COIN-OR::LEMON - Graph Library

source: lemon/doc/groups.dox @ 761:98a30824fe36

Last change on this file since 761:98a30824fe36 was 761:98a30824fe36, checked in by Peter Kovacs <kpeter@…>, 10 years ago

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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 lemon::concepts::Path
242*/
243
244/**
245@defgroup auxdat Auxiliary Data Structures
246@ingroup datas
247\brief Auxiliary data structures implemented in LEMON.
248
249This group contains some data structures implemented in LEMON in
250order to make it easier to implement combinatorial algorithms.
251*/
252
253/**
254@defgroup geomdat Geometric Data Structures
255@ingroup auxdat
256\brief Geometric data structures implemented in LEMON.
257
258This group contains geometric data structures implemented in LEMON.
259
260 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
261   vector with the usual operations.
262 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
263   rectangular bounding box of a set of \ref lemon::dim2::Point
264   "dim2::Point"'s.
265*/
266
267/**
268@defgroup matrices Matrices
269@ingroup auxdat
270\brief Two dimensional data storages implemented in LEMON.
271
272This group contains two dimensional data storages implemented in LEMON.
273*/
274
275/**
276@defgroup algs Algorithms
277\brief This group contains the several algorithms
278implemented in LEMON.
279
280This group contains the several algorithms
281implemented in LEMON.
282*/
283
284/**
285@defgroup search Graph Search
286@ingroup algs
287\brief Common graph search algorithms.
288
289This group contains the common graph search algorithms, namely
290\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
291*/
292
293/**
294@defgroup shortest_path Shortest Path Algorithms
295@ingroup algs
296\brief Algorithms for finding shortest paths.
297
298This group contains the algorithms for finding shortest paths in digraphs.
299
300 - \ref Dijkstra algorithm for finding shortest paths from a source node
301   when all arc lengths are non-negative.
302 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
303   from a source node when arc lenghts can be either positive or negative,
304   but the digraph should not contain directed cycles with negative total
305   length.
306 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
307   for solving the \e all-pairs \e shortest \e paths \e problem when arc
308   lenghts can be either positive or negative, but the digraph should
309   not contain directed cycles with negative total length.
310 - \ref Suurballe A successive shortest path algorithm for finding
311   arc-disjoint paths between two nodes having minimum total length.
312*/
313
314/**
315@defgroup spantree Minimum Spanning Tree Algorithms
316@ingroup algs
317\brief Algorithms for finding minimum cost spanning trees and arborescences.
318
319This group contains the algorithms for finding minimum cost spanning
320trees and arborescences.
321*/
322
323/**
324@defgroup max_flow Maximum Flow Algorithms
325@ingroup algs
326\brief Algorithms for finding maximum flows.
327
328This group contains the algorithms for finding maximum flows and
329feasible circulations.
330
331The \e maximum \e flow \e problem is to find a flow of maximum value between
332a single source and a single target. Formally, there is a \f$G=(V,A)\f$
333digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
334\f$s, t \in V\f$ source and target nodes.
335A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
336following optimization problem.
337
338\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
339\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
340    \quad \forall u\in V\setminus\{s,t\} \f]
341\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
342
343LEMON contains several algorithms for solving maximum flow problems:
344- \ref EdmondsKarp Edmonds-Karp algorithm.
345- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
346- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
347- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
348
349In most cases the \ref Preflow "Preflow" algorithm provides the
350fastest method for computing a maximum flow. All implementations
351also provide functions to query the minimum cut, which is the dual
352problem of maximum flow.
353
354\ref Circulation is a preflow push-relabel algorithm implemented directly
355for finding feasible circulations, which is a somewhat different problem,
356but it is strongly related to maximum flow.
357For more information, see \ref Circulation.
358*/
359
360/**
361@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
362@ingroup algs
363
364\brief Algorithms for finding minimum cost flows and circulations.
365
366This group contains the algorithms for finding minimum cost flows and
367circulations. For more information about this problem and its dual
368solution see \ref min_cost_flow "Minimum Cost Flow Problem".
369
370LEMON contains several algorithms for this problem.
371 - \ref NetworkSimplex Primal Network Simplex algorithm with various
372   pivot strategies.
373 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
374   cost scaling.
375 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
376   capacity scaling.
377 - \ref CancelAndTighten The Cancel and Tighten algorithm.
378 - \ref CycleCanceling Cycle-Canceling algorithms.
379
380In general NetworkSimplex is the most efficient implementation,
381but in special cases other algorithms could be faster.
