COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 660:d9cf3b5858ae

Last change on this file since 660:d9cf3b5858ae was 660:d9cf3b5858ae, checked in by Peter Kovacs <kpeter@…>, 11 years ago

Move list and edge sets to the graph module (#290)

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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 matrices Matrices
230@ingroup datas
231\brief Two dimensional data storages implemented in LEMON.
232
233This group contains two dimensional data storages implemented in LEMON.
234*/
235
236/**
237@defgroup paths Path Structures
238@ingroup datas
239\brief %Path structures implemented in LEMON.
240
241This group contains the path structures implemented in LEMON.
242
243LEMON provides flexible data structures to work with paths.
244All of them have similar interfaces and they can be copied easily with
245assignment operators and copy constructors. This makes it easy and
246efficient to have e.g. the Dijkstra algorithm to store its result in
247any kind of path structure.
248
249\sa lemon::concepts::Path
250*/
251
252/**
253@defgroup auxdat Auxiliary Data Structures
254@ingroup datas
255\brief Auxiliary data structures implemented in LEMON.
256
257This group contains some data structures implemented in LEMON in
258order to make it easier to implement combinatorial algorithms.
259*/
260
261/**
262@defgroup algs Algorithms
263\brief This group contains the several algorithms
264implemented in LEMON.
265
266This group contains the several algorithms
267implemented in LEMON.
268*/
269
270/**
271@defgroup search Graph Search
272@ingroup algs
273\brief Common graph search algorithms.
274
275This group contains the common graph search algorithms, namely
276\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
277*/
278
279/**
280@defgroup shortest_path Shortest Path Algorithms
281@ingroup algs
282\brief Algorithms for finding shortest paths.
283
284This group contains the algorithms for finding shortest paths in digraphs.
285
286 - \ref Dijkstra algorithm for finding shortest paths from a source node
287   when all arc lengths are non-negative.
288 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
289   from a source node when arc lenghts can be either positive or negative,
290   but the digraph should not contain directed cycles with negative total
291   length.
292 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
293   for solving the \e all-pairs \e shortest \e paths \e problem when arc
294   lenghts can be either positive or negative, but the digraph should
295   not contain directed cycles with negative total length.
296 - \ref Suurballe A successive shortest path algorithm for finding
297   arc-disjoint paths between two nodes having minimum total length.
298*/
299
300/**
301@defgroup max_flow Maximum Flow Algorithms
302@ingroup algs
303\brief Algorithms for finding maximum flows.
304
305This group contains the algorithms for finding maximum flows and
306feasible circulations.
307
308The \e maximum \e flow \e problem is to find a flow of maximum value between
309a single source and a single target. Formally, there is a \f$G=(V,A)\f$
310digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
311\f$s, t \in V\f$ source and target nodes.
312A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
313following optimization problem.
314
315\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
316\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
317    \quad \forall u\in V\setminus\{s,t\} \f]
318\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
319
320LEMON contains several algorithms for solving maximum flow problems:
321- \ref EdmondsKarp Edmonds-Karp algorithm.
322- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
323- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
324- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
325
326In most cases the \ref Preflow "Preflow" algorithm provides the
327fastest method for computing a maximum flow. All implementations
328also provide functions to query the minimum cut, which is the dual
329problem of maximum flow.
330
331\ref Circulation is a preflow push-relabel algorithm implemented directly
332for finding feasible circulations, which is a somewhat different problem,
333but it is strongly related to maximum flow.
334For more information, see \ref Circulation.
335*/
336
337/**
338@defgroup min_cost_flow Minimum Cost Flow Algorithms
339@ingroup algs
340
341\brief Algorithms for finding minimum cost flows and circulations.
342
343This group contains the algorithms for finding minimum cost flows and
344circulations.
345
346The \e minimum \e cost \e flow \e problem is to find a feasible flow of
347minimum total cost from a set of supply nodes to a set of demand nodes
348in a network with capacity constraints (lower and upper bounds)
349and arc costs.
350Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
351\f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
352upper bounds for the flow values on the arcs, for which
353\f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
354\f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
355on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
356signed supply values of the nodes.
357If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
358supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
359\f$-sup(u)\f$ demand.
360A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
361of the following optimization problem.
362
363\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
364\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
365    sup(u) \quad \forall u\in V \f]
366\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
367
368The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
369zero or negative in order to have a feasible solution (since the sum
370of the expressions on the left-hand side of the inequalities is zero).
371It means that the total demand must be greater or equal to the total
372supply and all the supplies have to be carried out from the supply nodes,
373but there could be demands that are not satisfied.
374If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
375constraints have to be satisfied with equality, i.e. all demands
376have to be satisfied and all supplies have to be used.
377
378If you need the opposite inequalities in the supply/demand constraints
379(i.e. the total demand is less than the total supply and all the demands
380have to be satisfied while there could be supplies that are not used),
381then you could easily transform the problem to the above form by reversing
382the direction of the arcs and taking the negative of the supply values
383(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
384However \ref NetworkSimplex algorithm also supports this form directly
385for the sake of convenience.
386
387A feasible solution for this problem can be found using \ref Circulation.
388
389Note that the above formulation is actually more general than the usual
390definition of the minimum cost flow problem, in which strict equalities
391are required in the supply/demand contraints, i.e.
392
393\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
394    sup(u) \quad \forall u\in V. \f]
395
396However if the sum of the supply values is zero, then these two problems
397are equivalent. So if you need the equality form, you have to ensure this
398additional contraint for the algorithms.
399
400The dual solution of the minimum cost flow problem is represented by node
401potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
402An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
403is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
404node potentials the following \e complementary \e slackness optimality
405conditions hold.
406
407 - For all \f$uv\in A\f$ arcs:
408   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
409   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
410   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
411 - For all \f$u\in V\f$ nodes:
412   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
413     then \f$\pi(u)=0\f$.
414 
415Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
416\f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
417\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
418
419All algorithms provide dual solution (node potentials) as well,
420if an optimal flow is found.
421
422LEMON contains several algorithms for solving minimum cost flow problems.
423 - \ref NetworkSimplex Primal Network Simplex algorithm with various
424   pivot strategies.
425 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
426   cost scaling.
427 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
428   capacity scaling.
429 - \ref CancelAndTighten The Cancel and Tighten algorithm.
430 - \ref CycleCanceling Cycle-Canceling algorithms.
431
432Most of these implementations support the general inequality form of the
433minimum cost flow problem, but CancelAndTighten and CycleCanceling
434only support the equality form due to the primal method they use.
435
436In general NetworkSimplex is the most efficient implementation,
437but in special cases other algorithms could be faster.
438For example, if the total supply and/or capacities are rather small,
439CapacityScaling is usually the fastest algorithm (without effective scaling).
440*/
441
442/**
443@defgroup min_cut Minimum Cut Algorithms
444@ingroup algs
445
446\brief Algorithms for finding minimum cut in graphs.
447
448This group contains the algorithms for finding minimum cut in graphs.
449
450The \e minimum \e cut \e problem is to find a non-empty and non-complete
451\f$X\f$ subset of the nodes with minimum overall capacity on
452outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
453\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
454cut is the \f$X\f$ solution of the next optimization problem:
455
456\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
457    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
458
459LEMON contains several algorithms related to minimum cut problems:
460
461- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
462  in directed graphs.
463- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
464  calculating minimum cut in undirected graphs.
465- \ref GomoryHu "Gomory-Hu tree computation" for calculating
466  all-pairs minimum cut in undirected graphs.
467
468If you want to find minimum cut just between two distinict nodes,
469see the \ref max_flow "maximum flow problem".
470*/
471
472/**
473@defgroup graph_properties Connectivity and Other Graph Properties
474@ingroup algs
475\brief Algorithms for discovering the graph properties
476
477This group contains the algorithms for discovering the graph properties
478like connectivity, bipartiteness, euler property, simplicity etc.
