COIN-OR::LEMON - Graph Library

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
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
19namespace lemon {
20
21/**
22@defgroup datas Data Structures
23This group contains the several data structures implemented in LEMON.
24*/
25
26/**
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
30
31The implementation of combinatorial algorithms heavily relies on
32efficient graph implementations. LEMON offers data structures which are
33planned to be easily used in an experimental phase of implementation studies,
34and thereafter the program code can be made efficient by small modifications.
35
36The most efficient implementation of diverse applications require the
37usage of different physical graph implementations. These differences
38appear in the size of graph we require to handle, memory or time usage
39limitations or in the set of operations through which the graph can be
40accessed.  LEMON provides several physical graph structures to meet
41the diverging requirements of the possible users.  In order to save on
42running time or on memory usage, some structures may fail to provide
43some graph features like arc/edge or node deletion.
44
45Alteration of standard containers need a very limited number of
46operations, these together satisfy the everyday requirements.
47In the case of graph structures, different operations are needed which do
48not alter the physical graph, but gives another view. If some nodes or
49arcs have to be hidden or the reverse oriented graph have to be used, then
50this is the case. It also may happen that in a flow implementation
51the residual graph can be accessed by another algorithm, or a node-set
52is to be shrunk for another algorithm.
53LEMON also provides a variety of graphs for these requirements called
54\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55in conjunction with other graph representations.
56
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
59with any graph structure.
60
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
62*/
63
64/**
65@defgroup graph_adaptors Adaptor Classes for Graphs
66@ingroup graphs
67\brief Adaptor classes for digraphs and graphs
68
69This group contains several useful adaptor classes for digraphs and graphs.
70
71The main parts of LEMON are the different graph structures, generic
72graph algorithms, graph concepts, which couple them, and graph
73adaptors. While the previous notions are more or less clear, the
74latter one needs further explanation. Graph adaptors are graph classes
75which serve for considering graph structures in different ways.
76
77A short example makes this much clearer.  Suppose that we have an
78instance \c g of a directed graph type, say ListDigraph and an algorithm
79\code
80template <typename Digraph>
81int algorithm(const Digraph&);
82\endcode
83is needed to run on the reverse oriented graph.  It may be expensive
84(in time or in memory usage) to copy \c g with the reversed
85arcs.  In this case, an adaptor class is used, which (according
86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87The adaptor uses the original digraph structure and digraph operations when
88methods of the reversed oriented graph are called.  This means that the adaptor
89have minor memory usage, and do not perform sophisticated algorithmic
90actions.  The purpose of it is to give a tool for the cases when a
91graph have to be used in a specific alteration.  If this alteration is
92obtained by a usual construction like filtering the node or the arc set or
93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
95\code
96template<typename Digraph> class ReverseDigraph;
97\endcode
98template class can be used. The code looks as follows
99\code
100ListDigraph g;
101ReverseDigraph<ListDigraph> rg(g);
102int result = algorithm(rg);
103\endcode
104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
106graph adaptors, complex algorithms can be implemented easily.
107
108In flow, circulation and matching problems, the residual
109graph is of particular importance. Combining an adaptor implementing
110this with shortest path algorithms or minimum mean cycle algorithms,
111a range of weighted and cardinality optimization algorithms can be
112obtained. For other examples, the interested user is referred to the
113detailed documentation of particular adaptors.
114
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
123
124Let us stand one more example here to simplify your work.
125ReverseDigraph has constructor
126\code
127ReverseDigraph(Digraph& digraph);
128\endcode
129This means that in a situation, when a <tt>const %ListDigraph&</tt>
130reference to a graph is given, then it have to be instantiated with
131<tt>Digraph=const %ListDigraph</tt>.
132\code
133int algorithm1(const ListDigraph& g) {
134  ReverseDigraph<const ListDigraph> rg(g);
135  return algorithm2(rg);
136}
137\endcode
138*/
139
140/**
141@defgroup maps Maps
142@ingroup datas
143\brief Map structures implemented in LEMON.
144
145This group contains the map structures implemented in LEMON.
146
147LEMON provides several special purpose maps and map adaptors that e.g. combine
148new maps from existing ones.
149
150<b>See also:</b> \ref map_concepts "Map Concepts".
