COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox

1.2 r1.2
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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 auxdat Auxiliary Data Structures
267@ingroup datas
268\brief Auxiliary data structures implemented in LEMON.
269
270This group contains some data structures implemented in LEMON in
271order to make it easier to implement combinatorial algorithms.
272*/
273
274/**
275@defgroup geomdat Geometric Data Structures
276@ingroup auxdat
277\brief Geometric data structures implemented in LEMON.
278
279This group contains geometric data structures implemented in LEMON.
280
281 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
282   vector with the usual operations.
283 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
284   rectangular bounding box of a set of \ref lemon::dim2::Point
285   "dim2::Point"'s.
286*/
287
288/**
289@defgroup algs Algorithms
290\brief This group contains the several algorithms
291implemented in LEMON.
292
293This group contains the several algorithms
294implemented in LEMON.
295*/
296
297/**
298@defgroup search Graph Search
299@ingroup algs
300\brief Common graph search algorithms.
301
302This group contains the common graph search algorithms, namely
303\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
304\ref clrs01algorithms.
305*/
306
307/**
308@defgroup shortest_path Shortest Path Algorithms
309@ingroup algs
310\brief Algorithms for finding shortest paths.
311
312This group contains the algorithms for finding shortest paths in digraphs
313\ref clrs01algorithms.
314
315 - \ref Dijkstra algorithm for finding shortest paths from a source node
316   when all arc lengths are non-negative.
317 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
318   from a source node when arc lenghts can be either positive or negative,
319   but the digraph should not contain directed cycles with negative total
320   length.
321 - \ref Suurballe A successive shortest path algorithm for finding
322   arc-disjoint paths between two nodes having minimum total length.
323*/
324
325/**
326@defgroup spantree Minimum Spanning Tree Algorithms
327@ingroup algs
328\brief Algorithms for finding minimum cost spanning trees and arborescences.
329
330This group contains the algorithms for finding minimum cost spanning
331trees and arborescences \ref clrs01algorithms.
332*/
333
334/**
335@defgroup max_flow Maximum Flow Algorithms
336@ingroup algs
337\brief Algorithms for finding maximum flows.
338
339This group contains the algorithms for finding maximum flows and
340feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
341
342The \e maximum \e flow \e problem is to find a flow of maximum value between
343a single source and a single target. Formally, there is a \f$G=(V,A)\f$
344digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
345\f$s, t \in V\f$ source and target nodes.
346A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
347following optimization problem.
348
349\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
350\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
351    \quad \forall u\in V\setminus\{s,t\} \f]
352\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
353
354\ref Preflow is an efficient implementation of Goldberg-Tarjan's
355preflow push-relabel algorithm \ref goldberg88newapproach for finding
356maximum flows. It also provides functions to query the minimum cut,
357which is the dual problem of maximum flow.
358
359\ref Circulation is a preflow push-relabel algorithm implemented directly
360for finding feasible circulations, which is a somewhat different problem,
361but it is strongly related to maximum flow.
362For more information, see \ref Circulation.
363*/
364
365/**
366@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
367@ingroup algs
368
369\brief Algorithms for finding minimum cost flows and circulations.
370
371This group contains the algorithms for finding minimum cost flows and
372circulations \ref amo93networkflows. For more information about this
373problem and its dual solution, see \ref min_cost_flow
374"Minimum Cost Flow Problem".
375
376LEMON contains several algorithms for this problem.
377 - \ref NetworkSimplex Primal Network Simplex algorithm with various
378   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
379 - \ref CostScaling Cost Scaling algorithm based on push/augment and
380   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
381   \ref bunnagel98efficient.
382 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
383   shortest path method \ref edmondskarp72theoretical.
384 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
385   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
386
387In general NetworkSimplex is the most efficient implementation,
388but in special cases other algorithms could be faster.
389For example, if the total supply and/or capacities are rather small,
390CapacityScaling is usually the fastest algorithm (without effective scaling).
391*/
392
393/**
394@defgroup min_cut Minimum Cut Algorithms
395@ingroup algs
396
397\brief Algorithms for finding minimum cut in graphs.
