1 | /* -*- C++ -*- |
---|
2 | * |
---|
3 | * This file is a part of LEMON, a generic C++ optimization library |
---|
4 | * |
---|
5 | * Copyright (C) 2003-2008 |
---|
6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
---|
7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
---|
8 | * |
---|
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. |
---|
12 | * |
---|
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 |
---|
15 | * purpose. |
---|
16 | * |
---|
17 | */ |
---|
18 | |
---|
19 | #ifndef LEMON_HARTMANN_ORLIN_H |
---|
20 | #define LEMON_HARTMANN_ORLIN_H |
---|
21 | |
---|
22 | /// \ingroup min_mean_cycle |
---|
23 | /// |
---|
24 | /// \file |
---|
25 | /// \brief Hartmann-Orlin's algorithm for finding a minimum mean cycle. |
---|
26 | |
---|
27 | #include <vector> |
---|
28 | #include <limits> |
---|
29 | #include <lemon/core.h> |
---|
30 | #include <lemon/path.h> |
---|
31 | #include <lemon/tolerance.h> |
---|
32 | #include <lemon/connectivity.h> |
---|
33 | |
---|
34 | namespace lemon { |
---|
35 | |
---|
36 | /// \brief Default traits class of HartmannOrlin algorithm. |
---|
37 | /// |
---|
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. |
---|
42 | #ifdef DOXYGEN |
---|
43 | template <typename GR, typename LEN> |
---|
44 | #else |
---|
45 | template <typename GR, typename LEN, |
---|
46 | bool integer = std::numeric_limits<typename LEN::Value>::is_integer> |
---|
47 | #endif |
---|
48 | struct HartmannOrlinDefaultTraits |
---|
49 | { |
---|
50 | /// The type of the digraph |
---|
51 | typedef GR 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; |
---|
56 | |
---|
57 | /// \brief The large value type used for internal computations |
---|
58 | /// |
---|
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; |
---|
64 | |
---|
65 | /// The tolerance type used for internal computations |
---|
66 | typedef lemon::Tolerance<LargeValue> Tolerance; |
---|
67 | |
---|
68 | /// \brief The path type of the found cycles |
---|
69 | /// |
---|
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 addFront() function. |
---|
73 | typedef lemon::Path<Digraph> Path; |
---|
74 | }; |
---|
75 | |
---|
76 | // Default traits class for integer value types |
---|
77 | template <typename GR, typename LEN> |
---|
78 | struct HartmannOrlinDefaultTraits<GR, LEN, true> |
---|
79 | { |
---|
80 | typedef GR Digraph; |
---|
81 | typedef LEN LengthMap; |
---|
82 | typedef typename LengthMap::Value Value; |
---|
83 | #ifdef LEMON_HAVE_LONG_LONG |
---|
84 | typedef long long LargeValue; |
---|
85 | #else |
---|
86 | typedef long LargeValue; |
---|
87 | #endif |
---|
88 | typedef lemon::Tolerance<LargeValue> Tolerance; |
---|
89 | typedef lemon::Path<Digraph> Path; |
---|
90 | }; |
---|
91 | |
---|
92 | |
---|
93 | /// \addtogroup min_mean_cycle |
---|
94 | /// @{ |
---|
95 | |
---|
96 | /// \brief Implementation of the Hartmann-Orlin algorithm for finding |
---|
97 | /// a minimum mean cycle. |
---|
98 | /// |
---|
99 | /// This class implements the Hartmann-Orlin algorithm for finding |
---|
100 | /// a directed cycle of minimum mean length (cost) in a digraph |
---|
101 | /// \ref amo93networkflows, \ref dasdan98minmeancycle. |
---|
102 | /// It is an improved version of \ref Karp "Karp"'s original algorithm, |
---|
103 | /// it applies an efficient early termination scheme. |
---|
104 | /// It runs in time O(ne) and uses space O(n<sup>2</sup>+e). |
