COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 590:b61354458b59

Last change on this file since 590:b61354458b59 was 590:b61354458b59, checked in by Peter Kovacs <kpeter@…>, 10 years ago

Imporvements for the matching algorithms (#264)

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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 semi_adaptors Semi-Adaptor Classes for Graphs
142@ingroup graphs
143\brief Graph types between real graphs and graph adaptors.
144
145This group contains some graph types between real graphs and graph adaptors.
146These classes wrap graphs to give new functionality as the adaptors do it.
147On the other hand they are not light-weight structures as the adaptors.
148*/
149
150/**
151@defgroup maps Maps
152@ingroup datas
153\brief Map structures implemented in LEMON.
154
155This group contains the map structures implemented in LEMON.
156
157LEMON provides several special purpose maps and map adaptors that e.g. combine
158new maps from existing ones.
159
160<b>See also:</b> \ref map_concepts "Map Concepts".
161*/
162
163/**
164@defgroup graph_maps Graph Maps
165@ingroup maps
166\brief Special graph-related maps.
167
168This group contains maps that are specifically designed to assign
169values to the nodes and arcs/edges of graphs.
170
171If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
172\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
173*/
174
175/**
176\defgroup map_adaptors Map Adaptors
177\ingroup maps
178\brief Tools to create new maps from existing ones
179
180This group contains map adaptors that are used to create "implicit"
181maps from other maps.
182
183Most of them are \ref concepts::ReadMap "read-only maps".
184They can make arithmetic and logical operations between one or two maps
185(negation, shifting, addition, multiplication, logical 'and', 'or',
186'not' etc.) or e.g. convert a map to another one of different Value type.
187
188The typical usage of this classes is passing implicit maps to
189algorithms.  If a function type algorithm is called then the function
190type map adaptors can be used comfortable. For example let's see the
191usage of map adaptors with the \c graphToEps() function.
192\code
193  Color nodeColor(int deg) {
194    if (deg >= 2) {
195      return Color(0.5, 0.0, 0.5);
196    } else if (deg == 1) {
197      return Color(1.0, 0.5, 1.0);
198    } else {
199      return Color(0.0, 0.0, 0.0);
200    }
201  }
202
203  Digraph::NodeMap<int> degree_map(graph);
204
205  graphToEps(graph, "graph.eps")
206    .coords(coords).scaleToA4().undirected()
207    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
208    .run();
209\endcode
210The \c functorToMap() function makes an \c int to \c Color map from the
211\c nodeColor() function. The \c composeMap() compose the \c degree_map
212and the previously created map. The composed map is a proper function to
213get the color of each node.
214
215The usage with class type algorithms is little bit harder. In this
216case the function type map adaptors can not be used, because the
217function map adaptors give back temporary objects.
218\code
219  Digraph graph;
220
221  typedef Digraph::ArcMap<double> DoubleArcMap;
222  DoubleArcMap length(graph);
223  DoubleArcMap speed(graph);
224
225  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
226  TimeMap time(length, speed);
227
228  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
229  dijkstra.run(source, target);
230\endcode
231We have a length map and a maximum speed map on the arcs of a digraph.
232The minimum time to pass the arc can be calculated as the division of
233the two maps which can be done implicitly with the \c DivMap template
234class. We use the implicit minimum time map as the length map of the
235\c Dijkstra algorithm.
236*/
237
238/**
239@defgroup matrices Matrices
240@ingroup datas
241\brief Two dimensional data storages implemented in LEMON.
242
243This group contains two dimensional data storages implemented in LEMON.
244*/
245
246/**
247@defgroup paths Path Structures
248@ingroup datas
249\brief %Path structures implemented in LEMON.
250
251This group contains the path structures implemented in LEMON.
252
253LEMON provides flexible data structures to work with paths.
254All of them have similar interfaces and they can be copied easily with
255assignment operators and copy constructors. This makes it easy and
256efficient to have e.g. the Dijkstra algorithm to store its result in
257any kind of path structure.
258
259\sa lemon::concepts::Path
260*/
261
262/**
263@defgroup auxdat Auxiliary Data Structures
264@ingroup datas
265\brief Auxiliary data structures implemented in LEMON.