479
480\image html edge_biconnected_components.png
481\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
482*/
483
484/**
485@defgroup planar Planarity Embedding and Drawing
486@ingroup algs
487\brief Algorithms for planarity checking, embedding and drawing
488
489This group contains the algorithms for planarity checking,
490embedding and drawing.
491
492\image html planar.png
493\image latex planar.eps "Plane graph" width=\textwidth
494*/
495
496/**
497@defgroup matching Matching Algorithms
498@ingroup algs
499\brief Algorithms for finding matchings in graphs and bipartite graphs.
500
501This group contains the algorithms for calculating
502matchings in graphs and bipartite graphs. The general matching problem is
503finding a subset of the edges for which each node has at most one incident
504edge.
505
506There are several different algorithms for calculate matchings in
507graphs.  The matching problems in bipartite graphs are generally
508easier than in general graphs. The goal of the matching optimization
509can be finding maximum cardinality, maximum weight or minimum cost
510matching. The search can be constrained to find perfect or
511maximum cardinality matching.
512
513The matching algorithms implemented in LEMON:
514- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
515  for calculating maximum cardinality matching in bipartite graphs.
516- \ref PrBipartiteMatching Push-relabel algorithm
517  for calculating maximum cardinality matching in bipartite graphs.
518- \ref MaxWeightedBipartiteMatching
519  Successive shortest path algorithm for calculating maximum weighted
520  matching and maximum weighted bipartite matching in bipartite graphs.
521- \ref MinCostMaxBipartiteMatching
522  Successive shortest path algorithm for calculating minimum cost maximum
523  matching in bipartite graphs.
524- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
525  maximum cardinality matching in general graphs.
526- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
527  maximum weighted matching in general graphs.
528- \ref MaxWeightedPerfectMatching
529  Edmond's blossom shrinking algorithm for calculating maximum weighted
530  perfect matching in general graphs.
531
532\image html bipartite_matching.png
533\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
534*/
535
536/**
537@defgroup spantree Minimum Spanning Tree Algorithms
538@ingroup algs
539\brief Algorithms for finding minimum cost spanning trees and arborescences.
540
541This group contains the algorithms for finding minimum cost spanning
542trees and arborescences.
543*/
544
545/**
546@defgroup auxalg Auxiliary Algorithms
547@ingroup algs
548\brief Auxiliary algorithms implemented in LEMON.
549
550This group contains some algorithms implemented in LEMON
551in order to make it easier to implement complex algorithms.
552*/
553
554/**
555@defgroup approx Approximation Algorithms
556@ingroup algs
557\brief Approximation algorithms.
558
559This group contains the approximation and heuristic algorithms
560implemented in LEMON.
561*/
562
563/**
564@defgroup gen_opt_group General Optimization Tools
565\brief This group contains some general optimization frameworks
566implemented in LEMON.
567
568This group contains some general optimization frameworks
569implemented in LEMON.
570*/
571
572/**
573@defgroup lp_group Lp and Mip Solvers
574@ingroup gen_opt_group
575\brief Lp and Mip solver interfaces for LEMON.
576
577This group contains Lp and Mip solver interfaces for LEMON. The
578various LP solvers could be used in the same manner with this
579interface.
580*/
581
582/**
583@defgroup lp_utils Tools for Lp and Mip Solvers
584@ingroup lp_group
585\brief Helper tools to the Lp and Mip solvers.
586
587This group adds some helper tools to general optimization framework
588implemented in LEMON.
589*/
590
591/**
592@defgroup metah Metaheuristics
593@ingroup gen_opt_group
594\brief Metaheuristics for LEMON library.
595
596This group contains some metaheuristic optimization tools.
597*/
598
599/**
600@defgroup utils Tools and Utilities
601\brief Tools and utilities for programming in LEMON
602
603Tools and utilities for programming in LEMON.
604*/
605
606/**
607@defgroup gutils Basic Graph Utilities
608@ingroup utils
609\brief Simple basic graph utilities.
