COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 651:3adf5e2d1e62

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1/* -*- mode: C++; indent-tabs-mode: nil; -*-
2 *
3 * This file is a part of LEMON, a generic C++ optimization library.
4 *
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19namespace lemon {
20
21/**
22@defgroup datas Data Structures
23This group contains the several data structures implemented in LEMON.
24*/
25
26/**
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
30
31The implementation of combinatorial algorithms heavily relies on
32efficient graph implementations. LEMON offers data structures which are
33planned to be easily used in an experimental phase of implementation studies,
34and thereafter the program code can be made efficient by small modifications.
35
36The most efficient implementation of diverse applications require the
37usage of different physical graph implementations. These differences
38appear in the size of graph we require to handle, memory or time usage
39limitations or in the set of operations through which the graph can be
40accessed.  LEMON provides several physical graph structures to meet
41the diverging requirements of the possible users.  In order to save on
42running time or on memory usage, some structures may fail to provide
43some graph features like arc/edge or node deletion.
44
45Alteration of standard containers need a very limited number of
46operations, these together satisfy the everyday requirements.
47In the case of graph structures, different operations are needed which do
48not alter the physical graph, but gives another view. If some nodes or
49arcs have to be hidden or the reverse oriented graph have to be used, then
50this is the case. It also may happen that in a flow implementation
51the residual graph can be accessed by another algorithm, or a node-set
52is to be shrunk for another algorithm.
53LEMON also provides a variety of graphs for these requirements called
54\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55in conjunction with other graph representations.
56
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
59with any graph structure.
60
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
62*/
63
64/**
65@defgroup graph_adaptors Adaptor Classes for Graphs
66@ingroup graphs
67\brief Adaptor classes for digraphs and graphs
68
69This group contains several useful adaptor classes for digraphs and graphs.
70
71The main parts of LEMON are the different graph structures, generic
72graph algorithms, graph concepts, which couple them, and graph
73adaptors. While the previous notions are more or less clear, the
74latter one needs further explanation. Graph adaptors are graph classes
75which serve for considering graph structures in different ways.
76
77A short example makes this much clearer.  Suppose that we have an
78instance \c g of a directed graph type, say ListDigraph and an algorithm
79\code
80template <typename Digraph>
81int algorithm(const Digraph&);
82\endcode
83is needed to run on the reverse oriented graph.  It may be expensive
84(in time or in memory usage) to copy \c g with the reversed
85arcs.  In this case, an adaptor class is used, which (according
86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87The adaptor uses the original digraph structure and digraph operations when
88methods of the reversed oriented graph are called.  This means that the adaptor
89have minor memory usage, and do not perform sophisticated algorithmic
90actions.  The purpose of it is to give a tool for the cases when a
91graph have to be used in a specific alteration.  If this alteration is
92obtained by a usual construction like filtering the node or the arc set or
93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
95\code
96template<typename Digraph> class ReverseDigraph;
97\endcode
98template class can be used. The code looks as follows
99\code
100ListDigraph g;
101ReverseDigraph<ListDigraph> rg(g);
102int result = algorithm(rg);
103\endcode
104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
106graph adaptors, complex algorithms can be implemented easily.
107
108In flow, circulation and matching problems, the residual
109graph is of particular importance. Combining an adaptor implementing
110this with shortest path algorithms or minimum mean cycle algorithms,
111a range of weighted and cardinality optimization algorithms can be
112obtained. For other examples, the interested user is referred to the
113detailed documentation of particular adaptors.
114
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
123
124Let us stand one more example here to simplify your work.
125ReverseDigraph has constructor
126\code
127ReverseDigraph(Digraph& digraph);
128\endcode
129This means that in a situation, when a <tt>const %ListDigraph&</tt>
130reference to a graph is given, then it have to be instantiated with
131<tt>Digraph=const %ListDigraph</tt>.
132\code
133int algorithm1(const ListDigraph& g) {
134  ReverseDigraph<const ListDigraph> rg(g);
135  return algorithm2(rg);
136}
137\endcode
138*/
139
140/**
141@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
142@ingroup graphs
143\brief Graph types between real graphs and graph adaptors.
144
145This group contains some graph types between real graphs and graph adaptors.
146These classes wrap graphs to give new functionality as the adaptors do it.
147On the other hand they are not light-weight structures as the adaptors.
148*/
149
150/**
151@defgroup maps Maps
152@ingroup datas
153\brief Map structures implemented in LEMON.
154
155This group contains the map structures implemented in LEMON.