151*/
152
153/**
154@defgroup graph_maps Graph Maps
155@ingroup maps
156\brief Special graph-related maps.
157
158This group contains maps that are specifically designed to assign
159values to the nodes and arcs/edges of graphs.
160
161If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
163*/
164
165/**
166\defgroup map_adaptors Map Adaptors
167\ingroup maps
168\brief Tools to create new maps from existing ones
169
170This group contains map adaptors that are used to create "implicit"
171maps from other maps.
172
173Most of them are \ref concepts::ReadMap "read-only maps".
174They can make arithmetic and logical operations between one or two maps
175(negation, shifting, addition, multiplication, logical 'and', 'or',
176'not' etc.) or e.g. convert a map to another one of different Value type.
177
178The typical usage of this classes is passing implicit maps to
179algorithms.  If a function type algorithm is called then the function
180type map adaptors can be used comfortable. For example let's see the
181usage of map adaptors with the \c graphToEps() function.
182\code
183  Color nodeColor(int deg) {
184    if (deg >= 2) {
185      return Color(0.5, 0.0, 0.5);
186    } else if (deg == 1) {
187      return Color(1.0, 0.5, 1.0);
188    } else {
189      return Color(0.0, 0.0, 0.0);
190    }
191  }
192
193  Digraph::NodeMap<int> degree_map(graph);
194
195  graphToEps(graph, "graph.eps")
196    .coords(coords).scaleToA4().undirected()
197    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
198    .run();
199\endcode
200The \c functorToMap() function makes an \c int to \c Color map from the
201\c nodeColor() function. The \c composeMap() compose the \c degree_map
202and the previously created map. The composed map is a proper function to
203get the color of each node.
204
205The usage with class type algorithms is little bit harder. In this
206case the function type map adaptors can not be used, because the
207function map adaptors give back temporary objects.
208\code
209  Digraph graph;
210
211  typedef Digraph::ArcMap<double> DoubleArcMap;
212  DoubleArcMap length(graph);
213  DoubleArcMap speed(graph);
214
215  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
216  TimeMap time(length, speed);
217
218  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
219  dijkstra.run(source, target);
220\endcode
221We have a length map and a maximum speed map on the arcs of a digraph.
222The minimum time to pass the arc can be calculated as the division of
223the two maps which can be done implicitly with the \c DivMap template
224class. We use the implicit minimum time map as the length map of the
225\c Dijkstra algorithm.
226*/
227
228/**
229@defgroup paths Path Structures
230@ingroup datas
231\brief %Path structures implemented in LEMON.
232
233This group contains the path structures implemented in LEMON.
234
235LEMON provides flexible data structures to work with paths.
236All of them have similar interfaces and they can be copied easily with
237assignment operators and copy constructors. This makes it easy and
238efficient to have e.g. the Dijkstra algorithm to store its result in
239any kind of path structure.
240
241\sa \ref concepts::Path "Path concept"
242*/
243
244/**
245@defgroup heaps Heap Structures
246@ingroup datas
247\brief %Heap structures implemented in LEMON.
248
249This group contains the heap structures implemented in LEMON.
250
251LEMON provides several heap classes. They are efficient implementations
252of the abstract data type \e priority \e queue. They store items with
253specified values called \e priorities in such a way that finding and
254removing the item with minimum priority are efficient.
255The basic operations are adding and erasing items, changing the priority
256of an item, etc.
257
258Heaps are crucial in several algorithms, such as Dijkstra and Prim.
259The heap implementations have the same interface, thus any of them can be
260used easily in such algorithms.
261
262\sa \ref concepts::Heap "Heap concept"
263*/
264
265/**
266@defgroup matrices Matrices
267@ingroup datas
268\brief Two dimensional data storages implemented in LEMON.
269
270This group contains two dimensional data storages implemented in LEMON.
271*/
272
273/**
274@defgroup auxdat Auxiliary Data Structures
275@ingroup datas
276\brief Auxiliary data structures implemented in LEMON.
277
278This group contains some data structures implemented in LEMON in
279order to make it easier to implement combinatorial algorithms.
280*/
281
282/**
283@defgroup geomdat Geometric Data Structures
284@ingroup auxdat
285\brief Geometric data structures implemented in LEMON.