266
267This group contains some data structures implemented in LEMON in
268order to make it easier to implement combinatorial algorithms.
269*/
270
271/**
272@defgroup algs Algorithms
273\brief This group contains the several algorithms
274implemented in LEMON.
275
276This group contains the several algorithms
277implemented in LEMON.
278*/
279
280/**
281@defgroup search Graph Search
282@ingroup algs
283\brief Common graph search algorithms.
284
285This group contains the common graph search algorithms, namely
286\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
287*/
288
289/**
290@defgroup shortest_path Shortest Path Algorithms
291@ingroup algs
292\brief Algorithms for finding shortest paths.
293
294This group contains the algorithms for finding shortest paths in digraphs.
295
296 - \ref Dijkstra algorithm for finding shortest paths from a source node
297   when all arc lengths are non-negative.
298 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
299   from a source node when arc lenghts can be either positive or negative,
300   but the digraph should not contain directed cycles with negative total
301   length.
302 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
303   for solving the \e all-pairs \e shortest \e paths \e problem when arc
304   lenghts can be either positive or negative, but the digraph should
305   not contain directed cycles with negative total length.
306 - \ref Suurballe A successive shortest path algorithm for finding
307   arc-disjoint paths between two nodes having minimum total length.
308*/
309
310/**
311@defgroup max_flow Maximum Flow Algorithms
312@ingroup algs
313\brief Algorithms for finding maximum flows.
314
315This group contains the algorithms for finding maximum flows and
316feasible circulations.
317
318The \e maximum \e flow \e problem is to find a flow of maximum value between
319a single source and a single target. Formally, there is a \f$G=(V,A)\f$
320digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
321\f$s, t \in V\f$ source and target nodes.
322A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
323following optimization problem.
324
325\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
326\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
327    \qquad \forall v\in V\setminus\{s,t\} \f]
328\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
329
330LEMON contains several algorithms for solving maximum flow problems:
331- \ref EdmondsKarp Edmonds-Karp algorithm.
332- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
333- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
334- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
335
336In most cases the \ref Preflow "Preflow" algorithm provides the
337fastest method for computing a maximum flow. All implementations
338provides functions to also query the minimum cut, which is the dual
339problem of the maximum flow.
340*/
341
342/**
343@defgroup min_cost_flow Minimum Cost Flow Algorithms
344@ingroup algs
345
346\brief Algorithms for finding minimum cost flows and circulations.
347
348This group contains the algorithms for finding minimum cost flows and
349circulations.
350
351The \e minimum \e cost \e flow \e problem is to find a feasible flow of
352minimum total cost from a set of supply nodes to a set of demand nodes
353in a network with capacity constraints and arc costs.
354Formally, let \f$G=(V,A)\f$ be a digraph,
355\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
356upper bounds for the flow values on the arcs,
357\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
358on the arcs, and
359\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
360of the nodes.
361A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
362the following optimization problem.
363
364\f[ \min\sum_{a\in A} f(a) cost(a) \f]
365\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
366    supply(v) \qquad \forall v\in V \f]
367\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
368
369LEMON contains several algorithms for solving minimum cost flow problems:
370 - \ref CycleCanceling Cycle-canceling algorithms.
371 - \ref CapacityScaling Successive shortest path algorithm with optional
372   capacity scaling.
373 - \ref CostScaling Push-relabel and augment-relabel algorithms based on
374   cost scaling.
375 - \ref NetworkSimplex Primal network simplex algorithm with various
376   pivot strategies.
377*/
378
379/**
380@defgroup min_cut Minimum Cut Algorithms
381@ingroup algs
382
383\brief Algorithms for finding minimum cut in graphs.
384
385This group contains the algorithms for finding minimum cut in graphs.
386
387The \e minimum \e cut \e problem is to find a non-empty and non-complete
388\f$X\f$ subset of the nodes with minimum overall capacity on
389outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
390\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
391cut is the \f$X\f$ solution of the next optimization problem:
392
393\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
394    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
395
396LEMON contains several algorithms related to minimum cut problems:
397
398- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
399  in directed graphs.
400- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
401  calculating minimum cut in undirected graphs.
