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doc/groups.dox

author | Alpar Juttner <alpar@cs.elte.hu> |

Tue, 20 Dec 2011 19:10:50 +0100 | |

branch | 1.2 |

changeset 944 | 02c93d1f00d7 |

parent 882 | 7af2ae7c1428 |

parent 880 | 38213abd2911 |

permissions | -rw-r--r-- |

Merge head merging to branch 1.2

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 */

19 namespace lemon {

21 /**

22 @defgroup datas Data Structures

23 This group contains the several data structures implemented in LEMON.

24 */

26 /**

27 @defgroup graphs Graph Structures

28 @ingroup datas

29 \brief Graph structures implemented in LEMON.

31 The implementation of combinatorial algorithms heavily relies on

32 efficient graph implementations. LEMON offers data structures which are

33 planned to be easily used in an experimental phase of implementation studies,

34 and thereafter the program code can be made efficient by small modifications.

36 The most efficient implementation of diverse applications require the

37 usage of different physical graph implementations. These differences

38 appear in the size of graph we require to handle, memory or time usage

39 limitations or in the set of operations through which the graph can be

40 accessed. LEMON provides several physical graph structures to meet

41 the diverging requirements of the possible users. In order to save on

42 running time or on memory usage, some structures may fail to provide

43 some graph features like arc/edge or node deletion.

45 Alteration of standard containers need a very limited number of

46 operations, these together satisfy the everyday requirements.

47 In the case of graph structures, different operations are needed which do

48 not alter the physical graph, but gives another view. If some nodes or

49 arcs have to be hidden or the reverse oriented graph have to be used, then

50 this is the case. It also may happen that in a flow implementation

51 the residual graph can be accessed by another algorithm, or a node-set

52 is to be shrunk for another algorithm.

53 LEMON also provides a variety of graphs for these requirements called

54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only

55 in conjunction with other graph representations.

57 You are free to use the graph structure that fit your requirements

58 the best, most graph algorithms and auxiliary data structures can be used

59 with any graph structure.

61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".

62 */

64 /**

65 @defgroup graph_adaptors Adaptor Classes for Graphs

66 @ingroup graphs

67 \brief Adaptor classes for digraphs and graphs

69 This group contains several useful adaptor classes for digraphs and graphs.

71 The main parts of LEMON are the different graph structures, generic

72 graph algorithms, graph concepts, which couple them, and graph

73 adaptors. While the previous notions are more or less clear, the

74 latter one needs further explanation. Graph adaptors are graph classes

75 which serve for considering graph structures in different ways.

77 A short example makes this much clearer. Suppose that we have an

78 instance \c g of a directed graph type, say ListDigraph and an algorithm

79 \code

80 template <typename Digraph>

81 int algorithm(const Digraph&);

82 \endcode

83 is 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

85 arcs. In this case, an adaptor class is used, which (according

86 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.

87 The adaptor uses the original digraph structure and digraph operations when

88 methods of the reversed oriented graph are called. This means that the adaptor

89 have minor memory usage, and do not perform sophisticated algorithmic

90 actions. The purpose of it is to give a tool for the cases when a

91 graph have to be used in a specific alteration. If this alteration is

92 obtained by a usual construction like filtering the node or the arc set or

93 considering a new orientation, then an adaptor is worthwhile to use.

94 To come back to the reverse oriented graph, in this situation

95 \code

96 template<typename Digraph> class ReverseDigraph;

97 \endcode

98 template class can be used. The code looks as follows

99 \code

100 ListDigraph g;

101 ReverseDigraph<ListDigraph> rg(g);

102 int result = algorithm(rg);

103 \endcode

104 During running the algorithm, the original digraph \c g is untouched.

105 This techniques give rise to an elegant code, and based on stable

106 graph adaptors, complex algorithms can be implemented easily.

108 In flow, circulation and matching problems, the residual

109 graph is of particular importance. Combining an adaptor implementing

110 this with shortest path algorithms or minimum mean cycle algorithms,

111 a range of weighted and cardinality optimization algorithms can be

112 obtained. For other examples, the interested user is referred to the

113 detailed documentation of particular adaptors.

115 The behavior of graph adaptors can be very different. Some of them keep

116 capabilities of the original graph while in other cases this would be

117 meaningless. This means that the concepts that they meet depend

118 on the graph adaptor, and the wrapped graph.

119 For example, if an arc of a reversed digraph is deleted, this is carried

120 out by deleting the corresponding arc of the original digraph, thus the

121 adaptor modifies the original digraph.