382For example, if the total supply and/or capacities are rather small,
383CapacityScaling is usually the fastest algorithm (without effective scaling).
384*/
385
386/**
387@defgroup min_cut Minimum Cut Algorithms
388@ingroup algs
389
390\brief Algorithms for finding minimum cut in graphs.
391
392This group contains the algorithms for finding minimum cut in graphs.
393
394The \e minimum \e cut \e problem is to find a non-empty and non-complete
395\f$X\f$ subset of the nodes with minimum overall capacity on
396outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
397\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
398cut is the \f$X\f$ solution of the next optimization problem:
399
400\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
401    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
402
403LEMON contains several algorithms related to minimum cut problems:
404
405- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
406  in directed graphs.
407- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
408  calculating minimum cut in undirected graphs.
409- \ref GomoryHu "Gomory-Hu tree computation" for calculating
410  all-pairs minimum cut in undirected graphs.
411
412If you want to find minimum cut just between two distinict nodes,
413see the \ref max_flow "maximum flow problem".
414*/
415
416/**
417@defgroup matching Matching Algorithms
418@ingroup algs
419\brief Algorithms for finding matchings in graphs and bipartite graphs.
420
421This group contains the algorithms for calculating
422matchings in graphs and bipartite graphs. The general matching problem is
423finding a subset of the edges for which each node has at most one incident
424edge.
425
426There are several different algorithms for calculate matchings in
427graphs.  The matching problems in bipartite graphs are generally
428easier than in general graphs. The goal of the matching optimization
429can be finding maximum cardinality, maximum weight or minimum cost
430matching. The search can be constrained to find perfect or
431maximum cardinality matching.
432
433The matching algorithms implemented in LEMON:
434- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
435  for calculating maximum cardinality matching in bipartite graphs.
436- \ref PrBipartiteMatching Push-relabel algorithm
437  for calculating maximum cardinality matching in bipartite graphs.
438- \ref MaxWeightedBipartiteMatching
439  Successive shortest path algorithm for calculating maximum weighted
440  matching and maximum weighted bipartite matching in bipartite graphs.
441- \ref MinCostMaxBipartiteMatching
442  Successive shortest path algorithm for calculating minimum cost maximum
443  matching in bipartite graphs.
444- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
445  maximum cardinality matching in general graphs.
446- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
447  maximum weighted matching in general graphs.
448- \ref MaxWeightedPerfectMatching
449  Edmond's blossom shrinking algorithm for calculating maximum weighted
450  perfect matching in general graphs.
451
452\image html bipartite_matching.png
453\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
454*/
455
456/**
457@defgroup graph_properties Connectivity and Other Graph Properties
458@ingroup algs
459\brief Algorithms for discovering the graph properties
460
461This group contains the algorithms for discovering the graph properties
462like connectivity, bipartiteness, euler property, simplicity etc.
463
464\image html connected_components.png
465\image latex connected_components.eps "Connected components" width=\textwidth
466*/
467
468/**
469@defgroup planar Planarity Embedding and Drawing
470@ingroup algs
471\brief Algorithms for planarity checking, embedding and drawing
472
473This group contains the algorithms for planarity checking,
474embedding and drawing.
475
476\image html planar.png
477\image latex planar.eps "Plane graph" width=\textwidth
478*/
479
480/**
481@defgroup approx Approximation Algorithms
482@ingroup algs
483\brief Approximation algorithms.
484
485This group contains the approximation and heuristic algorithms
486implemented in LEMON.
487*/
488
489/**
490@defgroup auxalg Auxiliary Algorithms
491@ingroup algs
492\brief Auxiliary algorithms implemented in LEMON.
493
494This group contains some algorithms implemented in LEMON
495in order to make it easier to implement complex algorithms.
496*/
497
498/**
499@defgroup gen_opt_group General Optimization Tools
500\brief This group contains some general optimization frameworks
501implemented in LEMON.
502
503This group contains some general optimization frameworks
504implemented in LEMON.
505*/
506
507/**
508@defgroup lp_group Lp and Mip Solvers
509@ingroup gen_opt_group
510\brief Lp and Mip solver interfaces for LEMON.
511
512This group contains Lp and Mip solver interfaces for LEMON. The
513various LP solvers could be used in the same manner with this
514interface.
515*/
516
517/**
518@defgroup lp_utils Tools for Lp and Mip Solvers
519@ingroup lp_group
520\brief Helper tools to the Lp and Mip solvers.
