Changes in doc/groups.dox [1023:e0cef67fe565:318:1e2d6ca80793] in lemon
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doc/groups.dox
r1023 r318 3 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 2003-20 105 * Copyright (C) 2003-2008 6 6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport 7 7 * (Egervary Research Group on Combinatorial Optimization, EGRES). … … 17 17 */ 18 18 19 namespace lemon {20 21 19 /** 22 20 @defgroup datas Data Structures 23 This group contains the several data structures implemented in LEMON.21 This group describes the several data structures implemented in LEMON. 24 22 */ 25 23 … … 63 61 64 62 /** 65 @defgroup graph_adaptorsAdaptor Classes for Graphs63 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs 66 64 @ingroup graphs 67 \brief Adaptor classes for digraphs and graphs 68 69 This group contains several useful adaptor classes for digraphs and graphs. 70 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. 76 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. 107 108 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. 114 115 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. 123 124 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 65 \brief Graph types between real graphs and graph adaptors. 66 67 This group describes some graph types between real graphs and graph adaptors. 68 These classes wrap graphs to give new functionality as the adaptors do it. 69 On the other hand they are not light-weight structures as the adaptors. 138 70 */ 139 71 … … 143 75 \brief Map structures implemented in LEMON. 144 76 145 This group contains the map structures implemented in LEMON.77 This group describes the map structures implemented in LEMON. 146 78 147 79 LEMON provides several special purpose maps and map adaptors that e.g. combine … … 156 88 \brief Special graph-related maps. 157 89 158 This group contains maps that are specifically designed to assign 159 values to the nodes and arcs/edges of graphs. 160 161 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap, 162 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts". 90 This group describes maps that are specifically designed to assign 91 values to the nodes and arcs of graphs. 163 92 */ 164 93 … … 168 97 \brief Tools to create new maps from existing ones 169 98 170 This group contains map adaptors that are used to create "implicit"99 This group describes map adaptors that are used to create "implicit" 171 100 maps from other maps. 172 101 173 Most of them are \ref concepts::ReadMap "read-only maps".102 Most of them are \ref lemon::concepts::ReadMap "read-only maps". 174 103 They can make arithmetic and logical operations between one or two maps 175 104 (negation, shifting, addition, multiplication, logical 'and', 'or', … … 227 156 228 157 /** 158 @defgroup matrices Matrices 159 @ingroup datas 160 \brief Two dimensional data storages implemented in LEMON. 161 162 This group describes two dimensional data storages implemented in LEMON. 163 */ 164 165 /** 229 166 @defgroup paths Path Structures 230 167 @ingroup datas 231 168 \brief %Path structures implemented in LEMON. 232 169 233 This group contains the path structures implemented in LEMON.170 This group describes the path structures implemented in LEMON. 234 171 235 172 LEMON provides flexible data structures to work with paths. … … 239 176 any kind of path structure. 240 177 241 \sa \ref concepts::Path "Path concept" 242 */ 243 244 /** 245 @defgroup heaps Heap Structures 246 @ingroup datas 247 \brief %Heap structures implemented in LEMON. 248 249 This group contains the heap structures implemented in LEMON. 250 251 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. 257 258 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. 261 262 \sa \ref concepts::Heap "Heap concept" 178 \sa lemon::concepts::Path 263 179 */ 264 180 … … 268 184 \brief Auxiliary data structures implemented in LEMON. 269 185 270 This group contains some data structures implemented in LEMON in186 This group describes some data structures implemented in LEMON in 271 187 order to make it easier to implement combinatorial algorithms. 272 188 */ 273 189 274 190 /** 275 @defgroup geomdat Geometric Data Structures276 @ingroup auxdat277 \brief Geometric data structures implemented in LEMON.278 279 This group contains geometric data structures implemented in LEMON.280 281 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional282 vector with the usual operations.283 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the284 rectangular bounding box of a set of \ref lemon::dim2::Point285 "dim2::Point"'s.286 */287 288 /**289 @defgroup matrices Matrices290 @ingroup auxdat291 \brief Two dimensional data storages implemented in LEMON.292 293 This group contains two dimensional data storages implemented in LEMON.294 */295 296 /**297 191 @defgroup algs Algorithms 298 \brief This group contains the several algorithms192 \brief This group describes the several algorithms 299 193 implemented in LEMON. 