---|
105 | /// |
---|
106 | /// \tparam GR The type of the digraph the algorithm runs on. |
---|
107 | /// \tparam LEN The type of the length map. The default |
---|
108 | /// map type is \ref concepts::Digraph::ArcMap "GR::ArcMap<int>". |
---|
109 | #ifdef DOXYGEN |
---|
110 | template <typename GR, typename LEN, typename TR> |
---|
111 | #else |
---|
112 | template < typename GR, |
---|
113 | typename LEN = typename GR::template ArcMap<int>, |
---|
114 | typename TR = HartmannOrlinDefaultTraits<GR, LEN> > |
---|
115 | #endif |
---|
116 | class HartmannOrlin |
---|
117 | { |
---|
118 | public: |
---|
119 | |
---|
120 | /// The type of the digraph |
---|
121 | typedef typename TR::Digraph Digraph; |
---|
122 | /// The type of the length map |
---|
123 | typedef typename TR::LengthMap LengthMap; |
---|
124 | /// The type of the arc lengths |
---|
125 | typedef typename TR::Value Value; |
---|
126 | |
---|
127 | /// \brief The large value type |
---|
128 | /// |
---|
129 | /// The large value type used for internal computations. |
---|
130 | /// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
---|
131 | /// it is \c long \c long if the \c Value type is integer, |
---|
132 | /// otherwise it is \c double. |
---|
133 | typedef typename TR::LargeValue LargeValue; |
---|
134 | |
---|
135 | /// The tolerance type |
---|
136 | typedef typename TR::Tolerance Tolerance; |
---|
137 | |
---|
138 | /// \brief The path type of the found cycles |
---|
139 | /// |
---|
140 | /// The path type of the found cycles. |
---|
141 | /// Using the \ref HartmannOrlinDefaultTraits "default traits class", |
---|
142 | /// it is \ref lemon::Path "Path<Digraph>". |
---|
143 | typedef typename TR::Path Path; |
---|
144 | |
---|
145 | /// The \ref HartmannOrlinDefaultTraits "traits class" of the algorithm |
---|
146 | typedef TR Traits; |
---|
147 | |
---|
148 | private: |
---|
149 | |
---|
150 | TEMPLATE_DIGRAPH_TYPEDEFS(Digraph); |
---|
151 | |
---|
152 | // Data sturcture for path data |
---|
153 | struct PathData |
---|
154 | { |
---|
155 | LargeValue dist; |
---|
156 | Arc pred; |
---|
157 | PathData(LargeValue d, Arc p = INVALID) : |
---|
158 | dist(d), pred(p) {} |
---|
159 | }; |
---|
160 | |
---|
161 | typedef typename Digraph::template NodeMap<std::vector<PathData> > |
---|
162 | PathDataNodeMap; |
---|
163 | |
---|
164 | private: |
---|
165 | |
---|
166 | // The digraph the algorithm runs on |
---|
167 | const Digraph &_gr; |
---|
168 | // The length of the arcs |
---|
169 | const LengthMap &_length; |
---|
170 | |
---|
171 | // Data for storing the strongly connected components |
---|
172 | int _comp_num; |
---|
173 | typename Digraph::template NodeMap<int> _comp; |
---|
174 | std::vector<std::vector<Node> > _comp_nodes; |
---|
175 | std::vector<Node>* _nodes; |
---|
176 | typename Digraph::template NodeMap<std::vector<Arc> > _out_arcs; |
---|
177 | |
---|
178 | // Data for the found cycles |
---|
179 | bool _curr_found, _best_found; |
---|
180 | LargeValue _curr_length, _best_length; |
---|
181 | int _curr_size, _best_size; |
---|
182 | Node _curr_node, _best_node; |
---|
183 | int _curr_level, _best_level; |
---|
184 | |
---|
185 | Path *_cycle_path; |
---|
186 | bool _local_path; |
---|
187 | |
---|
188 | // Node map for storing path data |
---|
189 | PathDataNodeMap _data; |
---|
190 | // The processed nodes in the last round |
