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) 2003-2010
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 auxdat Auxiliary Data Structures
267@ingroup datas
268\brief Auxiliary data structures implemented in LEMON.
269
270This group contains some data structures implemented in LEMON in
271order to make it easier to implement combinatorial algorithms.
272*/
273
274/**
275@defgroup geomdat Geometric Data Structures
276@ingroup auxdat
277\brief Geometric data structures implemented in LEMON.
278
279This group contains geometric data structures implemented in LEMON.
280
281 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
282   vector with the usual operations.
283 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
284   rectangular bounding box of a set of \ref lemon::dim2::Point
285   "dim2::Point"'s.
286*/
287
288/**
289@defgroup matrices Matrices
290@ingroup auxdat
291\brief Two dimensional data storages implemented in LEMON.
292
293This group contains two dimensional data storages implemented in LEMON.
294*/
295
296/**
297@defgroup algs Algorithms
298\brief This group contains the several algorithms
299implemented in LEMON.
300
301This group contains the several algorithms
302implemented in LEMON.
303*/
304
305/**
306@defgroup search Graph Search
307@ingroup algs
308\brief Common graph search algorithms.
309
310This group contains the common graph search algorithms, namely
311\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
312\ref clrs01algorithms.
313*/
314
315/**
316@defgroup shortest_path Shortest Path Algorithms
317@ingroup algs
318\brief Algorithms for finding shortest paths.
319
320This group contains the algorithms for finding shortest paths in digraphs
321\ref clrs01algorithms.
322
323 - \ref Dijkstra algorithm for finding shortest paths from a source node
324   when all arc lengths are non-negative.
325 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
326   from a source node when arc lenghts can be either positive or negative,
327   but the digraph should not contain directed cycles with negative total
328   length.
329 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
330   for solving the \e all-pairs \e shortest \e paths \e problem when arc
331   lenghts can be either positive or negative, but the digraph should
332   not contain directed cycles with negative total length.
333 - \ref Suurballe A successive shortest path algorithm for finding
334   arc-disjoint paths between two nodes having minimum total length.
335*/
336
337/**
338@defgroup spantree Minimum Spanning Tree Algorithms
339@ingroup algs
340\brief Algorithms for finding minimum cost spanning trees and arborescences.
341
342This group contains the algorithms for finding minimum cost spanning
343trees and arborescences \ref clrs01algorithms.
344*/
345
346/**
347@defgroup max_flow Maximum Flow Algorithms
348@ingroup algs
349\brief Algorithms for finding maximum flows.
350
351This group contains the algorithms for finding maximum flows and
352feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
353
354The \e maximum \e flow \e problem is to find a flow of maximum value between
355a single source and a single target. Formally, there is a \f$G=(V,A)\f$
356digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
357\f$s, t \in V\f$ source and target nodes.
358A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
359following optimization problem.
360
361\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
362\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
363    \quad \forall u\in V\setminus\{s,t\} \f]
364\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
365
366LEMON contains several algorithms for solving maximum flow problems:
367- \ref EdmondsKarp Edmonds-Karp algorithm
368  \ref edmondskarp72theoretical.
369- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
370  \ref goldberg88newapproach.
371- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
372  \ref dinic70algorithm, \ref sleator83dynamic.
373- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
374  \ref goldberg88newapproach, \ref sleator83dynamic.
375
376In most cases the \ref Preflow algorithm provides the
377fastest method for computing a maximum flow. All implementations
378also provide functions to query the minimum cut, which is the dual
379problem of maximum flow.
380
381\ref Circulation is a preflow push-relabel algorithm implemented directly
382for finding feasible circulations, which is a somewhat different problem,
383but it is strongly related to maximum flow.
384For more information, see \ref Circulation.
385*/
386
387/**
388@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
389@ingroup algs
390
391\brief Algorithms for finding minimum cost flows and circulations.
392
393This group contains the algorithms for finding minimum cost flows and
394circulations \ref amo93networkflows. For more information about this
395problem and its dual solution, see \ref min_cost_flow
396"Minimum Cost Flow Problem".
397
398LEMON contains several algorithms for this problem.
399 - \ref NetworkSimplex Primal Network Simplex algorithm with various
400   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
401 - \ref CostScaling Cost Scaling algorithm based on push/augment and
402   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
403   \ref bunnagel98efficient.
404 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
405   shortest path method \ref edmondskarp72theoretical.
406 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
407   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
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 min_mean_cycle Minimum Mean Cycle Algorithms
447@ingroup algs
448\brief Algorithms for finding minimum mean cycles.
449
450This group contains the algorithms for finding minimum mean cycles
451\ref clrs01algorithms, \ref amo93networkflows.
