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) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
8 *
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
12 *
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
15 * purpose.
16 *
17 */
18
19namespace lemon {
20
21/**
22@defgroup datas Data Structures
23This group contains the several data structures implemented in LEMON.
24*/
25
26/**
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
30
31The implementation of combinatorial algorithms heavily relies on
32efficient graph implementations. LEMON offers data structures which are
33planned to be easily used in an experimental phase of implementation studies,
34and thereafter the program code can be made efficient by small modifications.
35
36The most efficient implementation of diverse applications require the
37usage of different physical graph implementations. These differences
38appear in the size of graph we require to handle, memory or time usage
39limitations or in the set of operations through which the graph can be
40accessed.  LEMON provides several physical graph structures to meet
41the diverging requirements of the possible users.  In order to save on
42running time or on memory usage, some structures may fail to provide
43some graph features like arc/edge or node deletion.
44
45Alteration of standard containers need a very limited number of
46operations, these together satisfy the everyday requirements.
47In the case of graph structures, different operations are needed which do
48not alter the physical graph, but gives another view. If some nodes or
49arcs have to be hidden or the reverse oriented graph have to be used, then
50this is the case. It also may happen that in a flow implementation
51the residual graph can be accessed by another algorithm, or a node-set
52is to be shrunk for another algorithm.
53LEMON also provides a variety of graphs for these requirements called
54\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55in conjunction with other graph representations.
56
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
59with any graph structure.
60
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
62*/
63
64/**
65@defgroup graph_adaptors Adaptor Classes for Graphs
66@ingroup graphs
67\brief Adaptor classes for digraphs and graphs
68
69This group contains several useful adaptor classes for digraphs and graphs.
70
71The main parts of LEMON are the different graph structures, generic
72graph algorithms, graph concepts, which couple them, and graph
73adaptors. While the previous notions are more or less clear, the
74latter one needs further explanation. Graph adaptors are graph classes
75which serve for considering graph structures in different ways.
76
77A short example makes this much clearer.  Suppose that we have an
78instance \c g of a directed graph type, say ListDigraph and an algorithm
79\code
80template <typename Digraph>
81int algorithm(const Digraph&);
82\endcode
83is needed to run on the reverse oriented graph.  It may be expensive
84(in time or in memory usage) to copy \c g with the reversed
85arcs.  In this case, an adaptor class is used, which (according
86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87The adaptor uses the original digraph structure and digraph operations when
88methods of the reversed oriented graph are called.  This means that the adaptor
89have minor memory usage, and do not perform sophisticated algorithmic
90actions.  The purpose of it is to give a tool for the cases when a
91graph have to be used in a specific alteration.  If this alteration is
92obtained by a usual construction like filtering the node or the arc set or
93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
95\code
96template<typename Digraph> class ReverseDigraph;
97\endcode
98template class can be used. The code looks as follows
99\code
100ListDigraph g;
101ReverseDigraph<ListDigraph> rg(g);
102int result = algorithm(rg);
103\endcode
104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
106graph adaptors, complex algorithms can be implemented easily.
107
108In flow, circulation and matching problems, the residual
109graph is of particular importance. Combining an adaptor implementing
110this with shortest path algorithms or minimum mean cycle algorithms,
111a range of weighted and cardinality optimization algorithms can be
112obtained. For other examples, the interested user is referred to the
113detailed documentation of particular adaptors.
114
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
123
124Let us stand one more example here to simplify your work.
125ReverseDigraph has constructor
126\code
127ReverseDigraph(Digraph& digraph);
128\endcode
129This means that in a situation, when a <tt>const %ListDigraph&</tt>
130reference to a graph is given, then it have to be instantiated with
131<tt>Digraph=const %ListDigraph</tt>.
132\code
133int algorithm1(const ListDigraph& g) {
134  ReverseDigraph<const ListDigraph> rg(g);
135  return algorithm2(rg);
136}
137\endcode
138*/
139
140/**
141@defgroup maps Maps
142@ingroup datas
143\brief Map structures implemented in LEMON.
144
145This group contains the map structures implemented in LEMON.
146
147LEMON provides several special purpose maps and map adaptors that e.g. combine
148new maps from existing ones.
149
150<b>See also:</b> \ref map_concepts "Map Concepts".
151*/
152
153/**
154@defgroup graph_maps Graph Maps
155@ingroup maps
156\brief Special graph-related maps.