---|
191 | std::vector<Node> _process; |
---|
192 | |
---|
193 | Tolerance _tolerance; |
---|
194 | |
---|
195 | // Infinite constant |
---|
196 | const LargeValue INF; |
---|
197 | |
---|
198 | public: |
---|
199 | |
---|
200 | /// \name Named Template Parameters |
---|
201 | /// @{ |
---|
202 | |
---|
203 | template <typename T> |
---|
204 | struct SetLargeValueTraits : public Traits { |
---|
205 | typedef T LargeValue; |
---|
206 | typedef lemon::Tolerance<T> Tolerance; |
---|
207 | }; |
---|
208 | |
---|
209 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
210 | /// \c LargeValue type. |
---|
211 | /// |
---|
212 | /// \ref named-templ-param "Named parameter" for setting \c LargeValue |
---|
213 | /// type. It is used for internal computations in the algorithm. |
---|
214 | template <typename T> |
---|
215 | struct SetLargeValue |
---|
216 | : public HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > { |
---|
217 | typedef HartmannOrlin<GR, LEN, SetLargeValueTraits<T> > Create; |
---|
218 | }; |
---|
219 | |
---|
220 | template <typename T> |
---|
221 | struct SetPathTraits : public Traits { |
---|
222 | typedef T Path; |
---|
223 | }; |
---|
224 | |
---|
225 | /// \brief \ref named-templ-param "Named parameter" for setting |
---|
226 | /// \c %Path type. |
---|
227 | /// |
---|
228 | /// \ref named-templ-param "Named parameter" for setting the \c %Path |
---|
229 | /// type of the found cycles. |
---|
230 | /// It must conform to the \ref lemon::concepts::Path "Path" concept |
---|
231 | /// and it must have an \c addFront() function. |
---|
232 | template <typename T> |
---|
233 | struct SetPath |
---|
234 | : public HartmannOrlin<GR, LEN, SetPathTraits<T> > { |
---|
235 | typedef HartmannOrlin<GR, LEN, SetPathTraits<T> > Create; |
---|
236 | }; |
---|
237 | |
---|
238 | /// @} |
---|
239 | |
---|
240 | public: |
---|
241 | |
---|
242 | /// \brief Constructor. |
---|
243 | /// |
---|
244 | /// The constructor of the class. |
---|
245 | /// |
---|
246 | /// \param digraph The digraph the algorithm runs on. |
---|
247 | /// \param length The lengths (costs) of the arcs. |
---|
248 | HartmannOrlin( const Digraph &digraph, |
---|
249 | const LengthMap &length ) : |
---|
250 | _gr(digraph), _length(length), _comp(digraph), _out_arcs(digraph), |
---|
251 | _best_found(false), _best_length(0), _best_size(1), |
---|
252 | _cycle_path(NULL), _local_path(false), _data(digraph), |
---|
253 | INF(std::numeric_limits<LargeValue>::has_infinity ? |
---|
254 | std::numeric_limits<LargeValue>::infinity() : |
---|
255 | std::numeric_limits<LargeValue>::max()) |
---|
256 | {} |
---|
257 | |
---|
258 | /// Destructor. |
---|
259 | ~HartmannOrlin() { |
---|
260 | if (_local_path) delete _cycle_path; |
---|
261 | } |
---|
262 | |
---|
263 | /// \brief Set the path structure for storing the found cycle. |
---|
264 | /// |
---|
265 | /// This function sets an external path structure for storing the |
---|
266 | /// found cycle. |
---|
267 | /// |
---|
268 | /// If you don't call this function before calling \ref run() or |
---|
269 | /// \ref findMinMean(), it will allocate a local \ref Path "path" |
---|
270 | /// structure. The destuctor deallocates this automatically |
---|
271 | /// allocated object, of course. |
---|
272 | /// |
---|
273 | /// \note The algorithm calls only the \ref lemon::Path::addFront() |
---|