402- \ref GomoryHu "Gomory-Hu tree computation" for calculating
403  all-pairs minimum cut in undirected graphs.
404
405If you want to find minimum cut just between two distinict nodes,
406see the \ref max_flow "maximum flow problem".
407*/
408
409/**
410@defgroup graph_properties Connectivity and Other Graph Properties
411@ingroup algs
412\brief Algorithms for discovering the graph properties
413
414This group contains the algorithms for discovering the graph properties
415like connectivity, bipartiteness, euler property, simplicity etc.
416
417\image html edge_biconnected_components.png
418\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
419*/
420
421/**
422@defgroup planar Planarity Embedding and Drawing
423@ingroup algs
424\brief Algorithms for planarity checking, embedding and drawing
425
426This group contains the algorithms for planarity checking,
427embedding and drawing.
428
429\image html planar.png
430\image latex planar.eps "Plane graph" width=\textwidth
431*/
432
433/**
434@defgroup matching Matching Algorithms
435@ingroup algs
436\brief Algorithms for finding matchings in graphs and bipartite graphs.
437
438This group contains the algorithms for calculating
439matchings in graphs and bipartite graphs. The general matching problem is
440finding a subset of the edges for which each node has at most one incident
441edge.
442
443There are several different algorithms for calculate matchings in
444graphs.  The matching problems in bipartite graphs are generally
445easier than in general graphs. The goal of the matching optimization
446can be finding maximum cardinality, maximum weight or minimum cost
447matching. The search can be constrained to find perfect or
448maximum cardinality matching.
449
450The matching algorithms implemented in LEMON:
451- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
452  for calculating maximum cardinality matching in bipartite graphs.
453- \ref PrBipartiteMatching Push-relabel algorithm
454  for calculating maximum cardinality matching in bipartite graphs.
455- \ref MaxWeightedBipartiteMatching
456  Successive shortest path algorithm for calculating maximum weighted
457  matching and maximum weighted bipartite matching in bipartite graphs.
458- \ref MinCostMaxBipartiteMatching
459  Successive shortest path algorithm for calculating minimum cost maximum
460  matching in bipartite graphs.
461- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
462  maximum cardinality matching in general graphs.
463- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
464  maximum weighted matching in general graphs.
465- \ref MaxWeightedPerfectMatching
466  Edmond's blossom shrinking algorithm for calculating maximum weighted
467  perfect matching in general graphs.
468
469\image html bipartite_matching.png
470\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
471*/
472
473/**
474@defgroup spantree Minimum Spanning Tree Algorithms
475@ingroup algs
476\brief Algorithms for finding a minimum cost spanning tree in a graph.
477
478This group contains the algorithms for finding a minimum cost spanning
479tree in a graph.
480*/
481
482/**
483@defgroup auxalg Auxiliary Algorithms
484@ingroup algs
485\brief Auxiliary algorithms implemented in LEMON.
486
487This group contains some algorithms implemented in LEMON
488in order to make it easier to implement complex algorithms.
489*/
490
491/**
492@defgroup approx Approximation Algorithms
493@ingroup algs
494\brief Approximation algorithms.
495
496This group contains the approximation and heuristic algorithms
497implemented in LEMON.
498*/
499
500/**
501@defgroup gen_opt_group General Optimization Tools
502\brief This group contains some general optimization frameworks
503implemented in LEMON.
504
505This group contains some general optimization frameworks
506implemented in LEMON.
507*/
508
509/**
510@defgroup lp_group Lp and Mip Solvers
511@ingroup gen_opt_group
512\brief Lp and Mip solver interfaces for LEMON.
513
514This group contains Lp and Mip solver interfaces for LEMON. The
515various LP solvers could be used in the same manner with this
516interface.
517*/
518
519/**
520@defgroup lp_utils Tools for Lp and Mip Solvers
521@ingroup lp_group
522\brief Helper tools to the Lp and Mip solvers.
523
524This group adds some helper tools to general optimization framework
525implemented in LEMON.
526*/
527
528/**
529@defgroup metah Metaheuristics
530@ingroup gen_opt_group
531\brief Metaheuristics for LEMON library.
532
533This group contains some metaheuristic optimization tools.