398
399This group contains the algorithms for finding minimum cut in graphs.
400
401The \e minimum \e cut \e problem is to find a non-empty and non-complete
402\f$X\f$ subset of the nodes with minimum overall capacity on
403outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
404\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
405cut is the \f$X\f$ solution of the next optimization problem:
406
407\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
408    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
409
410LEMON contains several algorithms related to minimum cut problems:
411
412- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
413  in directed graphs.
414- \ref GomoryHu "Gomory-Hu tree computation" for calculating
415  all-pairs minimum cut in undirected graphs.
416
417If you want to find minimum cut just between two distinict nodes,
418see the \ref max_flow "maximum flow problem".
419*/
420
421/**
422@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
423@ingroup algs
424\brief Algorithms for finding minimum mean cycles.
425
426This group contains the algorithms for finding minimum mean cycles
427\ref clrs01algorithms, \ref amo93networkflows.
428
429The \e minimum \e mean \e cycle \e problem is to find a directed cycle
430of minimum mean length (cost) in a digraph.
431The mean length of a cycle is the average length of its arcs, i.e. the
432ratio between the total length of the cycle and the number of arcs on it.
433
434This problem has an important connection to \e conservative \e length
435\e functions, too. A length function on the arcs of a digraph is called
436conservative if and only if there is no directed cycle of negative total
437length. For an arbitrary length function, the negative of the minimum
438cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
439arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
440function.
441
442LEMON contains three algorithms for solving the minimum mean cycle problem:
443- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
444  \ref dasdan98minmeancycle.
445- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
446  version of Karp's algorithm \ref dasdan98minmeancycle.
447- \ref HowardMmc Howard's policy iteration algorithm
448  \ref dasdan98minmeancycle.
449
450In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
451most efficient one, though the best known theoretical bound on its running
452time is exponential.
453Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
454run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
455typically faster due to the applied early termination scheme.
456*/
457
458/**
459@defgroup matching Matching Algorithms
460@ingroup algs
461\brief Algorithms for finding matchings in graphs and bipartite graphs.
462
463This group contains the algorithms for calculating
464matchings in graphs and bipartite graphs. The general matching problem is
465finding a subset of the edges for which each node has at most one incident
466edge.
467
468There are several different algorithms for calculate matchings in
469graphs.  The matching problems in bipartite graphs are generally
470easier than in general graphs. The goal of the matching optimization
471can be finding maximum cardinality, maximum weight or minimum cost
472matching. The search can be constrained to find perfect or
473maximum cardinality matching.
474
475The matching algorithms implemented in LEMON:
476- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
477  maximum cardinality matching in general graphs.
478- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
479  maximum weighted matching in general graphs.
480- \ref MaxWeightedPerfectMatching
481  Edmond's blossom shrinking algorithm for calculating maximum weighted
482  perfect matching in general graphs.
483- \ref MaxFractionalMatching Push-relabel algorithm for calculating
484  maximum cardinality fractional matching in general graphs.
485- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
486  maximum weighted fractional matching in general graphs.
487- \ref MaxWeightedPerfectFractionalMatching
488  Augmenting path algorithm for calculating maximum weighted
489  perfect fractional matching in general graphs.
490
491\image html matching.png
492\image latex matching.eps "Min Cost Perfect 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 auxalg Auxiliary Algorithms
521@ingroup algs
522\brief Auxiliary algorithms implemented in LEMON.
523
524This group contains some algorithms implemented in LEMON
525in order to make it easier to implement complex algorithms.
526*/
527
528/**
529@defgroup gen_opt_group General Optimization Tools
530\brief This group contains some general optimization frameworks
531implemented in LEMON.
532
533This group contains some general optimization frameworks
534implemented in LEMON.
535*/
536
537/**
538@defgroup lp_group LP and MIP Solvers
539@ingroup gen_opt_group
540\brief LP and MIP solver interfaces for LEMON.
541
542This group contains LP and MIP solver interfaces for LEMON.
543Various LP solvers could be used in the same manner with this
544high-level interface.
545
546The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
547\ref cplex, \ref soplex.
