COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 869:636dadefe1e6

Last change on this file since 869:636dadefe1e6 was 869:636dadefe1e6, checked in by Balazs Dezso <deba@…>, 10 years ago

Add fractional matching algorithms (#314)

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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 algs Algorithms
284\brief This group contains the several algorithms
285implemented in LEMON.
286
287This group contains the several algorithms
288implemented in LEMON.
289*/
290
291/**
292@defgroup search Graph Search
293@ingroup algs
294\brief Common graph search algorithms.
295
296This group contains the common graph search algorithms, namely
297\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
298*/
299
300/**
301@defgroup shortest_path Shortest Path Algorithms
302@ingroup algs
303\brief Algorithms for finding shortest paths.
304
305This group contains the algorithms for finding shortest paths in digraphs.
306
307 - \ref Dijkstra algorithm for finding shortest paths from a source node
308   when all arc lengths are non-negative.
309 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
310   from a source node when arc lenghts can be either positive or negative,
311   but the digraph should not contain directed cycles with negative total
312   length.
313 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
314   for solving the \e all-pairs \e shortest \e paths \e problem when arc
315   lenghts can be either positive or negative, but the digraph should
316   not contain directed cycles with negative total length.
317 - \ref Suurballe A successive shortest path algorithm for finding
318   arc-disjoint paths between two nodes having minimum total length.
319*/
320
321/**
322@defgroup max_flow Maximum Flow Algorithms
323@ingroup algs
324\brief Algorithms for finding maximum flows.
325
326This group contains the algorithms for finding maximum flows and
327feasible circulations.
328
329The \e maximum \e flow \e problem is to find a flow of maximum value between
330a single source and a single target. Formally, there is a \f$G=(V,A)\f$
331digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
332\f$s, t \in V\f$ source and target nodes.
333A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
334following optimization problem.
335
336\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
337\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
338    \quad \forall u\in V\setminus\{s,t\} \f]
339\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
340
341LEMON contains several algorithms for solving maximum flow problems:
342- \ref EdmondsKarp Edmonds-Karp algorithm.
343- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
344- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
345- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
346
347In most cases the \ref Preflow "Preflow" algorithm provides the
348fastest method for computing a maximum flow. All implementations
349also provide functions to query the minimum cut, which is the dual
350problem of maximum flow.
351
352\ref Circulation is a preflow push-relabel algorithm implemented directly
353for finding feasible circulations, which is a somewhat different problem,
354but it is strongly related to maximum flow.
355For more information, see \ref Circulation.
356*/
357
358/**
359@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
360@ingroup algs
361
362\brief Algorithms for finding minimum cost flows and circulations.
363
364This group contains the algorithms for finding minimum cost flows and
365circulations. For more information about this problem and its dual
366solution see \ref min_cost_flow "Minimum Cost Flow Problem".
367
368LEMON contains several algorithms for this problem.
369 - \ref NetworkSimplex Primal Network Simplex algorithm with various
370   pivot strategies.
371 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
372   cost scaling.
373 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
374   capacity scaling.
375 - \ref CancelAndTighten The Cancel and Tighten algorithm.
376 - \ref CycleCanceling Cycle-Canceling algorithms.
377
378In general NetworkSimplex is the most efficient implementation,
379but in special cases other algorithms could be faster.
380For example, if the total supply and/or capacities are rather small,
381CapacityScaling is usually the fastest algorithm (without effective scaling).
382*/
383
384/**
385@defgroup min_cut Minimum Cut Algorithms
386@ingroup algs
387
388\brief Algorithms for finding minimum cut in graphs.
389
390This group contains the algorithms for finding minimum cut in graphs.
391
392The \e minimum \e cut \e problem is to find a non-empty and non-complete
393\f$X\f$ subset of the nodes with minimum overall capacity on
394outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
395\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
396cut is the \f$X\f$ solution of the next optimization problem:
397
398\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
399    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
400
401LEMON contains several algorithms related to minimum cut problems:
402
403- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
404  in directed graphs.
405- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
406  calculating minimum cut in undirected graphs.
407- \ref GomoryHu "Gomory-Hu tree computation" for calculating
408  all-pairs minimum cut in undirected graphs.