274 | /// "addFront()" function of the given path structure. |
---|
275 | /// |
---|
276 | /// \return <tt>(*this)</tt> |
---|
277 | HartmannOrlin& cycle(Path &path) { |
---|
278 | if (_local_path) { |
---|
279 | delete _cycle_path; |
---|
280 | _local_path = false; |
---|
281 | } |
---|
282 | _cycle_path = &path; |
---|
283 | return *this; |
---|
284 | } |
---|
285 | |
---|
286 | /// \brief Set the tolerance used by the algorithm. |
---|
287 | /// |
---|
288 | /// This function sets the tolerance object used by the algorithm. |
---|
289 | /// |
---|
290 | /// \return <tt>(*this)</tt> |
---|
291 | HartmannOrlin& tolerance(const Tolerance& tolerance) { |
---|
292 | _tolerance = tolerance; |
---|
293 | return *this; |
---|
294 | } |
---|
295 | |
---|
296 | /// \brief Return a const reference to the tolerance. |
---|
297 | /// |
---|
298 | /// This function returns a const reference to the tolerance object |
---|
299 | /// used by the algorithm. |
---|
300 | const Tolerance& tolerance() const { |
---|
301 | return _tolerance; |
---|
302 | } |
---|
303 | |
---|
304 | /// \name Execution control |
---|
305 | /// The simplest way to execute the algorithm is to call the \ref run() |
---|
306 | /// function.\n |
---|
307 | /// If you only need the minimum mean length, you may call |
---|
308 | /// \ref findMinMean(). |
---|
309 | |
---|
310 | /// @{ |
---|
311 | |
---|
312 | /// \brief Run the algorithm. |
---|
313 | /// |
---|
314 | /// This function runs the algorithm. |
---|
315 | /// It can be called more than once (e.g. if the underlying digraph |
---|
316 | /// and/or the arc lengths have been modified). |
---|
317 | /// |
---|
318 | /// \return \c true if a directed cycle exists in the digraph. |
---|
319 | /// |
---|
320 | /// \note <tt>mmc.run()</tt> is just a shortcut of the following code. |
---|
321 | /// \code |
---|
322 | /// return mmc.findMinMean() && mmc.findCycle(); |
---|
323 | /// \endcode |
---|
324 | bool run() { |
---|
325 | return findMinMean() && findCycle(); |
---|
326 | } |
---|
327 | |
---|
328 | /// \brief Find the minimum cycle mean. |
---|
329 | /// |
---|
330 | /// This function finds the minimum mean length of the directed |
---|
331 | /// cycles in the digraph. |
---|
332 | /// |
---|
333 | /// \return \c true if a directed cycle exists in the digraph. |
---|
334 | bool findMinMean() { |
---|
335 | // Initialization and find strongly connected components |
---|
336 | init(); |
---|
337 | findComponents(); |
---|
338 | |
---|
339 | // Find the minimum cycle mean in the components |
---|
340 | for (int comp = 0; comp < _comp_num; ++comp) { |
---|
341 | if (!initComponent(comp)) continue; |
---|
342 | processRounds(); |
---|
343 | |
---|
344 | // Update the best cycle (global minimum mean cycle) |
---|
345 | if ( _curr_found && (!_best_found || |
---|
346 | _curr_length * _best_size < _best_length * _curr_size) ) { |
---|
347 | _best_found = true; |
---|
348 | _best_length = _curr_length; |
---|
349 | _best_size = _curr_size; |
---|
350 | _best_node = _curr_node; |
---|
351 | _best_level = _curr_level; |
---|
352 | } |
---|
353 | } |
---|
354 | return _best_found; |
---|
355 | } |
---|
356 | |
---|
357 | /// \brief Find a minimum mean directed cycle. |
---|
358 | /// |
---|
359 | /// This function finds a directed cycle of minimum mean length |
---|
360 | /// in the digraph using the data computed by findMinMean(). |