157
158This group contains maps that are specifically designed to assign
159values to the nodes and arcs/edges of graphs.
160
161If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
163*/
164
165/**
166\defgroup map_adaptors Map Adaptors
167\ingroup maps
168\brief Tools to create new maps from existing ones
169
170This group contains map adaptors that are used to create "implicit"
171maps from other maps.
172
173Most of them are \ref concepts::ReadMap "read-only maps".
174They can make arithmetic and logical operations between one or two maps
175(negation, shifting, addition, multiplication, logical 'and', 'or',
176'not' etc.) or e.g. convert a map to another one of different Value type.
177
178The typical usage of this classes is passing implicit maps to
179algorithms.  If a function type algorithm is called then the function
180type map adaptors can be used comfortable. For example let's see the
181usage of map adaptors with the \c graphToEps() function.
182\code
183  Color nodeColor(int deg) {
184    if (deg >= 2) {
185      return Color(0.5, 0.0, 0.5);
186    } else if (deg == 1) {
187      return Color(1.0, 0.5, 1.0);
188    } else {
189      return Color(0.0, 0.0, 0.0);
190    }
191  }
192
193  Digraph::NodeMap<int> degree_map(graph);
194
195  graphToEps(graph, "graph.eps")
196    .coords(coords).scaleToA4().undirected()
197    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
198    .run();
199\endcode
200The \c functorToMap() function makes an \c int to \c Color map from the
201\c nodeColor() function. The \c composeMap() compose the \c degree_map
202and the previously created map. The composed map is a proper function to
203get the color of each node.
204
205The usage with class type algorithms is little bit harder. In this
206case the function type map adaptors can not be used, because the
207function map adaptors give back temporary objects.
208\code
209  Digraph graph;
210
211  typedef Digraph::ArcMap<double> DoubleArcMap;
212  DoubleArcMap length(graph);
213  DoubleArcMap speed(graph);
214
215  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
216  TimeMap time(length, speed);
217
218  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
219  dijkstra.run(source, target);
220\endcode
221We have a length map and a maximum speed map on the arcs of a digraph.
222The minimum time to pass the arc can be calculated as the division of
223the two maps which can be done implicitly with the \c DivMap template
224class. We use the implicit minimum time map as the length map of the
225\c Dijkstra algorithm.
226*/
227
228/**
229@defgroup paths Path Structures
230@ingroup datas
231\brief %Path structures implemented in LEMON.
232
233This group contains the path structures implemented in LEMON.
234
235LEMON provides flexible data structures to work with paths.
236All of them have similar interfaces and they can be copied easily with
237assignment operators and copy constructors. This makes it easy and
238efficient to have e.g. the Dijkstra algorithm to store its result in
239any kind of path structure.
240
241\sa \ref concepts::Path "Path concept"
242*/
243
244/**
245@defgroup heaps Heap Structures
246@ingroup datas
247\brief %Heap structures implemented in LEMON.
248
249This group contains the heap structures implemented in LEMON.
250
251LEMON provides several heap classes. They are efficient implementations
252of the abstract data type \e priority \e queue. They store items with
253specified values called \e priorities in such a way that finding and
254removing the item with minimum priority are efficient.
255The basic operations are adding and erasing items, changing the priority
256of an item, etc.
257
258Heaps are crucial in several algorithms, such as Dijkstra and Prim.
259The heap implementations have the same interface, thus any of them can be
260used easily in such algorithms.
261
262\sa \ref concepts::Heap "Heap concept"
263*/
264
265/**
266@defgroup matrices Matrices
267@ingroup datas
268\brief Two dimensional data storages implemented in LEMON.
269
270This group contains two dimensional data storages implemented in LEMON.
271*/
272
273/**
274@defgroup auxdat Auxiliary Data Structures
275@ingroup datas
276\brief Auxiliary data structures implemented in LEMON.
277
278This group contains some data structures implemented in LEMON in
279order to make it easier to implement combinatorial algorithms.
280*/
281
282/**
283@defgroup geomdat Geometric Data Structures
284@ingroup auxdat
285\brief Geometric data structures implemented in LEMON.
286
287This group contains geometric data structures implemented in LEMON.
288
289 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
290   vector with the usual operations.
291 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
292   rectangular bounding box of a set of \ref lemon::dim2::Point
293   "dim2::Point"'s.
