COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 882:7af2ae7c1428

1.2
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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 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 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 Suurballe A successive shortest path algorithm for finding
330   arc-disjoint paths between two nodes having minimum total length.
331*/
332
333/**
334@defgroup spantree Minimum Spanning Tree Algorithms
335@ingroup algs
336\brief Algorithms for finding minimum cost spanning trees and arborescences.
337
338This group contains the algorithms for finding minimum cost spanning
339trees and arborescences \ref clrs01algorithms.
340*/
341
342/**
343@defgroup max_flow Maximum Flow Algorithms
344@ingroup algs
345\brief Algorithms for finding maximum flows.
346
347This group contains the algorithms for finding maximum flows and
348feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
349
350The \e maximum \e flow \e problem is to find a flow of maximum value between
351a single source and a single target. Formally, there is a \f$G=(V,A)\f$
352digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
353\f$s, t \in V\f$ source and target nodes.
354A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
355following optimization problem.
356
357\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
358\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
359    \quad \forall u\in V\setminus\{s,t\} \f]
360\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
361
362\ref Preflow is an efficient implementation of Goldberg-Tarjan's
363preflow push-relabel algorithm \ref goldberg88newapproach for finding
364maximum flows. It also provides functions to query the minimum cut,
365which is the dual problem of maximum flow.
366
367\ref Circulation is a preflow push-relabel algorithm implemented directly
368for finding feasible circulations, which is a somewhat different problem,
369but it is strongly related to maximum flow.
370For more information, see \ref Circulation.
371*/
372
373/**
374@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
375@ingroup algs
376
377\brief Algorithms for finding minimum cost flows and circulations.
378
379This group contains the algorithms for finding minimum cost flows and
380circulations \ref amo93networkflows. For more information about this
381problem and its dual solution, see \ref min_cost_flow
382"Minimum Cost Flow Problem".
383
384LEMON contains several algorithms for this problem.
385 - \ref NetworkSimplex Primal Network Simplex algorithm with various
386   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
387 - \ref CostScaling Cost Scaling algorithm based on push/augment and
388   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
389   \ref bunnagel98efficient.
390 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
391   shortest path method \ref edmondskarp72theoretical.
392 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
393   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
394
395In general NetworkSimplex is the most efficient implementation,
396but in special cases other algorithms could be faster.
397For example, if the total supply and/or capacities are rather small,
398CapacityScaling is usually the fastest algorithm (without effective scaling).
399*/
400
401/**
402@defgroup min_cut Minimum Cut Algorithms
403@ingroup algs
404
405\brief Algorithms for finding minimum cut in graphs.
406
407This group contains the algorithms for finding minimum cut in graphs.
408
409The \e minimum \e cut \e problem is to find a non-empty and non-complete
410\f$X\f$ subset of the nodes with minimum overall capacity on
411outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
412\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
413cut is the \f$X\f$ solution of the next optimization problem:
414
415\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
416    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
417
418LEMON contains several algorithms related to minimum cut problems:
419
420- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
421  in directed graphs.
422- \ref GomoryHu "Gomory-Hu tree computation" for calculating
423  all-pairs minimum cut in undirected graphs.
424
425If you want to find minimum cut just between two distinict nodes,
426see the \ref max_flow "maximum flow problem".
427*/
428
429/**
430@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
431@ingroup algs
432\brief Algorithms for finding minimum mean cycles.
433
434This group contains the algorithms for finding minimum mean cycles
435\ref clrs01algorithms, \ref amo93networkflows.
436
437The \e minimum \e mean \e cycle \e problem is to find a directed cycle
438of minimum mean length (cost) in a digraph.
439The mean length of a cycle is the average length of its arcs, i.e. the
440ratio between the total length of the cycle and the number of arcs on it.
441
442This problem has an important connection to \e conservative \e length
443\e functions, too. A length function on the arcs of a digraph is called
444conservative if and only if there is no directed cycle of negative total
445length. For an arbitrary length function, the negative of the minimum
446cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
447arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
448function.