286
287This group contains geometric data structures implemented in LEMON.
288
289 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
290   vector with the usual operations.
291 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
292   rectangular bounding box of a set of \ref lemon::dim2::Point
293   "dim2::Point"'s.
294*/
295
296/**
297@defgroup matrices Matrices
298@ingroup auxdat
299\brief Two dimensional data storages implemented in LEMON.
300
301This group contains two dimensional data storages implemented in LEMON.
302*/
303
304/**
305@defgroup algs Algorithms
306\brief This group contains the several algorithms
307implemented in LEMON.
308
309This group contains the several algorithms
310implemented in LEMON.
311*/
312
313/**
314@defgroup search Graph Search
315@ingroup algs
316\brief Common graph search algorithms.
317
318This group contains the common graph search algorithms, namely
319\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
320*/
321
322/**
323@defgroup shortest_path Shortest Path Algorithms
324@ingroup algs
325\brief Algorithms for finding shortest paths.
326
327This group contains the algorithms for finding shortest paths in digraphs.
328
329 - \ref Dijkstra algorithm for finding shortest paths from a source node
330   when all arc lengths are non-negative.
331 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
332   from a source node when arc lenghts can be either positive or negative,
333   but the digraph should not contain directed cycles with negative total
334   length.
335 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
336   for solving the \e all-pairs \e shortest \e paths \e problem when arc
337   lenghts can be either positive or negative, but the digraph should
338   not contain directed cycles with negative total length.
339 - \ref Suurballe A successive shortest path algorithm for finding
340   arc-disjoint paths between two nodes having minimum total length.
341*/
342
343/**
344@defgroup spantree Minimum Spanning Tree Algorithms
345@ingroup algs
346\brief Algorithms for finding minimum cost spanning trees and arborescences.
347
348This group contains the algorithms for finding minimum cost spanning
349trees and arborescences.
350*/
351
352/**
353@defgroup max_flow Maximum Flow Algorithms
354@ingroup algs
355\brief Algorithms for finding maximum flows.
356
357This group contains the algorithms for finding maximum flows and
358feasible circulations.
359
360The \e maximum \e flow \e problem is to find a flow of maximum value between
361a single source and a single target. Formally, there is a \f$G=(V,A)\f$
362digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
363\f$s, t \in V\f$ source and target nodes.
364A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
365following optimization problem.
366
367\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
368\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
369    \quad \forall u\in V\setminus\{s,t\} \f]
370\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
371
372LEMON contains several algorithms for solving maximum flow problems:
373- \ref EdmondsKarp Edmonds-Karp algorithm.
374- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
375- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
376- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
377
378In most cases the \ref Preflow "Preflow" algorithm provides the
379fastest method for computing a maximum flow. All implementations
380also provide functions to query the minimum cut, which is the dual
381problem of maximum flow.
382
383\ref Circulation is a preflow push-relabel algorithm implemented directly
384for finding feasible circulations, which is a somewhat different problem,
385but it is strongly related to maximum flow.
386For more information, see \ref Circulation.
387*/
388
389/**
390@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
391@ingroup algs
392
393\brief Algorithms for finding minimum cost flows and circulations.
394
395This group contains the algorithms for finding minimum cost flows and
396circulations. For more information about this problem and its dual
397solution see \ref min_cost_flow "Minimum Cost Flow Problem".
398
399LEMON contains several algorithms for this problem.
400 - \ref NetworkSimplex Primal Network Simplex algorithm with various
401   pivot strategies.
402 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
403   cost scaling.
404 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
405   capacity scaling.
406 - \ref CancelAndTighten The Cancel and Tighten algorithm.
407 - \ref CycleCanceling Cycle-Canceling algorithms.
408
409In general NetworkSimplex is the most efficient implementation,
410but in special cases other algorithms could be faster.
411For example, if the total supply and/or capacities are rather small,
412CapacityScaling is usually the fastest algorithm (without effective scaling).
413*/
414
415/**
416@defgroup min_cut Minimum Cut Algorithms
417@ingroup algs
418
419\brief Algorithms for finding minimum cut in graphs.
420
421This group contains the algorithms for finding minimum cut in graphs.