409
410If you want to find minimum cut just between two distinict nodes,
411see the \ref max_flow "maximum flow problem".
412*/
413
414/**
415@defgroup graph_properties Connectivity and Other Graph Properties
416@ingroup algs
417\brief Algorithms for discovering the graph properties
418
419This group contains the algorithms for discovering the graph properties
420like connectivity, bipartiteness, euler property, simplicity etc.
421
422\image html edge_biconnected_components.png
423\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
424*/
425
426/**
427@defgroup planar Planarity Embedding and Drawing
428@ingroup algs
429\brief Algorithms for planarity checking, embedding and drawing
430
431This group contains the algorithms for planarity checking,
432embedding and drawing.
433
434\image html planar.png
435\image latex planar.eps "Plane graph" width=\textwidth
436*/
437
438/**
439@defgroup matching Matching Algorithms
440@ingroup algs
441\brief Algorithms for finding matchings in graphs and bipartite graphs.
442
443This group contains the algorithms for calculating
444matchings in graphs and bipartite graphs. The general matching problem is
445finding a subset of the edges for which each node has at most one incident
446edge.
447
448There are several different algorithms for calculate matchings in
449graphs.  The matching problems in bipartite graphs are generally
450easier than in general graphs. The goal of the matching optimization
451can be finding maximum cardinality, maximum weight or minimum cost
452matching. The search can be constrained to find perfect or
453maximum cardinality matching.
454
455The matching algorithms implemented in LEMON:
456- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
457  for calculating maximum cardinality matching in bipartite graphs.
458- \ref PrBipartiteMatching Push-relabel algorithm
459  for calculating maximum cardinality matching in bipartite graphs.
460- \ref MaxWeightedBipartiteMatching
461  Successive shortest path algorithm for calculating maximum weighted
462  matching and maximum weighted bipartite matching in bipartite graphs.
463- \ref MinCostMaxBipartiteMatching
464  Successive shortest path algorithm for calculating minimum cost maximum
465  matching in bipartite graphs.
466- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
467  maximum cardinality matching in general graphs.
468- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
469  maximum weighted matching in general graphs.
470- \ref MaxWeightedPerfectMatching
471  Edmond's blossom shrinking algorithm for calculating maximum weighted
472  perfect matching in general graphs.
473- \ref MaxFractionalMatching Push-relabel algorithm for calculating
474  maximum cardinality fractional matching in general graphs.
475- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
476  maximum weighted fractional matching in general graphs.
477- \ref MaxWeightedPerfectFractionalMatching
478  Augmenting path algorithm for calculating maximum weighted
479  perfect fractional 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 spantree Minimum Spanning Tree Algorithms
487@ingroup algs
488\brief Algorithms for finding minimum cost spanning trees and arborescences.
489
490This group contains the algorithms for finding minimum cost spanning
491trees and arborescences.
492*/
493
494/**
495@defgroup auxalg Auxiliary Algorithms
496@ingroup algs
497\brief Auxiliary algorithms implemented in LEMON.
498
499This group contains some algorithms implemented in LEMON
500in order to make it easier to implement complex algorithms.
501*/
502
503/**
504@defgroup approx Approximation Algorithms
505@ingroup algs
506\brief Approximation algorithms.
507
508This group contains the approximation and heuristic algorithms
509implemented in LEMON.
510*/
511
512/**
513@defgroup gen_opt_group General Optimization Tools
514\brief This group contains some general optimization frameworks
515implemented in LEMON.
516
517This group contains some general optimization frameworks
518implemented in LEMON.
519*/
520
521/**
522@defgroup lp_group Lp and Mip Solvers
523@ingroup gen_opt_group
524\brief Lp and Mip solver interfaces for LEMON.
525
526This group contains Lp and Mip solver interfaces for LEMON. The
527various LP solvers could be used in the same manner with this
528interface.
529*/
530
531/**
532@defgroup lp_utils Tools for Lp and Mip Solvers
533@ingroup lp_group
534\brief Helper tools to the Lp and Mip solvers.
535
536This group adds some helper tools to general optimization framework
537implemented in LEMON.
538*/
539
540/**
541@defgroup metah Metaheuristics
542@ingroup gen_opt_group
543\brief Metaheuristics for LEMON library.
544
545This group contains some metaheuristic optimization tools.