122 However in case of a residual digraph, this operation has no sense.

124 Let us stand one more example here to simplify your work.

125 ReverseDigraph has constructor

126 \code

127 ReverseDigraph(Digraph& digraph);

128 \endcode

129 This means that in a situation, when a <tt>const %ListDigraph&</tt>

130 reference to a graph is given, then it have to be instantiated with

131 <tt>Digraph=const %ListDigraph</tt>.

132 \code

133 int algorithm1(const ListDigraph& g) {

134 ReverseDigraph<const ListDigraph> rg(g);

135 return algorithm2(rg);

136 }

137 \endcode

138 */

140 /**

141 @defgroup maps Maps

142 @ingroup datas

143 \brief Map structures implemented in LEMON.

145 This group contains the map structures implemented in LEMON.

147 LEMON provides several special purpose maps and map adaptors that e.g. combine

148 new maps from existing ones.

150 <b>See also:</b> \ref map_concepts "Map Concepts".

151 */

153 /**

154 @defgroup graph_maps Graph Maps

155 @ingroup maps

156 \brief Special graph-related maps.

158 This group contains maps that are specifically designed to assign

159 values to the nodes and arcs/edges of graphs.

161 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,

162 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".

163 */

165 /**

166 \defgroup map_adaptors Map Adaptors

167 \ingroup maps

168 \brief Tools to create new maps from existing ones

170 This group contains map adaptors that are used to create "implicit"

171 maps from other maps.

173 Most of them are \ref concepts::ReadMap "read-only maps".

174 They 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.

178 The typical usage of this classes is passing implicit maps to

179 algorithms. If a function type algorithm is called then the function

180 type map adaptors can be used comfortable. For example let's see the

181 usage 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 }

193 Digraph::NodeMap<int> degree_map(graph);

195 graphToEps(graph, "graph.eps")

196 .coords(coords).scaleToA4().undirected()

197 .nodeColors(composeMap(functorToMap(nodeColor), degree_map))

198 .run();

199 \endcode

200 The \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

202 and the previously created map. The composed map is a proper function to

203 get the color of each node.

205 The usage with class type algorithms is little bit harder. In this

206 case the function type map adaptors can not be used, because the

207 function map adaptors give back temporary objects.

208 \code

209 Digraph graph;

211 typedef Digraph::ArcMap<double> DoubleArcMap;

212 DoubleArcMap length(graph);

213 DoubleArcMap speed(graph);

215 typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;

216 TimeMap time(length, speed);

218 Dijkstra<Digraph, TimeMap> dijkstra(graph, time);

219 dijkstra.run(source, target);

220 \endcode

221 We have a length map and a maximum speed map on the arcs of a digraph.

222 The minimum time to pass the arc can be calculated as the division of

223 the two maps which can be done implicitly with the \c DivMap template

224 class. We use the implicit minimum time map as the length map of the

225 \c Dijkstra algorithm.

226 */

228 /**

229 @defgroup paths Path Structures

230 @ingroup datas

231 \brief %Path structures implemented in LEMON.

233 This group contains the path structures implemented in LEMON.

235 LEMON provides flexible data structures to work with paths.

236 All of them have similar interfaces and they can be copied easily with

237 assignment operators and copy constructors. This makes it easy and

238 efficient to have e.g. the Dijkstra algorithm to store its result in

239 any kind of path structure.

241 \sa \ref concepts::Path "Path concept"

242 */

244 /**

245 @defgroup heaps Heap Structures

246 @ingroup datas

247 \brief %Heap structures implemented in LEMON.

249 This group contains the heap structures implemented in LEMON.

251 LEMON provides several heap classes. They are efficient implementations

252 of the abstract data type \e priority \e queue. They store items with

253 specified values called \e priorities in such a way that finding and

254 removing the item with minimum priority are efficient.

255 The basic operations are adding and erasing items, changing the priority

256 of an item, etc.

258 Heaps are crucial in several algorithms, such as Dijkstra and Prim.

259 The heap implementations have the same interface, thus any of them can be

260 used easily in such algorithms.

262 \sa \ref concepts::Heap "Heap concept"

263 */

265 /**

266 @defgroup auxdat Auxiliary Data Structures

267 @ingroup datas

268 \brief Auxiliary data structures implemented in LEMON.

270 This group contains some data structures implemented in LEMON in

271 order to make it easier to implement combinatorial algorithms.

272 */

274 /**

275 @defgroup geomdat Geometric Data Structures

276 @ingroup auxdat

277 \brief Geometric data structures implemented in LEMON.

279 This group contains geometric data structures implemented in LEMON.

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 */

288 /**

289 @defgroup algs Algorithms

290 \brief This group contains the several algorithms

291 implemented in LEMON.

293 This group contains the several algorithms

294 implemented in LEMON.

295 */

297 /**

298 @defgroup search Graph Search

299 @ingroup algs

300 \brief Common graph search algorithms.