156
157LEMON provides several special purpose maps and map adaptors that e.g. combine
158new maps from existing ones.
159
160<b>See also:</b> \ref map_concepts "Map Concepts".
161*/
162
163/**
164@defgroup graph_maps Graph Maps
165@ingroup maps
166\brief Special graph-related maps.
167
168This group contains maps that are specifically designed to assign
169values to the nodes and arcs/edges of graphs.
170
171If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
172\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
173*/
174
175/**
176\defgroup map_adaptors Map Adaptors
177\ingroup maps
178\brief Tools to create new maps from existing ones
179
180This group contains map adaptors that are used to create "implicit"
181maps from other maps.
182
183Most of them are \ref concepts::ReadMap "read-only maps".
184They can make arithmetic and logical operations between one or two maps
185(negation, shifting, addition, multiplication, logical 'and', 'or',
186'not' etc.) or e.g. convert a map to another one of different Value type.
187
188The typical usage of this classes is passing implicit maps to
189algorithms.  If a function type algorithm is called then the function
190type map adaptors can be used comfortable. For example let's see the
191usage of map adaptors with the \c graphToEps() function.
192\code
193  Color nodeColor(int deg) {
194    if (deg >= 2) {
195      return Color(0.5, 0.0, 0.5);
196    } else if (deg == 1) {
197      return Color(1.0, 0.5, 1.0);
198    } else {
199      return Color(0.0, 0.0, 0.0);
200    }
201  }
202
203  Digraph::NodeMap<int> degree_map(graph);
204
205  graphToEps(graph, "graph.eps")
206    .coords(coords).scaleToA4().undirected()
207    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
208    .run();
209\endcode
210The \c functorToMap() function makes an \c int to \c Color map from the
211\c nodeColor() function. The \c composeMap() compose the \c degree_map
212and the previously created map. The composed map is a proper function to
213get the color of each node.
214
215The usage with class type algorithms is little bit harder. In this
216case the function type map adaptors can not be used, because the
217function map adaptors give back temporary objects.
218\code
219  Digraph graph;
220
221  typedef Digraph::ArcMap<double> DoubleArcMap;
222  DoubleArcMap length(graph);
223  DoubleArcMap speed(graph);
224
225  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
226  TimeMap time(length, speed);
227
228  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
229  dijkstra.run(source, target);
230\endcode
231We have a length map and a maximum speed map on the arcs of a digraph.
232The minimum time to pass the arc can be calculated as the division of
233the two maps which can be done implicitly with the \c DivMap template
234class. We use the implicit minimum time map as the length map of the
235\c Dijkstra algorithm.
236*/
237
238/**
239@defgroup matrices Matrices
240@ingroup datas
241\brief Two dimensional data storages implemented in LEMON.
242
243This group contains two dimensional data storages implemented in LEMON.
244*/
245
246/**
247@defgroup paths Path Structures
248@ingroup datas
249\brief %Path structures implemented in LEMON.
250
251This group contains the path structures implemented in LEMON.
252
253LEMON provides flexible data structures to work with paths.
254All of them have similar interfaces and they can be copied easily with
255assignment operators and copy constructors. This makes it easy and
256efficient to have e.g. the Dijkstra algorithm to store its result in
257any kind of path structure.
258
259\sa lemon::concepts::Path
260*/
261
262/**
263@defgroup auxdat Auxiliary Data Structures
264@ingroup datas
265\brief Auxiliary data structures implemented in LEMON.
266
267This group contains some data structures implemented in LEMON in
268order to make it easier to implement combinatorial algorithms.
269*/
270
271/**
272@defgroup algs Algorithms
273\brief This group contains the several algorithms
274implemented in LEMON.
275
276This group contains the several algorithms
277implemented in LEMON.
278*/
279
280/**
281@defgroup search Graph Search
282@ingroup algs
283\brief Common graph search algorithms.
284
285This group contains the common graph search algorithms, namely
286\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
287*/
288
289/**
290@defgroup shortest_path Shortest Path Algorithms
291@ingroup algs
292\brief Algorithms for finding shortest paths.
293
294This group contains the algorithms for finding shortest paths in digraphs.
295
296 - \ref Dijkstra algorithm for finding shortest paths from a source node
297   when all arc lengths are non-negative.
298 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
299   from a source node when arc lenghts can be either positive or negative,
300   but the digraph should not contain directed cycles with negative total
301   length.
302 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
303   for solving the \e all-pairs \e shortest \e paths \e problem when arc
304   lenghts can be either positive or negative, but the digraph should
305   not contain directed cycles with negative total length.
