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doc/groups.dox

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

Wed, 07 Aug 2013 06:31:47 +0200 | |

branch | 1.1 |

changeset 1258 | bdfc038f364c |

parent 844 | c01a98ce01fd |

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

Merge #294 to branch 1.1

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) 2003-2011

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 lemon::concepts::Path

242 */

244 /**

245 @defgroup auxdat Auxiliary Data Structures

246 @ingroup datas

247 \brief Auxiliary data structures implemented in LEMON.

249 This group contains some data structures implemented in LEMON in

250 order to make it easier to implement combinatorial algorithms.

251 */

253 /**

254 @defgroup algs Algorithms

255 \brief This group contains the several algorithms

256 implemented in LEMON.

258 This group contains the several algorithms

259 implemented in LEMON.

260 */

262 /**

263 @defgroup search Graph Search

264 @ingroup algs

265 \brief Common graph search algorithms.

267 This group contains the common graph search algorithms, namely

268 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).

269 */

271 /**

272 @defgroup shortest_path Shortest Path Algorithms

273 @ingroup algs

274 \brief Algorithms for finding shortest paths.

276 This group contains the algorithms for finding shortest paths in digraphs.

278 - \ref Dijkstra Dijkstra's algorithm for finding shortest paths from a

279 source node when all arc lengths are non-negative.

280 - \ref Suurballe A successive shortest path algorithm for finding

281 arc-disjoint paths between two nodes having minimum total length.

282 */

284 /**

285 @defgroup max_flow Maximum Flow Algorithms

286 @ingroup algs

287 \brief Algorithms for finding maximum flows.

289 This group contains the algorithms for finding maximum flows and

290 feasible circulations.

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

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

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

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

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

297 following optimization problem.

299 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]

300 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)

301 \quad \forall u\in V\setminus\{s,t\} \f]

302 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]

304 \ref Preflow implements the preflow push-relabel algorithm of Goldberg and

305 Tarjan for solving this problem. It also provides functions to query the

306 minimum cut, which is the dual problem of maximum flow.

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

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

311 but it is strongly related to maximum flow.

312 For more information, see \ref Circulation.

313 */

315 /**

316 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms

317 @ingroup algs

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

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

322 circulations. For more information about this problem and its dual

323 solution see \ref min_cost_flow "Minimum Cost Flow Problem".

325 \ref NetworkSimplex is an efficient implementation of the primal Network

326 Simplex algorithm for finding minimum cost flows. It also provides dual

327 solution (node potentials), if an optimal flow is found.

328 */

330 /**

331 @defgroup min_cut Minimum Cut Algorithms

332 @ingroup algs

334 \brief Algorithms for finding minimum cut in graphs.

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

338 The \e minimum \e cut \e problem is to find a non-empty and non-complete

339 \f$X\f$ subset of the nodes with minimum overall capacity on

340 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a

341 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

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

344 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}

345 \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]

347 LEMON contains several algorithms related to minimum cut problems:

349 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut

350 in directed graphs.

351 - \ref GomoryHu "Gomory-Hu tree computation" for calculating

352 all-pairs minimum cut in undirected graphs.

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

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

356 */

358 /**

359 @defgroup graph_properties Connectivity and Other Graph Properties

360 @ingroup algs

361 \brief Algorithms for discovering the graph properties

363 This group contains the algorithms for discovering the graph properties

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

366 \image html edge_biconnected_components.png

367 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth

368 */

370 /**

371 @defgroup matching Matching Algorithms

372 @ingroup algs

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

375 This group contains the algorithms for calculating matchings in graphs.

376 The general matching problem is finding a subset of the edges for which

377 each node has at most one incident edge.

379 There are several different algorithms for calculate matchings in

380 graphs. The goal of the matching optimization

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

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

383 maximum cardinality matching.

385 The matching algorithms implemented in LEMON:

386 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating

387 maximum cardinality matching in general graphs.

388 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating

389 maximum weighted matching in general graphs.

390 - \ref MaxWeightedPerfectMatching

391 Edmond's blossom shrinking algorithm for calculating maximum weighted

392 perfect matching in general graphs.

394 \image html bipartite_matching.png

395 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth

396 */

398 /**

399 @defgroup spantree Minimum Spanning Tree Algorithms

400 @ingroup algs

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

403 This group contains the algorithms for finding minimum cost spanning

404 trees and arborescences.