294*/
295
296/**
297@defgroup matrices Matrices
298@ingroup auxdat
299\brief Two dimensional data storages implemented in LEMON.
300
301This group contains two dimensional data storages implemented in LEMON.
302*/
303
304/**
305@defgroup algs Algorithms
306\brief This group contains the several algorithms
307implemented in LEMON.
308
309This group contains the several algorithms
310implemented in LEMON.
311*/
312
313/**
314@defgroup search Graph Search
315@ingroup algs
316\brief Common graph search algorithms.
317
318This group contains the common graph search algorithms, namely
319\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
320\ref clrs01algorithms.
321*/
322
323/**
324@defgroup shortest_path Shortest Path Algorithms
325@ingroup algs
326\brief Algorithms for finding shortest paths.
327
328This group contains the algorithms for finding shortest paths in digraphs
329\ref clrs01algorithms.
330
331 - \ref Dijkstra algorithm for finding shortest paths from a source node
332   when all arc lengths are non-negative.
333 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
334   from a source node when arc lenghts can be either positive or negative,
335   but the digraph should not contain directed cycles with negative total
336   length.
337 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
338   for solving the \e all-pairs \e shortest \e paths \e problem when arc
339   lenghts can be either positive or negative, but the digraph should
340   not contain directed cycles with negative total length.
341 - \ref Suurballe A successive shortest path algorithm for finding
342   arc-disjoint paths between two nodes having minimum total length.
343*/
344
345/**
346@defgroup spantree Minimum Spanning Tree Algorithms
347@ingroup algs
348\brief Algorithms for finding minimum cost spanning trees and arborescences.
349
350This group contains the algorithms for finding minimum cost spanning
351trees and arborescences \ref clrs01algorithms.
352*/
353
354/**
355@defgroup max_flow Maximum Flow Algorithms
356@ingroup algs
357\brief Algorithms for finding maximum flows.
358
359This group contains the algorithms for finding maximum flows and
360feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
361
362The \e maximum \e flow \e problem is to find a flow of maximum value between
363a single source and a single target. Formally, there is a \f$G=(V,A)\f$
364digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
365\f$s, t \in V\f$ source and target nodes.
366A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
367following optimization problem.
368
369\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
370\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
371    \quad \forall u\in V\setminus\{s,t\} \f]
372\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
373
374LEMON contains several algorithms for solving maximum flow problems:
375- \ref EdmondsKarp Edmonds-Karp algorithm
376  \ref edmondskarp72theoretical.
377- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
378  \ref goldberg88newapproach.
379- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
380  \ref dinic70algorithm, \ref sleator83dynamic.
381- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
382  \ref goldberg88newapproach, \ref sleator83dynamic.
383
384In most cases the \ref Preflow algorithm provides the
385fastest method for computing a maximum flow. All implementations
386also provide functions to query the minimum cut, which is the dual
387problem of maximum flow.
388
389\ref Circulation is a preflow push-relabel algorithm implemented directly
390for finding feasible circulations, which is a somewhat different problem,
391but it is strongly related to maximum flow.
392For more information, see \ref Circulation.
393*/
394
395/**
396@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
397@ingroup algs
398
399\brief Algorithms for finding minimum cost flows and circulations.
400
401This group contains the algorithms for finding minimum cost flows and
402circulations \ref amo93networkflows. For more information about this
403problem and its dual solution, see \ref min_cost_flow
404"Minimum Cost Flow Problem".
405
406LEMON contains several algorithms for this problem.
407 - \ref NetworkSimplex Primal Network Simplex algorithm with various
408   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
409 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
410   cost scaling \ref goldberg90approximation, \ref goldberg97efficient,
411   \ref bunnagel98efficient.
412 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
413   capacity scaling \ref edmondskarp72theoretical.
414 - \ref CancelAndTighten The Cancel and Tighten algorithm
415   \ref goldberg89cyclecanceling.
416 - \ref CycleCanceling Cycle-Canceling algorithms
417   \ref klein67primal, \ref goldberg89cyclecanceling.
418
419In general NetworkSimplex is the most efficient implementation,
420but in special cases other algorithms could be faster.
421For example, if the total supply and/or capacities are rather small,
422CapacityScaling is usually the fastest algorithm (without effective scaling).
423*/
424
425/**
426@defgroup min_cut Minimum Cut Algorithms
427@ingroup algs
428
429\brief Algorithms for finding minimum cut in graphs.
