COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 768:0a42883c8221

Last change on this file since 768:0a42883c8221 was 768:0a42883c8221, checked in by Peter Kovacs <kpeter@…>, 15 years ago

Separate group for the min mean cycle classes (#179)

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