405 */

407 /**

408 @defgroup auxalg Auxiliary Algorithms

409 @ingroup algs

410 \brief Auxiliary algorithms implemented in LEMON.

412 This group contains some algorithms implemented in LEMON

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

414 */

416 /**

417 @defgroup gen_opt_group General Optimization Tools

418 \brief This group contains some general optimization frameworks

419 implemented in LEMON.

421 This group contains some general optimization frameworks

422 implemented in LEMON.

423 */

425 /**

426 @defgroup lp_group Lp and Mip Solvers

427 @ingroup gen_opt_group

428 \brief Lp and Mip solver interfaces for LEMON.

430 This group contains Lp and Mip solver interfaces for LEMON. The

431 various LP solvers could be used in the same manner with this

432 interface.

433 */

435 /**

436 @defgroup utils Tools and Utilities

437 \brief Tools and utilities for programming in LEMON

439 Tools and utilities for programming in LEMON.

440 */

442 /**

443 @defgroup gutils Basic Graph Utilities

444 @ingroup utils

445 \brief Simple basic graph utilities.

447 This group contains some simple basic graph utilities.

448 */

450 /**

451 @defgroup misc Miscellaneous Tools

452 @ingroup utils

453 \brief Tools for development, debugging and testing.

455 This group contains several useful tools for development,

456 debugging and testing.

457 */

459 /**

460 @defgroup timecount Time Measuring and Counting

461 @ingroup misc

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

464 This group contains simple tools for measuring the performance

465 of algorithms.

466 */

468 /**

469 @defgroup exceptions Exceptions

470 @ingroup utils

471 \brief Exceptions defined in LEMON.

473 This group contains the exceptions defined in LEMON.

474 */

476 /**

477 @defgroup io_group Input-Output

478 \brief Graph Input-Output methods

480 This group contains the tools for importing and exporting graphs

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

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

483 postscript (EPS) format.

484 */

486 /**

487 @defgroup lemon_io LEMON Graph Format

488 @ingroup io_group

489 \brief Reading and writing LEMON Graph Format.

491 This group contains methods for reading and writing

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

493 */

495 /**

496 @defgroup eps_io Postscript Exporting

497 @ingroup io_group

498 \brief General \c EPS drawer and graph exporter

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

501 graph exporting tools.

502 */

504 /**

505 @defgroup dimacs_group DIMACS format

506 @ingroup io_group

507 \brief Read and write files in DIMACS format

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

510 */

512 /**

513 @defgroup nauty_group NAUTY Format

514 @ingroup io_group

515 \brief Read \e Nauty format

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

518 */

520 /**

521 @defgroup concept Concepts

522 \brief Skeleton classes and concept checking classes

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

525 classes implemented in LEMON.

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

529 - These classes contain the documentations of the %concepts. In order

530 to avoid document multiplications, an implementation of a concept

531 simply refers to the corresponding concept class.

533 - These classes declare every functions, <tt>typedef</tt>s etc. an

534 implementation of the %concepts should provide, however completely

535 without implementations and real data structures behind the

536 interface. On the other hand they should provide nothing else. All

537 the algorithms working on a data structure meeting a certain concept

538 should compile with these classes. (Though it will not run properly,

539 of course.) In this way it is easily to check if an algorithm

540 doesn't use any extra feature of a certain implementation.

542 - The concept descriptor classes also provide a <em>checker class</em>

543 that makes it possible to check whether a certain implementation of a

544 concept indeed provides all the required features.

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

547 */

549 /**

550 @defgroup graph_concepts Graph Structure Concepts

551 @ingroup concept

552 \brief Skeleton and concept checking classes for graph structures

554 This group contains the skeletons and concept checking classes of LEMON's

555 graph structures and helper classes used to implement these.

556 */

558 /**

559 @defgroup map_concepts Map Concepts

560 @ingroup concept

561 \brief Skeleton and concept checking classes for maps

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

564 */

566 /**

567 \anchor demoprograms

569 @defgroup demos Demo Programs

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

572 the \c demo subdirectory of the source tree.

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

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

576 */

578 /**

579 @defgroup tools Standalone Utility Applications

581 Some utility applications are listed here.

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

584 them, as well.

585 */

587 }