302 This 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 */

307 /**

308 @defgroup shortest_path Shortest Path Algorithms

309 @ingroup algs

310 \brief Algorithms for finding shortest paths.

312 This group contains the algorithms for finding shortest paths in digraphs

313 \ref clrs01algorithms.

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 */

325 /**

326 @defgroup spantree Minimum Spanning Tree Algorithms

327 @ingroup algs

328 \brief Algorithms for finding minimum cost spanning trees and arborescences.

330 This group contains the algorithms for finding minimum cost spanning

331 trees and arborescences \ref clrs01algorithms.

332 */

334 /**

335 @defgroup max_flow Maximum Flow Algorithms

336 @ingroup algs

337 \brief Algorithms for finding maximum flows.

339 This group contains the algorithms for finding maximum flows and

340 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.

342 The \e maximum \e flow \e problem is to find a flow of maximum value between

343 a single source and a single target. Formally, there is a \f$G=(V,A)\f$

344 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and

345 \f$s, t \in V\f$ source and target nodes.

346 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the

347 following optimization problem.

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]

354 \ref Preflow is an efficient implementation of Goldberg-Tarjan's

355 preflow push-relabel algorithm \ref goldberg88newapproach for finding

356 maximum flows. It also provides functions to query the minimum cut,

357 which is the dual problem of maximum flow.

359 \ref Circulation is a preflow push-relabel algorithm implemented directly

360 for finding feasible circulations, which is a somewhat different problem,

361 but it is strongly related to maximum flow.

362 For more information, see \ref Circulation.

363 */

365 /**

366 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms

367 @ingroup algs

369 \brief Algorithms for finding minimum cost flows and circulations.

371 This group contains the algorithms for finding minimum cost flows and

372 circulations \ref amo93networkflows. For more information about this

373 problem and its dual solution, see \ref min_cost_flow

374 "Minimum Cost Flow Problem".

376 LEMON 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.

387 In general NetworkSimplex is the most efficient implementation,

388 but in special cases other algorithms could be faster.

389 For example, if the total supply and/or capacities are rather small,

390 CapacityScaling is usually the fastest algorithm (without effective scaling).

391 */

393 /**

394 @defgroup min_cut Minimum Cut Algorithms

395 @ingroup algs

397 \brief Algorithms for finding minimum cut in graphs.

399 This group contains the algorithms for finding minimum cut in graphs.

401 The \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

403 outgoing 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

405 cut is the \f$X\f$ solution of the next optimization problem:

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]

410 LEMON contains several algorithms related to minimum cut problems:

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.

417 If you want to find minimum cut just between two distinict nodes,

418 see the \ref max_flow "maximum flow problem".

419 */

421 /**

422 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms

423 @ingroup algs

424 \brief Algorithms for finding minimum mean cycles.

426 This group contains the algorithms for finding minimum mean cycles

427 \ref clrs01algorithms, \ref amo93networkflows.

429 The \e minimum \e mean \e cycle \e problem is to find a directed cycle

430 of minimum mean length (cost) in a digraph.

431 The mean length of a cycle is the average length of its arcs, i.e. the

432 ratio between the total length of the cycle and the number of arcs on it.

434 This 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

436 conservative if and only if there is no directed cycle of negative total

437 length. For an arbitrary length function, the negative of the minimum

438 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the

439 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length

440 function.

442 LEMON 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.

450 In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the

451 most efficient one, though the best known theoretical bound on its running

452 time is exponential.

453 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms

454 run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is

455 typically faster due to the applied early termination scheme.

456 */

458 /**

459 @defgroup matching Matching Algorithms

460 @ingroup algs

461 \brief Algorithms for finding matchings in graphs and bipartite graphs.

463 This group contains the algorithms for calculating

464 matchings in graphs and bipartite graphs. The general matching problem is

465 finding a subset of the edges for which each node has at most one incident

466 edge.

468 There are several different algorithms for calculate matchings in

469 graphs. The matching problems in bipartite graphs are generally

470 easier than in general graphs. The goal of the matching optimization

471 can be finding maximum cardinality, maximum weight or minimum cost

472 matching. The search can be constrained to find perfect or

473 maximum cardinality matching.

475 The 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.

491 \image html matching.png

492 \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth

493 */

495 /**

496 @defgroup graph_properties Connectivity and Other Graph Properties

497 @ingroup algs

498 \brief Algorithms for discovering the graph properties

500 This group contains the algorithms for discovering the graph properties

501 like connectivity, bipartiteness, euler property, simplicity etc.