449
450LEMON contains three algorithms for solving the minimum mean cycle problem:
451- \ref Karp "Karp"'s original algorithm \ref amo93networkflows,
452  \ref dasdan98minmeancycle.
453- \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
454  version of Karp's algorithm \ref dasdan98minmeancycle.
455- \ref Howard "Howard"'s policy iteration algorithm
456  \ref dasdan98minmeancycle.
457
458In practice, the Howard algorithm proved to be by far the most efficient
459one, though the best known theoretical bound on its running time is
460exponential.
461Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
462O(n<sup>2</sup>+e), but the latter one is typically faster due to the
463applied early termination scheme.
464*/
465
466/**
467@defgroup matching Matching Algorithms
468@ingroup algs
469\brief Algorithms for finding matchings in graphs and bipartite graphs.
470
471This group contains the algorithms for calculating
472matchings in graphs and bipartite graphs. The general matching problem is
473finding a subset of the edges for which each node has at most one incident
474edge.
475
476There are several different algorithms for calculate matchings in
477graphs.  The matching problems in bipartite graphs are generally
478easier than in general graphs. The goal of the matching optimization
479can be finding maximum cardinality, maximum weight or minimum cost
480matching. The search can be constrained to find perfect or
481maximum cardinality matching.
482
483The matching algorithms implemented in LEMON:
484- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
485  maximum cardinality matching in general graphs.
486- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
487  maximum weighted matching in general graphs.
488- \ref MaxWeightedPerfectMatching
489  Edmond's blossom shrinking algorithm for calculating maximum weighted
490  perfect matching in general graphs.
491- \ref MaxFractionalMatching Push-relabel algorithm for calculating
492  maximum cardinality fractional matching in general graphs.
493- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
494  maximum weighted fractional matching in general graphs.
495- \ref MaxWeightedPerfectFractionalMatching
496  Augmenting path algorithm for calculating maximum weighted
497  perfect fractional matching in general graphs.
498
499\image html matching.png
500\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
501*/
502
503/**
504@defgroup graph_properties Connectivity and Other Graph Properties
505@ingroup algs
506\brief Algorithms for discovering the graph properties
507
508This group contains the algorithms for discovering the graph properties
509like connectivity, bipartiteness, euler property, simplicity etc.
510
511\image html connected_components.png
512\image latex connected_components.eps "Connected components" width=\textwidth
513*/
514
515/**
516@defgroup planar Planarity Embedding and Drawing
517@ingroup algs
518\brief Algorithms for planarity checking, embedding and drawing
519
520This group contains the algorithms for planarity checking,
521embedding and drawing.
522
523\image html planar.png
524\image latex planar.eps "Plane graph" width=\textwidth
525*/
526
527/**
528@defgroup auxalg Auxiliary Algorithms
529@ingroup algs
530\brief Auxiliary algorithms implemented in LEMON.
531
532This group contains some algorithms implemented in LEMON
533in order to make it easier to implement complex algorithms.
534*/
535
536/**
537@defgroup gen_opt_group General Optimization Tools
538\brief This group contains some general optimization frameworks
539implemented in LEMON.
540
541This group contains some general optimization frameworks
542implemented in LEMON.
543*/
544
545/**
546@defgroup lp_group LP and MIP Solvers
547@ingroup gen_opt_group
548\brief LP and MIP solver interfaces for LEMON.
549
550This group contains LP and MIP solver interfaces for LEMON.
551Various LP solvers could be used in the same manner with this
552high-level interface.
553
554The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
555\ref cplex, \ref soplex.
556*/
557
558/**
559@defgroup utils Tools and Utilities
560\brief Tools and utilities for programming in LEMON
561
562Tools and utilities for programming in LEMON.
563*/
564
565/**
566@defgroup gutils Basic Graph Utilities
567@ingroup utils
568\brief Simple basic graph utilities.