430
431This group contains the algorithms for finding minimum cut in graphs.
432
433The \e minimum \e cut \e problem is to find a non-empty and non-complete
434\f$X\f$ subset of the nodes with minimum overall capacity on
435outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
436\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
437cut is the \f$X\f$ solution of the next optimization problem:
438
439\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
440    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
441
442LEMON contains several algorithms related to minimum cut problems:
443
444- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
445  in directed graphs.
446- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
447  calculating minimum cut in undirected graphs.
448- \ref GomoryHu "Gomory-Hu tree computation" for calculating
449  all-pairs minimum cut in undirected graphs.
450
451If you want to find minimum cut just between two distinict nodes,
452see the \ref max_flow "maximum flow problem".
453*/
454
455/**
456@defgroup matching Matching Algorithms
457@ingroup algs
458\brief Algorithms for finding matchings in graphs and bipartite graphs.
459
460This group contains the algorithms for calculating
461matchings in graphs and bipartite graphs. The general matching problem is
462finding a subset of the edges for which each node has at most one incident
463edge.
464
465There are several different algorithms for calculate matchings in
466graphs.  The matching problems in bipartite graphs are generally
467easier than in general graphs. The goal of the matching optimization
468can be finding maximum cardinality, maximum weight or minimum cost
469matching. The search can be constrained to find perfect or
470maximum cardinality matching.
471
472The matching algorithms implemented in LEMON:
473- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
474  for calculating maximum cardinality matching in bipartite graphs.
475- \ref PrBipartiteMatching Push-relabel algorithm
476  for calculating maximum cardinality matching in bipartite graphs.
477- \ref MaxWeightedBipartiteMatching
478  Successive shortest path algorithm for calculating maximum weighted
479  matching and maximum weighted bipartite matching in bipartite graphs.
480- \ref MinCostMaxBipartiteMatching
481  Successive shortest path algorithm for calculating minimum cost maximum
482  matching in bipartite graphs.
483- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
484  maximum cardinality matching in general graphs.
485- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
486  maximum weighted matching in general graphs.
487- \ref MaxWeightedPerfectMatching
488  Edmond's blossom shrinking algorithm for calculating maximum weighted
489  perfect matching in general graphs.
490
491\image html bipartite_matching.png
492\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
493*/
494
495/**
496@defgroup graph_properties Connectivity and Other Graph Properties
497@ingroup algs
498\brief Algorithms for discovering the graph properties
499
500This group contains the algorithms for discovering the graph properties
501like connectivity, bipartiteness, euler property, simplicity etc.
502
503\image html connected_components.png
504\image latex connected_components.eps "Connected components" width=\textwidth
505*/
506
507/**
508@defgroup planar Planarity Embedding and Drawing
509@ingroup algs
510\brief Algorithms for planarity checking, embedding and drawing
511
512This group contains the algorithms for planarity checking,
513embedding and drawing.
514
515\image html planar.png
516\image latex planar.eps "Plane graph" width=\textwidth
517*/
518
519/**
520@defgroup approx Approximation Algorithms
521@ingroup algs
522\brief Approximation algorithms.
523
524This group contains the approximation and heuristic algorithms
525implemented in LEMON.
526*/
527
528/**
529@defgroup auxalg Auxiliary Algorithms
530@ingroup algs
531\brief Auxiliary algorithms implemented in LEMON.
532
533This group contains some algorithms implemented in LEMON
534in order to make it easier to implement complex algorithms.
535*/
536
537/**
538@defgroup gen_opt_group General Optimization Tools
539\brief This group contains some general optimization frameworks
540implemented in LEMON.
541
542This group contains some general optimization frameworks
543implemented in LEMON.
544*/
545
546/**
547@defgroup lp_group LP and MIP Solvers
548@ingroup gen_opt_group
549\brief LP and MIP solver interfaces for LEMON.
550
551This group contains LP and MIP solver interfaces for LEMON.
552Various LP solvers could be used in the same manner with this
553high-level interface.
554
555The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
556\ref cplex, \ref soplex.
557*/
558
559/**
560@defgroup lp_utils Tools for Lp and Mip Solvers
561@ingroup lp_group
562\brief Helper tools to the Lp and Mip solvers.
563
564This group adds some helper tools to general optimization framework
565implemented in LEMON.
