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doc/groups.dox

author | Peter Kovacs <kpeter@inf.elte.hu> |

Sun, 23 Aug 2009 11:09:22 +0200 | |

changeset 782 | 853fcddcf282 |

parent 710 | 8b0df68370a4 |

child 789 | 8e68671af789 |

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

Doc improvements, fixes and unifications for graphs (#311)

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 */

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 matrices Matrices

230 @ingroup datas

231 \brief Two dimensional data storages implemented in LEMON.

233 This group contains two dimensional data storages implemented in LEMON.

234 */

236 /**

237 @defgroup paths Path Structures

238 @ingroup datas

239 \brief %Path structures implemented in LEMON.

241 This group contains the path structures implemented in LEMON.

243 LEMON provides flexible data structures to work with paths.

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

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

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

247 any kind of path structure.

249 \sa lemon::concepts::Path

250 */

252 /**

253 @defgroup auxdat Auxiliary Data Structures

254 @ingroup datas

255 \brief Auxiliary data structures implemented in LEMON.

257 This group contains some data structures implemented in LEMON in

258 order to make it easier to implement combinatorial algorithms.

259 */

261 /**

262 @defgroup algs Algorithms

263 \brief This group contains the several algorithms

264 implemented in LEMON.

266 This group contains the several algorithms

267 implemented in LEMON.

268 */

270 /**

271 @defgroup search Graph Search

272 @ingroup algs

273 \brief Common graph search algorithms.

275 This group contains the common graph search algorithms, namely

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

277 */

279 /**

280 @defgroup shortest_path Shortest Path Algorithms

281 @ingroup algs

282 \brief Algorithms for finding shortest paths.

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

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 */

300 /**

301 @defgroup max_flow Maximum Flow Algorithms

302 @ingroup algs

303 \brief Algorithms for finding maximum flows.

305 This group contains the algorithms for finding maximum flows and

306 feasible circulations.

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

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

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

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

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

313 following optimization problem.

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]

320 LEMON 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.

326 In most cases the \ref Preflow "Preflow" algorithm provides the

327 fastest method for computing a maximum flow. All implementations

328 also provide functions to query the minimum cut, which is the dual

329 problem of maximum flow.

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

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

333 but it is strongly related to maximum flow.

334 For more information, see \ref Circulation.

335 */

337 /**

338 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms

339 @ingroup algs

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

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

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

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

347 LEMON 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.

357 In general NetworkSimplex is the most efficient implementation,

358 but in special cases other algorithms could be faster.

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

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

361 */

363 /**

364 @defgroup min_cut Minimum Cut Algorithms

365 @ingroup algs

367 \brief Algorithms for finding minimum cut in graphs.

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

371 The \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

373 outgoing 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

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

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]

380 LEMON contains several algorithms related to minimum cut problems:

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.

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

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

391 */

393 /**

394 @defgroup graph_properties Connectivity and Other Graph Properties

395 @ingroup algs

396 \brief Algorithms for discovering the graph properties

398 This group contains the algorithms for discovering the graph properties

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

401 \image html edge_biconnected_components.png

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

403 */

405 /**

406 @defgroup planar Planarity Embedding and Drawing

407 @ingroup algs

408 \brief Algorithms for planarity checking, embedding and drawing

410 This group contains the algorithms for planarity checking,

411 embedding and drawing.

413 \image html planar.png

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

415 */

417 /**

418 @defgroup matching Matching Algorithms

419 @ingroup algs

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

422 This group contains the algorithms for calculating

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

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

425 edge.

427 There are several different algorithms for calculate matchings in

428 graphs. The matching problems in bipartite graphs are generally

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

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

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

432 maximum cardinality matching.

434 The matching algorithms implemented in LEMON:

435 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm

436 for calculating maximum cardinality matching in bipartite graphs.

437 - \ref PrBipartiteMatching Push-relabel algorithm

438 for calculating maximum cardinality matching in bipartite graphs.

439 - \ref MaxWeightedBipartiteMatching

440 Successive shortest path algorithm for calculating maximum weighted

441 matching and maximum weighted bipartite matching in bipartite graphs.

442 - \ref MinCostMaxBipartiteMatching

443 Successive shortest path algorithm for calculating minimum cost maximum

444 matching in bipartite graphs.

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

446 maximum cardinality matching in general graphs.

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

448 maximum weighted matching in general graphs.

449 - \ref MaxWeightedPerfectMatching

450 Edmond's blossom shrinking algorithm for calculating maximum weighted

451 perfect matching in general graphs.

