref named-templ-param "Named parameter" for setting \c LargeValue
209 /// type. It is used for internal computations in the algorithm.
210 template <typename T>
212 : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > {
213 typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create;
216 template <typename T>
217 struct SetPathTraits : public Traits {
221 /// \brief \ref named-templ-param "Named parameter" for setting
224 /// \ref named-templ-param "Named parameter" for setting the \c %Path
225 /// type of the found cycles.
226 /// It must conform to the \ref lemon::concepts::Path "Path" concept
227 /// and it must have an \c addFront() function.
228 template <typename T>
230 : public HartmannOrlin<GR, LEN, SetPathTraits<T> > {
231 typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create;
238 /// \brief Constructor.
240 /// The constructor of the class.
242 /// \param digraph The digraph the algorithm runs on.
243 /// \param length The lengths (costs) of the arcs.
244 HartmannOrlin( const Digraph &digraph,
245 const LengthMap &length ) :
246 _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph),
247 _best_found(false), _best_length(0), _best_size(1),
248 _cycle_path(NULL), _local_path(false), _data(digraph)
253 if (_local_path) delete _cycle_path;
256 /// \brief Set the path structure for storing the found cycle.
258 /// This function sets an external path structure for storing the
261 /// If you don't call this function before calling \ref run() or
262 /// \ref findMinMean(), it will allocate a local \ref Path "path"
263 /// structure. The destuctor deallocates this automatically
264 /// allocated object, of course.
266 /// \note The algorithm calls only the \ref lemon::Path::addFront()
267 /// "addFront()" function of the given path structure.
269 /// \return <tt>(*this)</tt>
270 HartmannOrlin& cycle(Path &path) {
279 /// \name Execution control
280 /// The simplest way to execute the algorithm is to call the \ref run()
282 /// If you only need the minimum mean length, you may call
283 /// \ref findMinMean().
287 /// \brief Run the algorithm.
289 /// This function runs the algorithm.
290 /// It can be called more than once (e.g. if the underlying digraph
291 /// and/or the arc lengths have been modified).
293 /// \return \c true if a directed cycle exists in the digraph.
295 /// \note <tt>mmc.run()</tt> is just a shortcut of the following code.
297 /// return mmc.findMinMean() && mmc.findCycle();
300 return findMinMean() && findCycle();
303 /// \brief Find the minimum cycle mean.
305 /// This function finds the minimum mean length of the directed
306 /// cycles in the digraph.
308 /// \return \c true if a directed cycle exists in the digraph.
310 // Initialization and find strongly connected components
314 // Find the minimum cycle mean in the components
315 for (int comp = 0; comp < _comp_num; ++comp) {
316 if (!initComponent(comp)) continue;
319 // Update the best cycle (global minimum mean cycle)
320 if ( _curr_found && (!_best_found ||
321 _curr_length * _best_size < _best_length * _curr_size) ) {
323 _best_length = _curr_length;
324 _best_size = _curr_size;
325 _best_node = _curr_node;
326 _best_level = _curr_level;
332 /// \brief Find a minimum mean directed cycle.
334 /// This function finds a directed cycle of minimum mean length
335 /// in the digraph using the data computed by findMinMean().
337 /// \return \c true if a directed cycle exists in the digraph.
339 /// \pre \ref findMinMean() must be called before using this function.
341 if (!_best_found) return false;
342 IntNodeMap reached(_gr, -1);
343 int r = _best_level + 1;
345 while (reached[u] < 0) {
347 u = _gr.source(_data[u][r].pred);
350 Arc e = _data[u][r].pred;
351 _cycle_path->addFront(e);
352 _best_length = _length[e];
355 while ((v = _gr.source(e)) != u) {
356 e = _data[v][--r].pred;
357 _cycle_path->addFront(e);
358 _best_length += _length[e];
366 /// \name Query Functions
367 /// The results of the algorithm can be obtained using these
369 /// The algorithm should be executed before using them.
373 /// \brief Return the total length of the found cycle.
375 /// This function returns the total length of the found cycle.
377 /// \pre \ref run() or \ref findMinMean() must be called before
378 /// using this function.
379 LargeValue cycleLength() const {
383 /// \brief Return the number of arcs on the found cycle.
385 /// This function returns the number of arcs on the found cycle.
387 /// \pre \ref run() or \ref findMinMean() must be called before
388 /// using this function.
389 int cycleArcNum() const {
393 /// \brief Return the mean length of the found cycle.
395 /// This function returns the mean length of the found cycle.
397 /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the
400 /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum();
403 /// \pre \ref run() or \ref findMinMean() must be called before
404 /// using this function.
405 double cycleMean() const {
406 return static_cast<double>(_best_length) / _best_size;
409 /// \brief Return the found cycle.
411 /// This function returns a const reference to the path structure
412 /// storing the found cycle.