306 - \ref Suurballe A successive shortest path algorithm for finding
307   arc-disjoint paths between two nodes having minimum total length.
308*/
309
310/**
311@defgroup max_flow Maximum Flow Algorithms
312@ingroup algs
313\brief Algorithms for finding maximum flows.
314
315This group contains the algorithms for finding maximum flows and
316feasible circulations.
317
318The \e maximum \e flow \e problem is to find a flow of maximum value between
319a single source and a single target. Formally, there is a \f$G=(V,A)\f$
320digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
321\f$s, t \in V\f$ source and target nodes.
322A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
323following optimization problem.
324
325\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
326\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
327    \quad \forall u\in V\setminus\{s,t\} \f]
328\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
329
330LEMON contains several algorithms for solving maximum flow problems:
331- \ref EdmondsKarp Edmonds-Karp algorithm.
332- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
333- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
334- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
335
336In most cases the \ref Preflow "Preflow" algorithm provides the
337fastest method for computing a maximum flow. All implementations
338also provide functions to query the minimum cut, which is the dual
339problem of maximum flow.
340
341\ref Circulation is a preflow push-relabel algorithm implemented directly
342for finding feasible circulations, which is a somewhat different problem,
343but it is strongly related to maximum flow.
344For more information, see \ref Circulation.
345*/
346
347/**
348@defgroup min_cost_flow Minimum Cost Flow Algorithms
349@ingroup algs
350
351\brief Algorithms for finding minimum cost flows and circulations.
352
353This group contains the algorithms for finding minimum cost flows and
354circulations.
355
356The \e minimum \e cost \e flow \e problem is to find a feasible flow of
357minimum total cost from a set of supply nodes to a set of demand nodes
358in a network with capacity constraints (lower and upper bounds)
359and arc costs.
360Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
361\f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
362upper bounds for the flow values on the arcs, for which
363\f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
364\f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
365on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
366signed supply values of the nodes.
367If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
368supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
369\f$-sup(u)\f$ demand.
370A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
371of the following optimization problem.
372
373\f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
374\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
375    sup(u) \quad \forall u\in V \f]
376\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
377
378The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
379zero or negative in order to have a feasible solution (since the sum
380of the expressions on the left-hand side of the inequalities is zero).
381It means that the total demand must be greater or equal to the total
382supply and all the supplies have to be carried out from the supply nodes,
383but there could be demands that are not satisfied.
384If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
385constraints have to be satisfied with equality, i.e. all demands
386have to be satisfied and all supplies have to be used.
387
388If you need the opposite inequalities in the supply/demand constraints
389(i.e. the total demand is less than the total supply and all the demands
390have to be satisfied while there could be supplies that are not used),
391then you could easily transform the problem to the above form by reversing
392the direction of the arcs and taking the negative of the supply values
393(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
394However \ref NetworkSimplex algorithm also supports this form directly
395for the sake of convenience.
396
397A feasible solution for this problem can be found using \ref Circulation.
398
399Note that the above formulation is actually more general than the usual
400definition of the minimum cost flow problem, in which strict equalities
401are required in the supply/demand contraints, i.e.
402
403\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
404    sup(u) \quad \forall u\in V. \f]
405
406However if the sum of the supply values is zero, then these two problems
407are equivalent. So if you need the equality form, you have to ensure this
408additional contraint for the algorithms.
409
410The dual solution of the minimum cost flow problem is represented by node
411potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
412An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
413is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
414node potentials the following \e complementary \e slackness optimality
415conditions hold.
416
417 - For all \f$uv\in A\f$ arcs:
418   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
419   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
420   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
421 - For all \f$u\in V\f$ nodes:
422   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
423     then \f$\pi(u)=0\f$.
424 
425Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
426\f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
427\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
428
429All algorithms provide dual solution (node potentials) as well,
430if an optimal flow is found.
431
432LEMON contains several algorithms for solving minimum cost flow problems.
433 - \ref NetworkSimplex Primal Network Simplex algorithm with various
434   pivot strategies.
435 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
436   cost scaling.
437 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
438   capacity scaling.
439 - \ref CancelAndTighten The Cancel and Tighten algorithm.
440 - \ref CycleCanceling Cycle-Canceling algorithms.
441
442Most of these implementations support the general inequality form of the
443minimum cost flow problem, but CancelAndTighten and CycleCanceling
444only support the equality form due to the primal method they use.
445
446In general NetworkSimplex is the most efficient implementation,
447but in special cases other algorithms could be faster.
448For example, if the total supply and/or capacities are rather small,
449CapacityScaling is usually the fastest algorithm (without effective scaling).