503 \image html connected_components.png

504 \image latex connected_components.eps "Connected components" width=\textwidth

505 */

507 /**

508 @defgroup planar Planarity Embedding and Drawing

509 @ingroup algs

510 \brief Algorithms for planarity checking, embedding and drawing

512 This group contains the algorithms for planarity checking,

513 embedding and drawing.

515 \image html planar.png

516 \image latex planar.eps "Plane graph" width=\textwidth

517 */

519 /**

520 @defgroup auxalg Auxiliary Algorithms

521 @ingroup algs

522 \brief Auxiliary algorithms implemented in LEMON.

524 This group contains some algorithms implemented in LEMON

525 in order to make it easier to implement complex algorithms.

526 */

528 /**

529 @defgroup gen_opt_group General Optimization Tools

530 \brief This group contains some general optimization frameworks

531 implemented in LEMON.

533 This group contains some general optimization frameworks

534 implemented in LEMON.

535 */

537 /**

538 @defgroup lp_group LP and MIP Solvers

539 @ingroup gen_opt_group

540 \brief LP and MIP solver interfaces for LEMON.

542 This group contains LP and MIP solver interfaces for LEMON.

543 Various LP solvers could be used in the same manner with this

544 high-level interface.

546 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,

547 \ref cplex, \ref soplex.

548 */

550 /**

551 @defgroup utils Tools and Utilities

552 \brief Tools and utilities for programming in LEMON

554 Tools and utilities for programming in LEMON.

555 */

557 /**

558 @defgroup gutils Basic Graph Utilities

559 @ingroup utils

560 \brief Simple basic graph utilities.

562 This group contains some simple basic graph utilities.

563 */

565 /**

566 @defgroup misc Miscellaneous Tools

567 @ingroup utils

568 \brief Tools for development, debugging and testing.

570 This group contains several useful tools for development,

571 debugging and testing.

572 */

574 /**

575 @defgroup timecount Time Measuring and Counting

576 @ingroup misc

577 \brief Simple tools for measuring the performance of algorithms.

579 This group contains simple tools for measuring the performance

580 of algorithms.

581 */

583 /**

584 @defgroup exceptions Exceptions

585 @ingroup utils

586 \brief Exceptions defined in LEMON.

588 This group contains the exceptions defined in LEMON.

589 */

591 /**

592 @defgroup io_group Input-Output

593 \brief Graph Input-Output methods

595 This group contains the tools for importing and exporting graphs

596 and graph related data. Now it supports the \ref lgf-format

597 "LEMON Graph Format", the \c DIMACS format and the encapsulated

598 postscript (EPS) format.

599 */

601 /**

602 @defgroup lemon_io LEMON Graph Format

603 @ingroup io_group

604 \brief Reading and writing LEMON Graph Format.

606 This group contains methods for reading and writing

607 \ref lgf-format "LEMON Graph Format".

608 */

610 /**

611 @defgroup eps_io Postscript Exporting

612 @ingroup io_group

613 \brief General \c EPS drawer and graph exporter

615 This group contains general \c EPS drawing methods and special

616 graph exporting tools.

617 */

619 /**

620 @defgroup dimacs_group DIMACS Format

621 @ingroup io_group

622 \brief Read and write files in DIMACS format

624 Tools to read a digraph from or write it to a file in DIMACS format data.

625 */

627 /**

628 @defgroup nauty_group NAUTY Format

629 @ingroup io_group

630 \brief Read \e Nauty format

632 Tool to read graphs from \e Nauty format data.

633 */

635 /**

636 @defgroup concept Concepts

637 \brief Skeleton classes and concept checking classes

639 This group contains the data/algorithm skeletons and concept checking

640 classes implemented in LEMON.

642 The purpose of the classes in this group is fourfold.

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.

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.

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.

661 - Finally, They can serve as a skeleton of a new implementation of a concept.

662 */

664 /**

665 @defgroup graph_concepts Graph Structure Concepts

666 @ingroup concept

667 \brief Skeleton and concept checking classes for graph structures

669 This group contains the skeletons and concept checking classes of

670 graph structures.

671 */

673 /**

674 @defgroup map_concepts Map Concepts

675 @ingroup concept

676 \brief Skeleton and concept checking classes for maps

678 This group contains the skeletons and concept checking classes of maps.

679 */

681 /**

682 @defgroup tools Standalone Utility Applications

684 Some utility applications are listed here.

686 The standard compilation procedure (<tt>./configure;make</tt>) will compile

687 them, as well.

688 */

690 /**

691 \anchor demoprograms

693 @defgroup demos Demo Programs

695 Some demo programs are listed here. Their full source codes can be found in

696 the \c demo subdirectory of the source tree.

698 In order to compile them, use the <tt>make demo</tt> or the

699 <tt>make check</tt> commands.

700 */

702 }