414 /// \pre \ref run() or \ref findCycle() must be called before using
416 const Path& cycle() const {
428 _cycle_path = new Path;
430 _cycle_path->clear();
434 _cycle_path->clear();
435 for (NodeIt u(_gr); u != INVALID; ++u)
439 // Find strongly connected components and initialize _comp_nodes
441 void findComponents() {
442 _comp_num = stronglyConnectedComponents(_gr, _comp);
443 _comp_nodes.resize(_comp_num);
444 if (_comp_num == 1) {
445 _comp_nodes[0].clear();
446 for (NodeIt n(_gr); n != INVALID; ++n) {
447 _comp_nodes[0].push_back(n);
448 _out_arcs[n].clear();
449 for (OutArcIt a(_gr, n); a != INVALID; ++a) {
450 _out_arcs[n].push_back(a);
454 for (int i = 0; i < _comp_num; ++i)
455 _comp_nodes[i].clear();
456 for (NodeIt n(_gr); n != INVALID; ++n) {
458 _comp_nodes[k].push_back(n);
459 _out_arcs[n].clear();
460 for (OutArcIt a(_gr, n); a != INVALID; ++a) {
461 if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a);
467 // Initialize path data for the current component
468 bool initComponent(int comp) {
469 _nodes = &(_comp_nodes[comp]);
470 int n = _nodes->size();
471 if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) {
474 for (int i = 0; i < n; ++i) {
475 _data[(*_nodes)[i]].resize(n + 1);
480 // Process all rounds of computing path data for the current component.
481 // _data[v][k] is the length of a shortest directed walk from the root
482 // node to node v containing exactly k arcs.
483 void processRounds() {
484 Node start = (*_nodes)[0];
485 _data[start][0] = PathData(true, 0);
487 _process.push_back(start);
489 int k, n = _nodes->size();
491 bool terminate = false;
492 for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) {
493 processNextBuildRound(k);
494 if (k == next_check || k == n) {
495 terminate = checkTermination(k);
496 next_check = next_check * 3 / 2;
499 for ( ; k <= n && !terminate; ++k) {
500 processNextFullRound(k);
501 if (k == next_check || k == n) {
502 terminate = checkTermination(k);
503 next_check = next_check * 3 / 2;
508 // Process one round and rebuild _process
509 void processNextBuildRound(int k) {
510 std::vector<Node> next;
514 for (int i = 0; i < int(_process.size()); ++i) {
516 for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
519 d = _data[u][k-1].dist + _length[e];
520 if (!_data[v][k].found) {
522 _data[v][k] = PathData(true, _data[u][k-1].dist + _length[e], e);
524 else if (_tolerance.less(d, _data[v][k].dist)) {
525 _data[v][k] = PathData(true, d, e);
532 // Process one round using _nodes instead of _process
533 void processNextFullRound(int k) {
537 for (int i = 0; i < int(_nodes->size()); ++i) {
539 for (int j = 0; j < int(_out_arcs[u].size()); ++j) {
542 d = _data[u][k-1].dist + _length[e];
543 if (!_data[v][k].found || _tolerance.less(d, _data[v][k].dist)) {
544 _data[v][k] = PathData(true, d, e);
550 // Check early termination
551 bool checkTermination(int k) {
552 typedef std::pair<int, int> Pair;
553 typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0));
554 typename GR::template NodeMap<LargeValue> pi(_gr);
555 int n = _nodes->size();
560 // Search for cycles that are already found
562 for (int i = 0; i < n; ++i) {
564 if (!_data[u][k].found) continue;
565 for (int j = k; j >= 0; --j) {
566 if (level[u].first == i && level[u].second > 0) {
568 length = _data[u][level[u].second].dist - _data[u][j].dist;
569 size = level[u].second - j;
570 if (!_curr_found || length * _curr_size < _curr_length * size) {
571 _curr_length = length;
574 _curr_level = level[u].second;
578 level[u] = Pair(i, j);
579 u = _gr.source(_data[u][j].pred);
583 // If at least one cycle is found, check the optimality condition
585 if (_curr_found && k < n) {
586 // Find node potentials
587 for (int i = 0; i < n; ++i) {
589 pi[u] = std::numeric_limits<LargeValue>::max();
590 for (int j = 0; j <= k; ++j) {
591 d = _data[u][j].dist * _curr_size - j * _curr_length;
592 if (_data[u][j].found && _tolerance.less(d, pi[u])) {
598 // Check the optimality condition for all arcs
600 for (ArcIt a(_gr); a != INVALID; ++a) {
601 if (_tolerance.less(_length[a] * _curr_size - _curr_length,
602 pi[_gr.target(a)] - pi[_gr.source(a)]) ) {
612 }; //class HartmannOrlin
618 #endif //LEMON_HARTMANN_ORLIN_H