422
423The \e minimum \e cut \e problem is to find a non-empty and non-complete
424\f$X\f$ subset of the nodes with minimum overall capacity on
425outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
426\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
427cut is the \f$X\f$ solution of the next optimization problem:
428
429\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
430    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
431
432LEMON contains several algorithms related to minimum cut problems:
433
434- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
435  in directed graphs.
436- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
437  calculating minimum cut in undirected graphs.
438- \ref GomoryHu "Gomory-Hu tree computation" for calculating
439  all-pairs minimum cut in undirected graphs.
440
441If you want to find minimum cut just between two distinict nodes,
442see the \ref max_flow "maximum flow problem".
443*/
444
445/**
446@defgroup matching Matching Algorithms
447@ingroup algs
448\brief Algorithms for finding matchings in graphs and bipartite graphs.
449
450This group contains the algorithms for calculating
451matchings in graphs and bipartite graphs. The general matching problem is
452finding a subset of the edges for which each node has at most one incident
453edge.
454
455There are several different algorithms for calculate matchings in
456graphs.  The matching problems in bipartite graphs are generally
457easier than in general graphs. The goal of the matching optimization
458can be finding maximum cardinality, maximum weight or minimum cost
459matching. The search can be constrained to find perfect or
460maximum cardinality matching.
461
462The matching algorithms implemented in LEMON:
463- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
464  for calculating maximum cardinality matching in bipartite graphs.
465- \ref PrBipartiteMatching Push-relabel algorithm
466  for calculating maximum cardinality matching in bipartite graphs.
467- \ref MaxWeightedBipartiteMatching
468  Successive shortest path algorithm for calculating maximum weighted
469  matching and maximum weighted bipartite matching in bipartite graphs.
470- \ref MinCostMaxBipartiteMatching
471  Successive shortest path algorithm for calculating minimum cost maximum
472  matching in bipartite graphs.
473- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
474  maximum cardinality matching in general graphs.
475- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
476  maximum weighted matching in general graphs.
477- \ref MaxWeightedPerfectMatching
478  Edmond's blossom shrinking algorithm for calculating maximum weighted
479  perfect matching in general graphs.
480
481\image html bipartite_matching.png
482\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
483*/
484
485/**
486@defgroup graph_properties Connectivity and Other Graph Properties
487@ingroup algs
488\brief Algorithms for discovering the graph properties
489
490This group contains the algorithms for discovering the graph properties
491like connectivity, bipartiteness, euler property, simplicity etc.
492
493\image html connected_components.png
494\image latex connected_components.eps "Connected components" width=\textwidth
495*/
496
497/**
498@defgroup planar Planarity Embedding and Drawing
499@ingroup algs
500\brief Algorithms for planarity checking, embedding and drawing
501
502This group contains the algorithms for planarity checking,
503embedding and drawing.
504
505\image html planar.png
506\image latex planar.eps "Plane graph" width=\textwidth
507*/
508
509/**
510@defgroup approx Approximation Algorithms
511@ingroup algs
512\brief Approximation algorithms.
513
514This group contains the approximation and heuristic algorithms
515implemented in LEMON.
516*/
517
518/**
519@defgroup auxalg Auxiliary Algorithms
520@ingroup algs
521\brief Auxiliary algorithms implemented in LEMON.
522
523This group contains some algorithms implemented in LEMON
524in order to make it easier to implement complex algorithms.
525*/
526
527/**
528@defgroup gen_opt_group General Optimization Tools
529\brief This group contains some general optimization frameworks
530implemented in LEMON.
531
532This group contains some general optimization frameworks
533implemented in LEMON.
534*/
535
536/**
537@defgroup lp_group Lp and Mip Solvers
538@ingroup gen_opt_group
539\brief Lp and Mip solver interfaces for LEMON.
540
541This group contains Lp and Mip solver interfaces for LEMON. The
542various LP solvers could be used in the same manner with this
543interface.
544*/
545
546/**
547@defgroup lp_utils Tools for Lp and Mip Solvers
548@ingroup lp_group
549\brief Helper tools to the Lp and Mip solvers.
550
551This group adds some helper tools to general optimization framework
552implemented in LEMON.
553*/
554
555/**
556@defgroup metah Metaheuristics
557@ingroup gen_opt_group
558\brief Metaheuristics for LEMON library.