534*/
535
536/**
537@defgroup utils Tools and Utilities
538\brief Tools and utilities for programming in LEMON
539
540Tools and utilities for programming in LEMON.
541*/
542
543/**
544@defgroup gutils Basic Graph Utilities
545@ingroup utils
546\brief Simple basic graph utilities.
547
548This group contains some simple basic graph utilities.
549*/
550
551/**
552@defgroup misc Miscellaneous Tools
553@ingroup utils
554\brief Tools for development, debugging and testing.
555
556This group contains several useful tools for development,
557debugging and testing.
558*/
559
560/**
561@defgroup timecount Time Measuring and Counting
562@ingroup misc
563\brief Simple tools for measuring the performance of algorithms.
564
565This group contains simple tools for measuring the performance
566of algorithms.
567*/
568
569/**
570@defgroup exceptions Exceptions
571@ingroup utils
572\brief Exceptions defined in LEMON.
573
574This group contains the exceptions defined in LEMON.
575*/
576
577/**
578@defgroup io_group Input-Output
579\brief Graph Input-Output methods
580
581This group contains the tools for importing and exporting graphs
582and graph related data. Now it supports the \ref lgf-format
583"LEMON Graph Format", the \c DIMACS format and the encapsulated
584postscript (EPS) format.
585*/
586
587/**
588@defgroup lemon_io LEMON Graph Format
589@ingroup io_group
590\brief Reading and writing LEMON Graph Format.
591
592This group contains methods for reading and writing
593\ref lgf-format "LEMON Graph Format".
594*/
595
596/**
597@defgroup eps_io Postscript Exporting
598@ingroup io_group
599\brief General \c EPS drawer and graph exporter
600
601This group contains general \c EPS drawing methods and special
602graph exporting tools.
603*/
604
605/**
606@defgroup dimacs_group DIMACS format
607@ingroup io_group
608\brief Read and write files in DIMACS format
609
610Tools to read a digraph from or write it to a file in DIMACS format data.
611*/
612
613/**
614@defgroup nauty_group NAUTY Format
615@ingroup io_group
616\brief Read \e Nauty format
617
618Tool to read graphs from \e Nauty format data.
619*/
620
621/**
622@defgroup concept Concepts
623\brief Skeleton classes and concept checking classes
624
625This group contains the data/algorithm skeletons and concept checking
626classes implemented in LEMON.
627
628The purpose of the classes in this group is fourfold.
629
630- These classes contain the documentations of the %concepts. In order
631  to avoid document multiplications, an implementation of a concept
632  simply refers to the corresponding concept class.
633
634- These classes declare every functions, <tt>typedef</tt>s etc. an
635  implementation of the %concepts should provide, however completely
636  without implementations and real data structures behind the
637  interface. On the other hand they should provide nothing else. All
638  the algorithms working on a data structure meeting a certain concept
639  should compile with these classes. (Though it will not run properly,
640  of course.) In this way it is easily to check if an algorithm
641  doesn't use any extra feature of a certain implementation.
642
643- The concept descriptor classes also provide a <em>checker class</em>
644  that makes it possible to check whether a certain implementation of a
645  concept indeed provides all the required features.
646
647- Finally, They can serve as a skeleton of a new implementation of a concept.
648*/
649
650/**
651@defgroup graph_concepts Graph Structure Concepts
652@ingroup concept
653\brief Skeleton and concept checking classes for graph structures
654
655This group contains the skeletons and concept checking classes of LEMON's
656graph structures and helper classes used to implement these.
657*/
658
659/**
660@defgroup map_concepts Map Concepts
661@ingroup concept
662\brief Skeleton and concept checking classes for maps
663
664This group contains the skeletons and concept checking classes of maps.
665*/
666
667/**
668\anchor demoprograms
669
670@defgroup demos Demo Programs
671
672Some demo programs are listed here. Their full source codes can be found in
673the \c demo subdirectory of the source tree.
674
675In order to compile them, use the <tt>make demo</tt> or the
676<tt>make check</tt> commands.
677*/
678
679/**
680@defgroup tools Standalone Utility Applications
681
682Some utility applications are listed here.
683
684The standard compilation procedure (<tt>./configure;make</tt>) will compile
685them, as well.
686*/
687
688}
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