453 \image html bipartite_matching.png

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

455 */

457 /**

458 @defgroup spantree Minimum Spanning Tree Algorithms

459 @ingroup algs

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

462 This group contains the algorithms for finding minimum cost spanning

463 trees and arborescences.

464 */

466 /**

467 @defgroup auxalg Auxiliary Algorithms

468 @ingroup algs

469 \brief Auxiliary algorithms implemented in LEMON.

471 This group contains some algorithms implemented in LEMON

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

473 */

475 /**

476 @defgroup approx Approximation Algorithms

477 @ingroup algs

478 \brief Approximation algorithms.

480 This group contains the approximation and heuristic algorithms

481 implemented in LEMON.

482 */

484 /**

485 @defgroup gen_opt_group General Optimization Tools

486 \brief This group contains some general optimization frameworks

487 implemented in LEMON.

489 This group contains some general optimization frameworks

490 implemented in LEMON.

491 */

493 /**

494 @defgroup lp_group Lp and Mip Solvers

495 @ingroup gen_opt_group

496 \brief Lp and Mip solver interfaces for LEMON.

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

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

500 interface.

501 */

503 /**

504 @defgroup lp_utils Tools for Lp and Mip Solvers

505 @ingroup lp_group

506 \brief Helper tools to the Lp and Mip solvers.

508 This group adds some helper tools to general optimization framework

509 implemented in LEMON.

510 */

512 /**

513 @defgroup metah Metaheuristics

514 @ingroup gen_opt_group

515 \brief Metaheuristics for LEMON library.

517 This group contains some metaheuristic optimization tools.

518 */

520 /**

521 @defgroup utils Tools and Utilities

522 \brief Tools and utilities for programming in LEMON

524 Tools and utilities for programming in LEMON.

525 */

527 /**

528 @defgroup gutils Basic Graph Utilities

529 @ingroup utils

530 \brief Simple basic graph utilities.

532 This group contains some simple basic graph utilities.

533 */

535 /**

536 @defgroup misc Miscellaneous Tools

537 @ingroup utils

538 \brief Tools for development, debugging and testing.

540 This group contains several useful tools for development,

541 debugging and testing.

542 */

544 /**

545 @defgroup timecount Time Measuring and Counting

546 @ingroup misc

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

549 This group contains simple tools for measuring the performance

550 of algorithms.

551 */

553 /**

554 @defgroup exceptions Exceptions

555 @ingroup utils

556 \brief Exceptions defined in LEMON.

558 This group contains the exceptions defined in LEMON.

559 */

561 /**

562 @defgroup io_group Input-Output

563 \brief Graph Input-Output methods

565 This group contains the tools for importing and exporting graphs

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

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

568 postscript (EPS) format.

569 */

571 /**

572 @defgroup lemon_io LEMON Graph Format

573 @ingroup io_group

574 \brief Reading and writing LEMON Graph Format.

576 This group contains methods for reading and writing

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

578 */

580 /**

581 @defgroup eps_io Postscript Exporting

582 @ingroup io_group

583 \brief General \c EPS drawer and graph exporter

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

586 graph exporting tools.

587 */

589 /**

590 @defgroup dimacs_group DIMACS format

591 @ingroup io_group

592 \brief Read and write files in DIMACS format

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

595 */

597 /**

598 @defgroup nauty_group NAUTY Format

599 @ingroup io_group

600 \brief Read \e Nauty format

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

603 */

605 /**

606 @defgroup concept Concepts

607 \brief Skeleton classes and concept checking classes

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

610 classes implemented in LEMON.

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

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

615 to avoid document multiplications, an implementation of a concept

616 simply refers to the corresponding concept class.

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

619 implementation of the %concepts should provide, however completely

620 without implementations and real data structures behind the

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

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

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

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

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

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

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

629 concept indeed provides all the required features.

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

632 */

634 /**

635 @defgroup graph_concepts Graph Structure Concepts

636 @ingroup concept

637 \brief Skeleton and concept checking classes for graph structures

639 This group contains the skeletons and concept checking classes of

640 graph structures.

641 */

643 /**

644 @defgroup map_concepts Map Concepts

645 @ingroup concept

646 \brief Skeleton and concept checking classes for maps

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

649 */

651 /**

652 \anchor demoprograms

654 @defgroup demos Demo Programs

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

657 the \c demo subdirectory of the source tree.

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

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

661 */

663 /**

664 @defgroup tools Standalone Utility Applications

666 Some utility applications are listed here.

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

669 them, as well.

670 */

672 }