569
570This group contains some simple basic graph utilities.
571*/
572
573/**
574@defgroup misc Miscellaneous Tools
575@ingroup utils
576\brief Tools for development, debugging and testing.
577
578This group contains several useful tools for development,
579debugging and testing.
580*/
581
582/**
583@defgroup timecount Time Measuring and Counting
584@ingroup misc
585\brief Simple tools for measuring the performance of algorithms.
586
587This group contains simple tools for measuring the performance
588of algorithms.
589*/
590
591/**
592@defgroup exceptions Exceptions
593@ingroup utils
594\brief Exceptions defined in LEMON.
595
596This group contains the exceptions defined in LEMON.
597*/
598
599/**
600@defgroup io_group Input-Output
601\brief Graph Input-Output methods
602
603This group contains the tools for importing and exporting graphs
604and graph related data. Now it supports the \ref lgf-format
605"LEMON Graph Format", the \c DIMACS format and the encapsulated
606postscript (EPS) format.
607*/
608
609/**
610@defgroup lemon_io LEMON Graph Format
611@ingroup io_group
612\brief Reading and writing LEMON Graph Format.
613
614This group contains methods for reading and writing
615\ref lgf-format "LEMON Graph Format".
616*/
617
618/**
619@defgroup eps_io Postscript Exporting
620@ingroup io_group
621\brief General \c EPS drawer and graph exporter
622
623This group contains general \c EPS drawing methods and special
624graph exporting tools.
625*/
626
627/**
628@defgroup dimacs_group DIMACS Format
629@ingroup io_group
630\brief Read and write files in DIMACS format
631
632Tools to read a digraph from or write it to a file in DIMACS format data.
633*/
634
635/**
636@defgroup nauty_group NAUTY Format
637@ingroup io_group
638\brief Read \e Nauty format
639
640Tool to read graphs from \e Nauty format data.
641*/
642
643/**
644@defgroup concept Concepts
645\brief Skeleton classes and concept checking classes
646
647This group contains the data/algorithm skeletons and concept checking
648classes implemented in LEMON.
649
650The purpose of the classes in this group is fourfold.
651
652- These classes contain the documentations of the %concepts. In order
653  to avoid document multiplications, an implementation of a concept
654  simply refers to the corresponding concept class.
655
656- These classes declare every functions, <tt>typedef</tt>s etc. an
657  implementation of the %concepts should provide, however completely
658  without implementations and real data structures behind the
659  interface. On the other hand they should provide nothing else. All
660  the algorithms working on a data structure meeting a certain concept
661  should compile with these classes. (Though it will not run properly,
662  of course.) In this way it is easily to check if an algorithm
663  doesn't use any extra feature of a certain implementation.
664
665- The concept descriptor classes also provide a <em>checker class</em>
666  that makes it possible to check whether a certain implementation of a
667  concept indeed provides all the required features.
668
669- Finally, They can serve as a skeleton of a new implementation of a concept.
670*/
671
672/**
673@defgroup graph_concepts Graph Structure Concepts
674@ingroup concept
675\brief Skeleton and concept checking classes for graph structures
676
677This group contains the skeletons and concept checking classes of
678graph structures.
679*/
680
681/**
682@defgroup map_concepts Map Concepts
683@ingroup concept
684\brief Skeleton and concept checking classes for maps
685
686This group contains the skeletons and concept checking classes of maps.
687*/
688
689/**
690@defgroup tools Standalone Utility Applications
691
692Some utility applications are listed here.
693
694The standard compilation procedure (<tt>./configure;make</tt>) will compile
695them, as well.
696*/
697
698/**
699\anchor demoprograms
700
701@defgroup demos Demo Programs
702
703Some demo programs are listed here. Their full source codes can be found in
704the \c demo subdirectory of the source tree.
705
706In order to compile them, use the <tt>make demo</tt> or the
707<tt>make check</tt> commands.
708*/
709
710}
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