---|
361 | /// |
---|
362 | /// \return \c true if a directed cycle exists in the digraph. |
---|
363 | /// |
---|
364 | /// \pre \ref findMinMean() must be called before using this function. |
---|
365 | bool findCycle() { |
---|
366 | if (!_best_found) return false; |
---|
367 | IntNodeMap reached(_gr, -1); |
---|
368 | int r = _best_level + 1; |
---|
369 | Node u = _best_node; |
---|
370 | while (reached[u] < 0) { |
---|
371 | reached[u] = --r; |
---|
372 | u = _gr.source(_data[u][r].pred); |
---|
373 | } |
---|
374 | r = reached[u]; |
---|
375 | Arc e = _data[u][r].pred; |
---|
376 | _cycle_path->addFront(e); |
---|
377 | _best_length = _length[e]; |
---|
378 | _best_size = 1; |
---|
379 | Node v; |
---|
380 | while ((v = _gr.source(e)) != u) { |
---|
381 | e = _data[v][--r].pred; |
---|
382 | _cycle_path->addFront(e); |
---|
383 | _best_length += _length[e]; |
---|
384 | ++_best_size; |
---|
385 | } |
---|
386 | return true; |
---|
387 | } |
---|
388 | |
---|
389 | /// @} |
---|
390 | |
---|
391 | /// \name Query Functions |
---|
392 | /// The results of the algorithm can be obtained using these |
---|
393 | /// functions.\n |
---|
394 | /// The algorithm should be executed before using them. |
---|
395 | |
---|
396 | /// @{ |
---|
397 | |
---|
398 | /// \brief Return the total length of the found cycle. |
---|
399 | /// |
---|
400 | /// This function returns the total length of the found cycle. |
---|
401 | /// |
---|
402 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
403 | /// using this function. |
---|
404 | LargeValue cycleLength() const { |
---|
405 | return _best_length; |
---|
406 | } |
---|
407 | |
---|
408 | /// \brief Return the number of arcs on the found cycle. |
---|
409 | /// |
---|
410 | /// This function returns the number of arcs on the found cycle. |
---|
411 | /// |
---|
412 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
413 | /// using this function. |
---|
414 | int cycleArcNum() const { |
---|
415 | return _best_size; |
---|
416 | } |
---|
417 | |
---|
418 | /// \brief Return the mean length of the found cycle. |
---|
419 | /// |
---|
420 | /// This function returns the mean length of the found cycle. |
---|
421 | /// |
---|
422 | /// \note <tt>alg.cycleMean()</tt> is just a shortcut of the |
---|
423 | /// following code. |
---|
424 | /// \code |
---|
425 | /// return static_cast<double>(alg.cycleLength()) / alg.cycleArcNum(); |
---|
426 | /// \endcode |
---|
427 | /// |
---|
428 | /// \pre \ref run() or \ref findMinMean() must be called before |
---|
429 | /// using this function. |
---|
430 | double cycleMean() const { |
---|
431 | return static_cast<double>(_best_length) / _best_size; |
---|
432 | } |
---|
433 | |
---|
434 | /// \brief Return the found cycle. |
---|
435 | /// |
---|
436 | /// This function returns a const reference to the path structure |
---|
437 | /// storing the found cycle. |
---|
438 | /// |
---|
439 | /// \pre \ref run() or \ref findCycle() must be called before using |
---|
440 | /// this function. |
---|
441 | const Path& cycle() const { |
---|
442 | return *_cycle_path; |
---|
443 | } |
---|
444 | |
---|
445 | ///@} |
---|
446 | |
---|
447 | private: |
---|
448 | |
---|
449 | // Initialization |
---|
450 | void init() { |
---|
451 | if (!_cycle_path) { |
---|
452 | _local_path = true; |
---|
453 | _cycle_path = new Path; |
---|
454 | } |
---|
455 | _cycle_path->clear(); |