559
560This group contains some metaheuristic optimization tools.
561*/
562
563/**
564@defgroup utils Tools and Utilities
565\brief Tools and utilities for programming in LEMON
566
567Tools and utilities for programming in LEMON.
568*/
569
570/**
571@defgroup gutils Basic Graph Utilities
572@ingroup utils
573\brief Simple basic graph utilities.
574
575This group contains some simple basic graph utilities.
576*/
577
578/**
579@defgroup misc Miscellaneous Tools
580@ingroup utils
581\brief Tools for development, debugging and testing.
582
583This group contains several useful tools for development,
584debugging and testing.
585*/
586
587/**
588@defgroup timecount Time Measuring and Counting
589@ingroup misc
590\brief Simple tools for measuring the performance of algorithms.
591
592This group contains simple tools for measuring the performance
593of algorithms.
594*/
595
596/**
597@defgroup exceptions Exceptions
598@ingroup utils
599\brief Exceptions defined in LEMON.
600
601This group contains the exceptions defined in LEMON.
602*/
603
604/**
605@defgroup io_group Input-Output
606\brief Graph Input-Output methods
607
608This group contains the tools for importing and exporting graphs
609and graph related data. Now it supports the \ref lgf-format
610"LEMON Graph Format", the \c DIMACS format and the encapsulated
611postscript (EPS) format.
612*/
613
614/**
615@defgroup lemon_io LEMON Graph Format
616@ingroup io_group
617\brief Reading and writing LEMON Graph Format.
618
619This group contains methods for reading and writing
620\ref lgf-format "LEMON Graph Format".
621*/
622
623/**
624@defgroup eps_io Postscript Exporting
625@ingroup io_group
626\brief General \c EPS drawer and graph exporter
627
628This group contains general \c EPS drawing methods and special
629graph exporting tools.
630*/
631
632/**
633@defgroup dimacs_group DIMACS Format
634@ingroup io_group
635\brief Read and write files in DIMACS format
636
637Tools to read a digraph from or write it to a file in DIMACS format data.
638*/
639
640/**
641@defgroup nauty_group NAUTY Format
642@ingroup io_group
643\brief Read \e Nauty format
644
645Tool to read graphs from \e Nauty format data.
646*/
647
648/**
649@defgroup concept Concepts
650\brief Skeleton classes and concept checking classes
651
652This group contains the data/algorithm skeletons and concept checking
653classes implemented in LEMON.
654
655The purpose of the classes in this group is fourfold.
656
657- These classes contain the documentations of the %concepts. In order
658  to avoid document multiplications, an implementation of a concept
659  simply refers to the corresponding concept class.
660
661- These classes declare every functions, <tt>typedef</tt>s etc. an
662  implementation of the %concepts should provide, however completely
663  without implementations and real data structures behind the
664  interface. On the other hand they should provide nothing else. All
665  the algorithms working on a data structure meeting a certain concept
666  should compile with these classes. (Though it will not run properly,
667  of course.) In this way it is easily to check if an algorithm
668  doesn't use any extra feature of a certain implementation.
669
670- The concept descriptor classes also provide a <em>checker class</em>
671  that makes it possible to check whether a certain implementation of a
672  concept indeed provides all the required features.
673
674- Finally, They can serve as a skeleton of a new implementation of a concept.
675*/
676
677/**
678@defgroup graph_concepts Graph Structure Concepts
679@ingroup concept
680\brief Skeleton and concept checking classes for graph structures
681
682This group contains the skeletons and concept checking classes of
683graph structures.
684*/
685
686/**
687@defgroup map_concepts Map Concepts
688@ingroup concept
689\brief Skeleton and concept checking classes for maps
690
691This group contains the skeletons and concept checking classes of maps.
692*/
693
694/**
695@defgroup tools Standalone Utility Applications
696
697Some utility applications are listed here.
698
699The standard compilation procedure (<tt>./configure;make</tt>) will compile
700them, as well.
701*/
702
703/**
704\anchor demoprograms
705
706@defgroup demos Demo Programs
707
708Some demo programs are listed here. Their full source codes can be found in
709the \c demo subdirectory of the source tree.
710
711In order to compile them, use the <tt>make demo</tt> or the
712<tt>make check</tt> commands.
713*/
714
715}
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