450*/
451
452/**
453@defgroup min_cut Minimum Cut Algorithms
454@ingroup algs
455
456\brief Algorithms for finding minimum cut in graphs.
457
458This group contains the algorithms for finding minimum cut in graphs.
459
460The \e minimum \e cut \e problem is to find a non-empty and non-complete
461\f$X\f$ subset of the nodes with minimum overall capacity on
462outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
463\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
464cut is the \f$X\f$ solution of the next optimization problem:
465
466\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
467    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
468
469LEMON contains several algorithms related to minimum cut problems:
470
471- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
472  in directed graphs.
473- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
474  calculating minimum cut in undirected graphs.
475- \ref GomoryHu "Gomory-Hu tree computation" for calculating
476  all-pairs minimum cut in undirected graphs.
477
478If you want to find minimum cut just between two distinict nodes,
479see the \ref max_flow "maximum flow problem".
480*/
481
482/**
483@defgroup graph_properties Connectivity and Other Graph Properties
484@ingroup algs
485\brief Algorithms for discovering the graph properties
486
487This group contains the algorithms for discovering the graph properties
488like connectivity, bipartiteness, euler property, simplicity etc.
489
490\image html edge_biconnected_components.png
491\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
492*/
493
494/**
495@defgroup planar Planarity Embedding and Drawing
496@ingroup algs
497\brief Algorithms for planarity checking, embedding and drawing
498
499This group contains the algorithms for planarity checking,
500embedding and drawing.
501
502\image html planar.png
503\image latex planar.eps "Plane graph" width=\textwidth
504*/
505
506/**
507@defgroup matching Matching Algorithms
508@ingroup algs
509\brief Algorithms for finding matchings in graphs and bipartite graphs.
510
511This group contains the algorithms for calculating
512matchings in graphs and bipartite graphs. The general matching problem is
513finding a subset of the edges for which each node has at most one incident
514edge.
515
516There are several different algorithms for calculate matchings in
517graphs.  The matching problems in bipartite graphs are generally
518easier than in general graphs. The goal of the matching optimization
519can be finding maximum cardinality, maximum weight or minimum cost
520matching. The search can be constrained to find perfect or
521maximum cardinality matching.
522
523The matching algorithms implemented in LEMON:
524- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
525  for calculating maximum cardinality matching in bipartite graphs.
526- \ref PrBipartiteMatching Push-relabel algorithm
527  for calculating maximum cardinality matching in bipartite graphs.
528- \ref MaxWeightedBipartiteMatching
529  Successive shortest path algorithm for calculating maximum weighted
530  matching and maximum weighted bipartite matching in bipartite graphs.
531- \ref MinCostMaxBipartiteMatching
532  Successive shortest path algorithm for calculating minimum cost maximum
533  matching in bipartite graphs.
534- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
535  maximum cardinality matching in general graphs.
536- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
537  maximum weighted matching in general graphs.
538- \ref MaxWeightedPerfectMatching
539  Edmond's blossom shrinking algorithm for calculating maximum weighted
540  perfect matching in general graphs.
541
542\image html bipartite_matching.png
543\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
544*/
545
546/**
547@defgroup spantree Minimum Spanning Tree Algorithms
548@ingroup algs
549\brief Algorithms for finding minimum cost spanning trees and arborescences.
550
551This group contains the algorithms for finding minimum cost spanning
552trees and arborescences.
553*/
554
555/**
556@defgroup auxalg Auxiliary Algorithms
557@ingroup algs
558\brief Auxiliary algorithms implemented in LEMON.
559
560This group contains some algorithms implemented in LEMON
561in order to make it easier to implement complex algorithms.
562*/
563
564/**
565@defgroup approx Approximation Algorithms
566@ingroup algs
567\brief Approximation algorithms.
568
569This group contains the approximation and heuristic algorithms
570implemented in LEMON.
571*/
572
573/**
574@defgroup gen_opt_group General Optimization Tools
575\brief This group contains some general optimization frameworks
576implemented in LEMON.
577
578This group contains some general optimization frameworks
579implemented in LEMON.
580*/
581
582/**
583@defgroup lp_group Lp and Mip Solvers
584@ingroup gen_opt_group
585\brief Lp and Mip solver interfaces for LEMON.
586
587This group contains Lp and Mip solver interfaces for LEMON. The
588various LP solvers could be used in the same manner with this
589interface.
590*/
591
592/**
593@defgroup lp_utils Tools for Lp and Mip Solvers
594@ingroup lp_group
595\brief Helper tools to the Lp and Mip solvers.