---|
456 | _best_found = false; |
---|
457 | _best_length = 0; |
---|
458 | _best_size = 1; |
---|
459 | _cycle_path->clear(); |
---|
460 | for (NodeIt u(_gr); u != INVALID; ++u) |
---|
461 | _data[u].clear(); |
---|
462 | } |
---|
463 | |
---|
464 | // Find strongly connected components and initialize _comp_nodes |
---|
465 | // and _out_arcs |
---|
466 | void findComponents() { |
---|
467 | _comp_num = stronglyConnectedComponents(_gr, _comp); |
---|
468 | _comp_nodes.resize(_comp_num); |
---|
469 | if (_comp_num == 1) { |
---|
470 | _comp_nodes[0].clear(); |
---|
471 | for (NodeIt n(_gr); n != INVALID; ++n) { |
---|
472 | _comp_nodes[0].push_back(n); |
---|
473 | _out_arcs[n].clear(); |
---|
474 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
---|
475 | _out_arcs[n].push_back(a); |
---|
476 | } |
---|
477 | } |
---|
478 | } else { |
---|
479 | for (int i = 0; i < _comp_num; ++i) |
---|
480 | _comp_nodes[i].clear(); |
---|
481 | for (NodeIt n(_gr); n != INVALID; ++n) { |
---|
482 | int k = _comp[n]; |
---|
483 | _comp_nodes[k].push_back(n); |
---|
484 | _out_arcs[n].clear(); |
---|
485 | for (OutArcIt a(_gr, n); a != INVALID; ++a) { |
---|
486 | if (_comp[_gr.target(a)] == k) _out_arcs[n].push_back(a); |
---|
487 | } |
---|
488 | } |
---|
489 | } |
---|
490 | } |
---|
491 | |
---|
492 | // Initialize path data for the current component |
---|
493 | bool initComponent(int comp) { |
---|
494 | _nodes = &(_comp_nodes[comp]); |
---|
495 | int n = _nodes->size(); |
---|
496 | if (n < 1 || (n == 1 && _out_arcs[(*_nodes)[0]].size() == 0)) { |
---|
497 | return false; |
---|
498 | } |
---|
499 | for (int i = 0; i < n; ++i) { |
---|
500 | _data[(*_nodes)[i]].resize(n + 1, PathData(INF)); |
---|
501 | } |
---|
502 | return true; |
---|
503 | } |
---|
504 | |
---|
505 | // Process all rounds of computing path data for the current component. |
---|
506 | // _data[v][k] is the length of a shortest directed walk from the root |
---|
507 | // node to node v containing exactly k arcs. |
---|
508 | void processRounds() { |
---|
509 | Node start = (*_nodes)[0]; |
---|
510 | _data[start][0] = PathData(0); |
---|
511 | _process.clear(); |
---|
512 | _process.push_back(start); |
---|
513 | |
---|
514 | int k, n = _nodes->size(); |
---|
515 | int next_check = 4; |
---|
516 | bool terminate = false; |
---|
517 | for (k = 1; k <= n && int(_process.size()) < n && !terminate; ++k) { |
---|
518 | processNextBuildRound(k); |
---|
519 | if (k == next_check || k == n) { |
---|
520 | terminate = checkTermination(k); |
---|
521 | next_check = next_check * 3 / 2; |
---|
522 | } |
---|
523 | } |
---|
524 | for ( ; k <= n && !terminate; ++k) { |
---|
525 | processNextFullRound(k); |
---|
526 | if (k == next_check || k == n) { |
---|
527 | terminate = checkTermination(k); |
---|
528 | next_check = next_check * 3 / 2; |
---|
529 | } |
---|
530 | } |
---|
531 | } |
---|
532 | |
---|
533 | // Process one round and rebuild _process |
---|
534 | void processNextBuildRound(int k) { |
---|
535 | std::vector<Node> next; |
---|
536 | Node u, v; |
---|
537 | Arc e; |
---|
538 | LargeValue d; |
---|
539 | for (int i = 0; i < int(_process.size()); ++i) { |
---|
540 | u = _process[i]; |
---|
541 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
---|
542 | e = _out_arcs[u][j]; |
---|
543 | v = _gr.target(e); |
---|
544 | d = _data[u][k-1].dist + _length[e]; |