546*/
547
548/**
549@defgroup utils Tools and Utilities
550\brief Tools and utilities for programming in LEMON
551
552Tools and utilities for programming in LEMON.
553*/
554
555/**
556@defgroup gutils Basic Graph Utilities
557@ingroup utils
558\brief Simple basic graph utilities.
559
560This group contains some simple basic graph utilities.
561*/
562
563/**
564@defgroup misc Miscellaneous Tools
565@ingroup utils
566\brief Tools for development, debugging and testing.
567
568This group contains several useful tools for development,
569debugging and testing.
570*/
571
572/**
573@defgroup timecount Time Measuring and Counting
574@ingroup misc
575\brief Simple tools for measuring the performance of algorithms.
576
577This group contains simple tools for measuring the performance
578of algorithms.
579*/
580
581/**
582@defgroup exceptions Exceptions
583@ingroup utils
584\brief Exceptions defined in LEMON.
585
586This group contains the exceptions defined in LEMON.
587*/
588
589/**
590@defgroup io_group Input-Output
591\brief Graph Input-Output methods
592
593This group contains the tools for importing and exporting graphs
594and graph related data. Now it supports the \ref lgf-format
595"LEMON Graph Format", the \c DIMACS format and the encapsulated
596postscript (EPS) format.
597*/
598
599/**
600@defgroup lemon_io LEMON Graph Format
601@ingroup io_group
602\brief Reading and writing LEMON Graph Format.
603
604This group contains methods for reading and writing
605\ref lgf-format "LEMON Graph Format".
606*/
607
608/**
609@defgroup eps_io Postscript Exporting
610@ingroup io_group
611\brief General \c EPS drawer and graph exporter
612
613This group contains general \c EPS drawing methods and special
614graph exporting tools.
615*/
616
617/**
618@defgroup dimacs_group DIMACS format
619@ingroup io_group
620\brief Read and write files in DIMACS format
621
622Tools to read a digraph from or write it to a file in DIMACS format data.
623*/
624
625/**
626@defgroup nauty_group NAUTY Format
627@ingroup io_group
628\brief Read \e Nauty format
629
630Tool to read graphs from \e Nauty format data.
631*/
632
633/**
634@defgroup concept Concepts
635\brief Skeleton classes and concept checking classes
636
637This group contains the data/algorithm skeletons and concept checking
638classes implemented in LEMON.
639
640The purpose of the classes in this group is fourfold.
641
642- These classes contain the documentations of the %concepts. In order
643  to avoid document multiplications, an implementation of a concept
644  simply refers to the corresponding concept class.
645
646- These classes declare every functions, <tt>typedef</tt>s etc. an
647  implementation of the %concepts should provide, however completely
648  without implementations and real data structures behind the
649  interface. On the other hand they should provide nothing else. All
650  the algorithms working on a data structure meeting a certain concept
651  should compile with these classes. (Though it will not run properly,
652  of course.) In this way it is easily to check if an algorithm
653  doesn't use any extra feature of a certain implementation.
654
655- The concept descriptor classes also provide a <em>checker class</em>
656  that makes it possible to check whether a certain implementation of a
657  concept indeed provides all the required features.
658
659- Finally, They can serve as a skeleton of a new implementation of a concept.
660*/
661
662/**
663@defgroup graph_concepts Graph Structure Concepts
664@ingroup concept
665\brief Skeleton and concept checking classes for graph structures
666
667This group contains the skeletons and concept checking classes of LEMON's
668graph structures and helper classes used to implement these.
669*/
670
671/**
672@defgroup map_concepts Map Concepts
673@ingroup concept
674\brief Skeleton and concept checking classes for maps
675
676This group contains the skeletons and concept checking classes of maps.
677*/
678
679/**
680\anchor demoprograms
681
682@defgroup demos Demo Programs
683
684Some demo programs are listed here. Their full source codes can be found in
685the \c demo subdirectory of the source tree.
686
687In order to compile them, use the <tt>make demo</tt> or the
688<tt>make check</tt> commands.
689*/
690
691/**
692@defgroup tools Standalone Utility Applications
693
694Some utility applications are listed here.
695
696The standard compilation procedure (<tt>./configure;make</tt>) will compile
697them, as well.
698*/
699
700}
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