521
522This group adds some helper tools to general optimization framework
523implemented in LEMON.
524*/
525
526/**
527@defgroup metah Metaheuristics
528@ingroup gen_opt_group
529\brief Metaheuristics for LEMON library.
530
531This group contains some metaheuristic optimization tools.
532*/
533
534/**
535@defgroup utils Tools and Utilities
536\brief Tools and utilities for programming in LEMON
537
538Tools and utilities for programming in LEMON.
539*/
540
541/**
542@defgroup gutils Basic Graph Utilities
543@ingroup utils
544\brief Simple basic graph utilities.
545
546This group contains some simple basic graph utilities.
547*/
548
549/**
550@defgroup misc Miscellaneous Tools
551@ingroup utils
552\brief Tools for development, debugging and testing.
553
554This group contains several useful tools for development,
555debugging and testing.
556*/
557
558/**
559@defgroup timecount Time Measuring and Counting
560@ingroup misc
561\brief Simple tools for measuring the performance of algorithms.
562
563This group contains simple tools for measuring the performance
564of algorithms.
565*/
566
567/**
568@defgroup exceptions Exceptions
569@ingroup utils
570\brief Exceptions defined in LEMON.
571
572This group contains the exceptions defined in LEMON.
573*/
574
575/**
576@defgroup io_group Input-Output
577\brief Graph Input-Output methods
578
579This group contains the tools for importing and exporting graphs
580and graph related data. Now it supports the \ref lgf-format
581"LEMON Graph Format", the \c DIMACS format and the encapsulated
582postscript (EPS) format.
583*/
584
585/**
586@defgroup lemon_io LEMON Graph Format
587@ingroup io_group
588\brief Reading and writing LEMON Graph Format.
589
590This group contains methods for reading and writing
591\ref lgf-format "LEMON Graph Format".
592*/
593
594/**
595@defgroup eps_io Postscript Exporting
596@ingroup io_group
597\brief General \c EPS drawer and graph exporter
598
599This group contains general \c EPS drawing methods and special
600graph exporting tools.
601*/
602
603/**
604@defgroup dimacs_group DIMACS Format
605@ingroup io_group
606\brief Read and write files in DIMACS format
607
608Tools to read a digraph from or write it to a file in DIMACS format data.
609*/
610
611/**
612@defgroup nauty_group NAUTY Format
613@ingroup io_group
614\brief Read \e Nauty format
615
616Tool to read graphs from \e Nauty format data.
617*/
618
619/**
620@defgroup concept Concepts
621\brief Skeleton classes and concept checking classes
622
623This group contains the data/algorithm skeletons and concept checking
624classes implemented in LEMON.
625
626The purpose of the classes in this group is fourfold.
627
628- These classes contain the documentations of the %concepts. In order
629  to avoid document multiplications, an implementation of a concept
630  simply refers to the corresponding concept class.
631
632- These classes declare every functions, <tt>typedef</tt>s etc. an
633  implementation of the %concepts should provide, however completely
634  without implementations and real data structures behind the
635  interface. On the other hand they should provide nothing else. All
636  the algorithms working on a data structure meeting a certain concept
637  should compile with these classes. (Though it will not run properly,
638  of course.) In this way it is easily to check if an algorithm
639  doesn't use any extra feature of a certain implementation.
640
641- The concept descriptor classes also provide a <em>checker class</em>
642  that makes it possible to check whether a certain implementation of a
643  concept indeed provides all the required features.
644
645- Finally, They can serve as a skeleton of a new implementation of a concept.
646*/
647
648/**
649@defgroup graph_concepts Graph Structure Concepts
650@ingroup concept
651\brief Skeleton and concept checking classes for graph structures
652
653This group contains the skeletons and concept checking classes of LEMON's
654graph structures and helper classes used to implement these.
655*/
656
657/**
658@defgroup map_concepts Map Concepts
659@ingroup concept
660\brief Skeleton and concept checking classes for maps
661
662This group contains the skeletons and concept checking classes of maps.
663*/
664
665/**
666@defgroup tools Standalone Utility Applications
667
668Some utility applications are listed here.
669
670The standard compilation procedure (<tt>./configure;make</tt>) will compile
671them, as well.
672*/
673
674/**
675\anchor demoprograms
676
677@defgroup demos Demo Programs
678
679Some demo programs are listed here. Their full source codes can be found in
680the \c demo subdirectory of the source tree.
681
682In order to compile them, use the <tt>make demo</tt> or the
683<tt>make check</tt> commands.
684*/
685
686}
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