548*/
549
550/**
551@defgroup utils Tools and Utilities
552\brief Tools and utilities for programming in LEMON
553
554Tools and utilities for programming in LEMON.
555*/
556
557/**
558@defgroup gutils Basic Graph Utilities
559@ingroup utils
560\brief Simple basic graph utilities.
561
562This group contains some simple basic graph utilities.
563*/
564
565/**
566@defgroup misc Miscellaneous Tools
567@ingroup utils
568\brief Tools for development, debugging and testing.
569
570This group contains several useful tools for development,
571debugging and testing.
572*/
573
574/**
575@defgroup timecount Time Measuring and Counting
576@ingroup misc
577\brief Simple tools for measuring the performance of algorithms.
578
579This group contains simple tools for measuring the performance
580of algorithms.
581*/
582
583/**
584@defgroup exceptions Exceptions
585@ingroup utils
586\brief Exceptions defined in LEMON.
587
588This group contains the exceptions defined in LEMON.
589*/
590
591/**
592@defgroup io_group Input-Output
593\brief Graph Input-Output methods
594
595This group contains the tools for importing and exporting graphs
596and graph related data. Now it supports the \ref lgf-format
597"LEMON Graph Format", the \c DIMACS format and the encapsulated
598postscript (EPS) format.
599*/
600
601/**
602@defgroup lemon_io LEMON Graph Format
603@ingroup io_group
604\brief Reading and writing LEMON Graph Format.
605
606This group contains methods for reading and writing
607\ref lgf-format "LEMON Graph Format".
608*/
609
610/**
611@defgroup eps_io Postscript Exporting
612@ingroup io_group
613\brief General \c EPS drawer and graph exporter
614
615This group contains general \c EPS drawing methods and special
616graph exporting tools.
617*/
618
619/**
620@defgroup dimacs_group DIMACS Format
621@ingroup io_group
622\brief Read and write files in DIMACS format
623
624Tools to read a digraph from or write it to a file in DIMACS format data.
625*/
626
627/**
628@defgroup nauty_group NAUTY Format
629@ingroup io_group
630\brief Read \e Nauty format
631
632Tool to read graphs from \e Nauty format data.
633*/
634
635/**
636@defgroup concept Concepts
637\brief Skeleton classes and concept checking classes
638
639This group contains the data/algorithm skeletons and concept checking
640classes implemented in LEMON.
641
642The purpose of the classes in this group is fourfold.
643
644- These classes contain the documentations of the %concepts. In order
645  to avoid document multiplications, an implementation of a concept
646  simply refers to the corresponding concept class.
647
648- These classes declare every functions, <tt>typedef</tt>s etc. an
649  implementation of the %concepts should provide, however completely
650  without implementations and real data structures behind the
651  interface. On the other hand they should provide nothing else. All
652  the algorithms working on a data structure meeting a certain concept
653  should compile with these classes. (Though it will not run properly,
654  of course.) In this way it is easily to check if an algorithm
655  doesn't use any extra feature of a certain implementation.
656
657- The concept descriptor classes also provide a <em>checker class</em>
658  that makes it possible to check whether a certain implementation of a
659  concept indeed provides all the required features.
660
661- Finally, They can serve as a skeleton of a new implementation of a concept.
662*/
663
664/**
665@defgroup graph_concepts Graph Structure Concepts
666@ingroup concept
667\brief Skeleton and concept checking classes for graph structures
668
669This group contains the skeletons and concept checking classes of
670graph structures.
671*/
672
673/**
674@defgroup map_concepts Map Concepts
675@ingroup concept
676\brief Skeleton and concept checking classes for maps
677
678This group contains the skeletons and concept checking classes of maps.
679*/
680
681/**
682@defgroup tools Standalone Utility Applications
683
684Some utility applications are listed here.
685
686The standard compilation procedure (<tt>./configure;make</tt>) will compile
687them, as well.
688*/
689
690/**
691\anchor demoprograms
692
693@defgroup demos Demo Programs
694
695Some demo programs are listed here. Their full source codes can be found in
696the \c demo subdirectory of the source tree.
697
698In order to compile them, use the <tt>make demo</tt> or the
699<tt>make check</tt> commands.
700*/
701
702}
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