566*/
567
568/**
569@defgroup metah Metaheuristics
570@ingroup gen_opt_group
571\brief Metaheuristics for LEMON library.
572
573This group contains some metaheuristic optimization tools.
574*/
575
576/**
577@defgroup utils Tools and Utilities
578\brief Tools and utilities for programming in LEMON
579
580Tools and utilities for programming in LEMON.
581*/
582
583/**
584@defgroup gutils Basic Graph Utilities
585@ingroup utils
586\brief Simple basic graph utilities.
587
588This group contains some simple basic graph utilities.
589*/
590
591/**
592@defgroup misc Miscellaneous Tools
593@ingroup utils
594\brief Tools for development, debugging and testing.
595
596This group contains several useful tools for development,
597debugging and testing.
598*/
599
600/**
601@defgroup timecount Time Measuring and Counting
602@ingroup misc
603\brief Simple tools for measuring the performance of algorithms.
604
605This group contains simple tools for measuring the performance
606of algorithms.
607*/
608
609/**
610@defgroup exceptions Exceptions
611@ingroup utils
612\brief Exceptions defined in LEMON.
613
614This group contains the exceptions defined in LEMON.
615*/
616
617/**
618@defgroup io_group Input-Output
619\brief Graph Input-Output methods
620
621This group contains the tools for importing and exporting graphs
622and graph related data. Now it supports the \ref lgf-format
623"LEMON Graph Format", the \c DIMACS format and the encapsulated
624postscript (EPS) format.
625*/
626
627/**
628@defgroup lemon_io LEMON Graph Format
629@ingroup io_group
630\brief Reading and writing LEMON Graph Format.
631
632This group contains methods for reading and writing
633\ref lgf-format "LEMON Graph Format".
634*/
635
636/**
637@defgroup eps_io Postscript Exporting
638@ingroup io_group
639\brief General \c EPS drawer and graph exporter
640
641This group contains general \c EPS drawing methods and special
642graph exporting tools.
643*/
644
645/**
646@defgroup dimacs_group DIMACS Format
647@ingroup io_group
648\brief Read and write files in DIMACS format
649
650Tools to read a digraph from or write it to a file in DIMACS format data.
651*/
652
653/**
654@defgroup nauty_group NAUTY Format
655@ingroup io_group
656\brief Read \e Nauty format
657
658Tool to read graphs from \e Nauty format data.
659*/
660
661/**
662@defgroup concept Concepts
663\brief Skeleton classes and concept checking classes
664
665This group contains the data/algorithm skeletons and concept checking
666classes implemented in LEMON.
667
668The purpose of the classes in this group is fourfold.
669
670- These classes contain the documentations of the %concepts. In order
671  to avoid document multiplications, an implementation of a concept
672  simply refers to the corresponding concept class.
673
674- These classes declare every functions, <tt>typedef</tt>s etc. an
675  implementation of the %concepts should provide, however completely
676  without implementations and real data structures behind the
677  interface. On the other hand they should provide nothing else. All
678  the algorithms working on a data structure meeting a certain concept
679  should compile with these classes. (Though it will not run properly,
680  of course.) In this way it is easily to check if an algorithm
681  doesn't use any extra feature of a certain implementation.
682
683- The concept descriptor classes also provide a <em>checker class</em>
684  that makes it possible to check whether a certain implementation of a
685  concept indeed provides all the required features.
686
687- Finally, They can serve as a skeleton of a new implementation of a concept.
688*/
689
690/**
691@defgroup graph_concepts Graph Structure Concepts
692@ingroup concept
693\brief Skeleton and concept checking classes for graph structures
694
695This group contains the skeletons and concept checking classes of
696graph structures.
697*/
698
699/**
700@defgroup map_concepts Map Concepts
701@ingroup concept
702\brief Skeleton and concept checking classes for maps
703
704This group contains the skeletons and concept checking classes of maps.
705*/
706
707/**
708@defgroup tools Standalone Utility Applications
709
710Some utility applications are listed here.
711
712The standard compilation procedure (<tt>./configure;make</tt>) will compile
713them, as well.
714*/
715
716/**
717\anchor demoprograms
718
719@defgroup demos Demo Programs
720
721Some demo programs are listed here. Their full source codes can be found in
722the \c demo subdirectory of the source tree.
723
724In order to compile them, use the <tt>make demo</tt> or the
725<tt>make check</tt> commands.
726*/
727
728}
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