610
611This group contains some simple basic graph utilities.
612*/
613
614/**
615@defgroup misc Miscellaneous Tools
616@ingroup utils
617\brief Tools for development, debugging and testing.
618
619This group contains several useful tools for development,
620debugging and testing.
621*/
622
623/**
624@defgroup timecount Time Measuring and Counting
625@ingroup misc
626\brief Simple tools for measuring the performance of algorithms.
627
628This group contains simple tools for measuring the performance
629of algorithms.
630*/
631
632/**
633@defgroup exceptions Exceptions
634@ingroup utils
635\brief Exceptions defined in LEMON.
636
637This group contains the exceptions defined in LEMON.
638*/
639
640/**
641@defgroup io_group Input-Output
642\brief Graph Input-Output methods
643
644This group contains the tools for importing and exporting graphs
645and graph related data. Now it supports the \ref lgf-format
646"LEMON Graph Format", the \c DIMACS format and the encapsulated
647postscript (EPS) format.
648*/
649
650/**
651@defgroup lemon_io LEMON Graph Format
652@ingroup io_group
653\brief Reading and writing LEMON Graph Format.
654
655This group contains methods for reading and writing
656\ref lgf-format "LEMON Graph Format".
657*/
658
659/**
660@defgroup eps_io Postscript Exporting
661@ingroup io_group
662\brief General \c EPS drawer and graph exporter
663
664This group contains general \c EPS drawing methods and special
665graph exporting tools.
666*/
667
668/**
669@defgroup dimacs_group DIMACS format
670@ingroup io_group
671\brief Read and write files in DIMACS format
672
673Tools to read a digraph from or write it to a file in DIMACS format data.
674*/
675
676/**
677@defgroup nauty_group NAUTY Format
678@ingroup io_group
679\brief Read \e Nauty format
680
681Tool to read graphs from \e Nauty format data.
682*/
683
684/**
685@defgroup concept Concepts
686\brief Skeleton classes and concept checking classes
687
688This group contains the data/algorithm skeletons and concept checking
689classes implemented in LEMON.
690
691The purpose of the classes in this group is fourfold.
692
693- These classes contain the documentations of the %concepts. In order
694  to avoid document multiplications, an implementation of a concept
695  simply refers to the corresponding concept class.
696
697- These classes declare every functions, <tt>typedef</tt>s etc. an
698  implementation of the %concepts should provide, however completely
699  without implementations and real data structures behind the
700  interface. On the other hand they should provide nothing else. All
701  the algorithms working on a data structure meeting a certain concept
702  should compile with these classes. (Though it will not run properly,
703  of course.) In this way it is easily to check if an algorithm
704  doesn't use any extra feature of a certain implementation.
705
706- The concept descriptor classes also provide a <em>checker class</em>
707  that makes it possible to check whether a certain implementation of a
708  concept indeed provides all the required features.
709
710- Finally, They can serve as a skeleton of a new implementation of a concept.
711*/
712
713/**
714@defgroup graph_concepts Graph Structure Concepts
715@ingroup concept
716\brief Skeleton and concept checking classes for graph structures
717
718This group contains the skeletons and concept checking classes of LEMON's
719graph structures and helper classes used to implement these.
720*/
721
722/**
723@defgroup map_concepts Map Concepts
724@ingroup concept
725\brief Skeleton and concept checking classes for maps
726
727This group contains the skeletons and concept checking classes of maps.
728*/
729
730/**
731\anchor demoprograms
732
733@defgroup demos Demo Programs
734
735Some demo programs are listed here. Their full source codes can be found in
736the \c demo subdirectory of the source tree.
737
738In order to compile them, use the <tt>make demo</tt> or the
739<tt>make check</tt> commands.
740*/
741
742/**
743@defgroup tools Standalone Utility Applications
744
745Some utility applications are listed here.
746
747The standard compilation procedure (<tt>./configure;make</tt>) will compile
748them, as well.
749*/
750
751}
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