596
597This group adds some helper tools to general optimization framework
598implemented in LEMON.
599*/
600
601/**
602@defgroup metah Metaheuristics
603@ingroup gen_opt_group
604\brief Metaheuristics for LEMON library.
605
606This group contains some metaheuristic optimization tools.
607*/
608
609/**
610@defgroup utils Tools and Utilities
611\brief Tools and utilities for programming in LEMON
612
613Tools and utilities for programming in LEMON.
614*/
615
616/**
617@defgroup gutils Basic Graph Utilities
618@ingroup utils
619\brief Simple basic graph utilities.
620
621This group contains some simple basic graph utilities.
622*/
623
624/**
625@defgroup misc Miscellaneous Tools
626@ingroup utils
627\brief Tools for development, debugging and testing.
628
629This group contains several useful tools for development,
630debugging and testing.
631*/
632
633/**
634@defgroup timecount Time Measuring and Counting
635@ingroup misc
636\brief Simple tools for measuring the performance of algorithms.
637
638This group contains simple tools for measuring the performance
639of algorithms.
640*/
641
642/**
643@defgroup exceptions Exceptions
644@ingroup utils
645\brief Exceptions defined in LEMON.
646
647This group contains the exceptions defined in LEMON.
648*/
649
650/**
651@defgroup io_group Input-Output
652\brief Graph Input-Output methods
653
654This group contains the tools for importing and exporting graphs
655and graph related data. Now it supports the \ref lgf-format
656"LEMON Graph Format", the \c DIMACS format and the encapsulated
657postscript (EPS) format.
658*/
659
660/**
661@defgroup lemon_io LEMON Graph Format
662@ingroup io_group
663\brief Reading and writing LEMON Graph Format.
664
665This group contains methods for reading and writing
666\ref lgf-format "LEMON Graph Format".
667*/
668
669/**
670@defgroup eps_io Postscript Exporting
671@ingroup io_group
672\brief General \c EPS drawer and graph exporter
673
674This group contains general \c EPS drawing methods and special
675graph exporting tools.
676*/
677
678/**
679@defgroup dimacs_group DIMACS format
680@ingroup io_group
681\brief Read and write files in DIMACS format
682
683Tools to read a digraph from or write it to a file in DIMACS format data.
684*/
685
686/**
687@defgroup nauty_group NAUTY Format
688@ingroup io_group
689\brief Read \e Nauty format
690
691Tool to read graphs from \e Nauty format data.
692*/
693
694/**
695@defgroup concept Concepts
696\brief Skeleton classes and concept checking classes
697
698This group contains the data/algorithm skeletons and concept checking
699classes implemented in LEMON.
700
701The purpose of the classes in this group is fourfold.
702
703- These classes contain the documentations of the %concepts. In order
704  to avoid document multiplications, an implementation of a concept
705  simply refers to the corresponding concept class.
706
707- These classes declare every functions, <tt>typedef</tt>s etc. an
708  implementation of the %concepts should provide, however completely
709  without implementations and real data structures behind the
710  interface. On the other hand they should provide nothing else. All
711  the algorithms working on a data structure meeting a certain concept
712  should compile with these classes. (Though it will not run properly,
713  of course.) In this way it is easily to check if an algorithm
714  doesn't use any extra feature of a certain implementation.
715
716- The concept descriptor classes also provide a <em>checker class</em>
717  that makes it possible to check whether a certain implementation of a
718  concept indeed provides all the required features.
719
720- Finally, They can serve as a skeleton of a new implementation of a concept.
721*/
722
723/**
724@defgroup graph_concepts Graph Structure Concepts
725@ingroup concept
726\brief Skeleton and concept checking classes for graph structures
727
728This group contains the skeletons and concept checking classes of LEMON's
729graph structures and helper classes used to implement these.
730*/
731
732/**
733@defgroup map_concepts Map Concepts
734@ingroup concept
735\brief Skeleton and concept checking classes for maps
736
737This group contains the skeletons and concept checking classes of maps.
738*/
739
740/**
741\anchor demoprograms
742
743@defgroup demos Demo Programs
744
745Some demo programs are listed here. Their full source codes can be found in
746the \c demo subdirectory of the source tree.
747
748In order to compile them, use the <tt>make demo</tt> or the
749<tt>make check</tt> commands.
750*/
751
752/**
753@defgroup tools Standalone Utility Applications
754
755Some utility applications are listed here.
756
757The standard compilation procedure (<tt>./configure;make</tt>) will compile
758them, as well.
759*/
760
761}
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