452
453The \e minimum \e mean \e cycle \e problem is to find a directed cycle
454of minimum mean length (cost) in a digraph.
455The mean length of a cycle is the average length of its arcs, i.e. the
456ratio between the total length of the cycle and the number of arcs on it.
457
458This problem has an important connection to \e conservative \e length
459\e functions, too. A length function on the arcs of a digraph is called
460conservative if and only if there is no directed cycle of negative total
461length. For an arbitrary length function, the negative of the minimum
462cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
463arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
464function.
465
466LEMON contains three algorithms for solving the minimum mean cycle problem:
467- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
468  \ref dasdan98minmeancycle.
469- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
470  version of Karp's algorithm \ref dasdan98minmeancycle.
471- \ref HowardMmc Howard's policy iteration algorithm
472  \ref dasdan98minmeancycle.
473
474In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
475most efficient one, though the best known theoretical bound on its running
476time is exponential.
477Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
478run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
479typically faster due to the applied early termination scheme.
480*/
481
482/**
483@defgroup matching Matching Algorithms
484@ingroup algs
485\brief Algorithms for finding matchings in graphs and bipartite graphs.
486
487This group contains the algorithms for calculating
488matchings in graphs and bipartite graphs. The general matching problem is
489finding a subset of the edges for which each node has at most one incident
490edge.
491
492There are several different algorithms for calculate matchings in
493graphs.  The matching problems in bipartite graphs are generally
494easier than in general graphs. The goal of the matching optimization
495can be finding maximum cardinality, maximum weight or minimum cost
496matching. The search can be constrained to find perfect or
497maximum cardinality matching.
498
499The matching algorithms implemented in LEMON:
500- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
501  for calculating maximum cardinality matching in bipartite graphs.
502- \ref PrBipartiteMatching Push-relabel algorithm
503  for calculating maximum cardinality matching in bipartite graphs.
504- \ref MaxWeightedBipartiteMatching
505  Successive shortest path algorithm for calculating maximum weighted
506  matching and maximum weighted bipartite matching in bipartite graphs.
507- \ref MinCostMaxBipartiteMatching
508  Successive shortest path algorithm for calculating minimum cost maximum
509  matching in bipartite graphs.
510- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
511  maximum cardinality matching in general graphs.
512- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
513  maximum weighted matching in general graphs.
514- \ref MaxWeightedPerfectMatching
515  Edmond's blossom shrinking algorithm for calculating maximum weighted
516  perfect matching in general graphs.
517- \ref MaxFractionalMatching Push-relabel algorithm for calculating
518  maximum cardinality fractional matching in general graphs.
519- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
520  maximum weighted fractional matching in general graphs.
521- \ref MaxWeightedPerfectFractionalMatching
522  Augmenting path algorithm for calculating maximum weighted
523  perfect fractional matching in general graphs.
524
525\image html matching.png
526\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
527*/
528
529/**
530@defgroup graph_properties Connectivity and Other Graph Properties
531@ingroup algs
532\brief Algorithms for discovering the graph properties
533
534This group contains the algorithms for discovering the graph properties
535like connectivity, bipartiteness, euler property, simplicity etc.
536
537\image html connected_components.png
538\image latex connected_components.eps "Connected components" width=\textwidth
539*/
540
541/**
542@defgroup planar Planarity Embedding and Drawing
543@ingroup algs
544\brief Algorithms for planarity checking, embedding and drawing
545
546This group contains the algorithms for planarity checking,
547embedding and drawing.
548
549\image html planar.png
550\image latex planar.eps "Plane graph" width=\textwidth
551*/
552
553/**
554@defgroup approx Approximation Algorithms
555@ingroup algs
556\brief Approximation algorithms.
557
558This group contains the approximation and heuristic algorithms
559implemented in LEMON.
560*/
561
562/**
563@defgroup auxalg Auxiliary Algorithms
564@ingroup algs
565\brief Auxiliary algorithms implemented in LEMON.
566
567This group contains some algorithms implemented in LEMON
568in order to make it easier to implement complex algorithms.
569*/
570
571/**
572@defgroup gen_opt_group General Optimization Tools
573\brief This group contains some general optimization frameworks
574implemented in LEMON.
575
576This group contains some general optimization frameworks
577implemented in LEMON.
578*/
579
580/**
581@defgroup lp_group LP and MIP Solvers
582@ingroup gen_opt_group
583\brief LP and MIP solver interfaces for LEMON.
584
585This group contains LP and MIP solver interfaces for LEMON.
586Various LP solvers could be used in the same manner with this
587high-level interface.
588
589The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
590\ref cplex, \ref soplex.