---|
545 | if (_tolerance.less(d, _data[v][k].dist)) { |
---|
546 | if (_data[v][k].dist == INF) next.push_back(v); |
---|
547 | _data[v][k] = PathData(d, e); |
---|
548 | } |
---|
549 | } |
---|
550 | } |
---|
551 | _process.swap(next); |
---|
552 | } |
---|
553 | |
---|
554 | // Process one round using _nodes instead of _process |
---|
555 | void processNextFullRound(int k) { |
---|
556 | Node u, v; |
---|
557 | Arc e; |
---|
558 | LargeValue d; |
---|
559 | for (int i = 0; i < int(_nodes->size()); ++i) { |
---|
560 | u = (*_nodes)[i]; |
---|
561 | for (int j = 0; j < int(_out_arcs[u].size()); ++j) { |
---|
562 | e = _out_arcs[u][j]; |
---|
563 | v = _gr.target(e); |
---|
564 | d = _data[u][k-1].dist + _length[e]; |
---|
565 | if (_tolerance.less(d, _data[v][k].dist)) { |
---|
566 | _data[v][k] = PathData(d, e); |
---|
567 | } |
---|
568 | } |
---|
569 | } |
---|
570 | } |
---|
571 | |
---|
572 | // Check early termination |
---|
573 | bool checkTermination(int k) { |
---|
574 | typedef std::pair<int, int> Pair; |
---|
575 | typename GR::template NodeMap<Pair> level(_gr, Pair(-1, 0)); |
---|
576 | typename GR::template NodeMap<LargeValue> pi(_gr); |
---|
577 | int n = _nodes->size(); |
---|
578 | LargeValue length; |
---|
579 | int size; |
---|
580 | Node u; |
---|
581 | |
---|
582 | // Search for cycles that are already found |
---|
583 | _curr_found = false; |
---|
584 | for (int i = 0; i < n; ++i) { |
---|
585 | u = (*_nodes)[i]; |
---|
586 | if (_data[u][k].dist == INF) continue; |
---|
587 | for (int j = k; j >= 0; --j) { |
---|
588 | if (level[u].first == i && level[u].second > 0) { |
---|
589 | // A cycle is found |
---|
590 | length = _data[u][level[u].second].dist - _data[u][j].dist; |
---|
591 | size = level[u].second - j; |
---|
592 | if (!_curr_found || length * _curr_size < _curr_length * size) { |
---|
593 | _curr_length = length; |
---|
594 | _curr_size = size; |
---|
595 | _curr_node = u; |
---|
596 | _curr_level = level[u].second; |
---|
597 | _curr_found = true; |
---|
598 | } |
---|
599 | } |
---|
600 | level[u] = Pair(i, j); |
---|
601 | if (j != 0) { |
---|
602 | u = _gr.source(_data[u][j].pred); |
---|
603 | } |
---|
604 | } |
---|
605 | } |
---|
606 | |
---|
607 | // If at least one cycle is found, check the optimality condition |
---|
608 | LargeValue d; |
---|
609 | if (_curr_found && k < n) { |
---|
610 | // Find node potentials |
---|
611 | for (int i = 0; i < n; ++i) { |
---|
612 | u = (*_nodes)[i]; |
---|
613 | pi[u] = INF; |
---|
614 | for (int j = 0; j <= k; ++j) { |
---|
615 | if (_data[u][j].dist < INF) { |
---|
616 | d = _data[u][j].dist * _curr_size - j * _curr_length; |
---|
617 | if (_tolerance.less(d, pi[u])) pi[u] = d; |
---|
618 | } |
---|
619 | } |
---|
620 | } |
---|
621 | |
---|
622 | // Check the optimality condition for all arcs |
---|
623 | bool done = true; |
---|
624 | for (ArcIt a(_gr); a != INVALID; ++a) { |
---|
625 | if (_tolerance.less(_length[a] * _curr_size - _curr_length, |
---|
626 | pi[_gr.target(a)] - pi[_gr.source(a)]) ) { |
---|
627 | done = false; |
---|
628 | break; |
---|
629 | } |
---|
630 | } |
---|
631 | return done; |
---|
632 | } |
---|
633 | return (k == n); |
---|
634 | } |
---|
635 | |
---|
636 | }; //class HartmannOrlin |
---|
637 | |
---|
638 | ///@} |
---|
639 | |
---|
640 | } //namespace lemon |
---|
641 | |
---|
642 | #endif //LEMON_HARTMANN_ORLIN_H |
---|