591*/
592
593/**
594@defgroup lp_utils Tools for Lp and Mip Solvers
595@ingroup lp_group
596\brief Helper tools to the Lp and Mip solvers.
597
598This group adds some helper tools to general optimization framework
599implemented in LEMON.
600*/
601
602/**
603@defgroup metah Metaheuristics
604@ingroup gen_opt_group
605\brief Metaheuristics for LEMON library.
606
607This group contains some metaheuristic optimization tools.
608*/
609
610/**
611@defgroup utils Tools and Utilities
612\brief Tools and utilities for programming in LEMON
613
614Tools and utilities for programming in LEMON.
615*/
616
617/**
618@defgroup gutils Basic Graph Utilities
619@ingroup utils
620\brief Simple basic graph utilities.
621
622This group contains some simple basic graph utilities.
623*/
624
625/**
626@defgroup misc Miscellaneous Tools
627@ingroup utils
628\brief Tools for development, debugging and testing.
629
630This group contains several useful tools for development,
631debugging and testing.
632*/
633
634/**
635@defgroup timecount Time Measuring and Counting
636@ingroup misc
637\brief Simple tools for measuring the performance of algorithms.
638
639This group contains simple tools for measuring the performance
640of algorithms.
641*/
642
643/**
644@defgroup exceptions Exceptions
645@ingroup utils
646\brief Exceptions defined in LEMON.
647
648This group contains the exceptions defined in LEMON.
649*/
650
651/**
652@defgroup io_group Input-Output
653\brief Graph Input-Output methods
654
655This group contains the tools for importing and exporting graphs
656and graph related data. Now it supports the \ref lgf-format
657"LEMON Graph Format", the \c DIMACS format and the encapsulated
658postscript (EPS) format.
659*/
660
661/**
662@defgroup lemon_io LEMON Graph Format
663@ingroup io_group
664\brief Reading and writing LEMON Graph Format.
665
666This group contains methods for reading and writing
667\ref lgf-format "LEMON Graph Format".
668*/
669
670/**
671@defgroup eps_io Postscript Exporting
672@ingroup io_group
673\brief General \c EPS drawer and graph exporter
674
675This group contains general \c EPS drawing methods and special
676graph exporting tools.
677*/
678
679/**
680@defgroup dimacs_group DIMACS Format
681@ingroup io_group
682\brief Read and write files in DIMACS format
683
684Tools to read a digraph from or write it to a file in DIMACS format data.
685*/
686
687/**
688@defgroup nauty_group NAUTY Format
689@ingroup io_group
690\brief Read \e Nauty format
691
692Tool to read graphs from \e Nauty format data.
693*/
694
695/**
696@defgroup concept Concepts
697\brief Skeleton classes and concept checking classes
698
699This group contains the data/algorithm skeletons and concept checking
700classes implemented in LEMON.
701
702The purpose of the classes in this group is fourfold.
703
704- These classes contain the documentations of the %concepts. In order
705  to avoid document multiplications, an implementation of a concept
706  simply refers to the corresponding concept class.
707
708- These classes declare every functions, <tt>typedef</tt>s etc. an
709  implementation of the %concepts should provide, however completely
710  without implementations and real data structures behind the
711  interface. On the other hand they should provide nothing else. All
712  the algorithms working on a data structure meeting a certain concept
713  should compile with these classes. (Though it will not run properly,
714  of course.) In this way it is easily to check if an algorithm
715  doesn't use any extra feature of a certain implementation.
716
717- The concept descriptor classes also provide a <em>checker class</em>
718  that makes it possible to check whether a certain implementation of a
719  concept indeed provides all the required features.
720
721- Finally, They can serve as a skeleton of a new implementation of a concept.
722*/
723
724/**
725@defgroup graph_concepts Graph Structure Concepts
726@ingroup concept
727\brief Skeleton and concept checking classes for graph structures
728
729This group contains the skeletons and concept checking classes of
730graph structures.
731*/
732
733/**
734@defgroup map_concepts Map Concepts
735@ingroup concept
736\brief Skeleton and concept checking classes for maps
737
738This group contains the skeletons and concept checking classes of maps.
739*/
740
741/**
742@defgroup tools Standalone Utility Applications
743
744Some utility applications are listed here.
745
746The standard compilation procedure (<tt>./configure;make</tt>) will compile
747them, as well.
748*/
749
750/**
751\anchor demoprograms
752
753@defgroup demos Demo Programs
754
755Some demo programs are listed here. Their full source codes can be found in
756the \c demo subdirectory of the source tree.
757
758In order to compile them, use the <tt>make demo</tt> or the
759<tt>make check</tt> commands.
760*/
761
762}
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