300 194 301 This group contains the several algorithms195 This group describes the several algorithms 302 196 implemented in LEMON. 303 197 */ … … 308 202 \brief Common graph search algorithms. 309 203 310 This group contains the common graph search algorithms, namely 311 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS) 312 \ref clrs01algorithms. 204 This group describes the common graph search algorithms like 205 Breadth-First Search (BFS) and Depth-First Search (DFS). 313 206 */ 314 207 … … 318 211 \brief Algorithms for finding shortest paths. 319 212 320 This group contains the algorithms for finding shortest paths in digraphs 321 \ref clrs01algorithms. 322 323 - \ref Dijkstra algorithm for finding shortest paths from a source node 324 when all arc lengths are non-negative. 325 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths 326 from a source node when arc lenghts can be either positive or negative, 327 but the digraph should not contain directed cycles with negative total 328 length. 329 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms 330 for solving the \e all-pairs \e shortest \e paths \e problem when arc 331 lenghts can be either positive or negative, but the digraph should 332 not contain directed cycles with negative total length. 333 - \ref Suurballe A successive shortest path algorithm for finding 334 arc-disjoint paths between two nodes having minimum total length. 335 */ 336 337 /** 338 @defgroup spantree Minimum Spanning Tree Algorithms 339 @ingroup algs 340 \brief Algorithms for finding minimum cost spanning trees and arborescences. 341 342 This group contains the algorithms for finding minimum cost spanning 343 trees and arborescences \ref clrs01algorithms. 213 This group describes the algorithms for finding shortest paths in graphs. 344 214 */ 345 215 … … 349 219 \brief Algorithms for finding maximum flows. 350 220 351 This group contains the algorithms for finding maximum flows and 352 feasible circulations \ref clrs01algorithms, \ref amo93networkflows. 353 354 The \e maximum \e flow \e problem is to find a flow of maximum value between 355 a single source and a single target. Formally, there is a \f$G=(V,A)\f$ 356 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and 357 \f$s, t \in V\f$ source and target nodes. 358 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the 359 following optimization problem. 360 361 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f] 362 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu) 363 \quad \forall u\in V\setminus\{s,t\} \f] 364 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] 221 This group describes the algorithms for finding maximum flows and 222 feasible circulations. 223 224 The maximum flow problem is to find a flow between a single source and 225 a single target that is maximum. Formally, there is a \f$G=(V,A)\f$ 226 directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity 227 function and given \f$s, t \in V\f$ source and target node. The 228 maximum flow is the \f$f_a\f$ solution of the next optimization problem: 229 230 \f[ 0 \le f_a \le c_a \f] 231 \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} 232 \qquad \forall u \in V \setminus \{s,t\}\f] 233 \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f] 365 234 366 235 LEMON contains several algorithms for solving maximum flow problems: 367 - \ref EdmondsKarp Edmonds-Karp algorithm 368 \ref edmondskarp72theoretical. 369 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm 370 \ref goldberg88newapproach. 371 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees 372 \ref dinic70algorithm, \ref sleator83dynamic. 373 - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees 374 \ref goldberg88newapproach, \ref sleator83dynamic. 375 376 In most cases the \ref Preflow algorithm provides the 377 fastest method for computing a maximum flow. All implementations 378 also provide functions to query the minimum cut, which is the dual 379 problem of maximum flow. 380 381 \ref Circulation is a preflow push-relabel algorithm implemented directly 382 for finding feasible circulations, which is a somewhat different problem, 383 but it is strongly related to maximum flow. 384 For more information, see \ref Circulation. 385 */ 386 387 /** 388 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms 236 - \ref lemon::EdmondsKarp "Edmonds-Karp" 237 - \ref lemon::Preflow "Goldberg's Preflow algorithm" 238 - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees" 239 - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees" 240 241 In most cases the \ref lemon::Preflow "Preflow" algorithm provides the 242 fastest method to compute the maximum flow. All impelementations 243 provides functions to query the minimum cut, which is the dual linear 244 programming problem of the maximum flow. 245 */ 246 247 /** 248 @defgroup min_cost_flow Minimum Cost Flow Algorithms 389 249 @ingroup algs 390 250 391 251 \brief Algorithms for finding minimum cost flows and circulations. 392 252 393 This group contains the algorithms for finding minimum cost flows and 394 circulations \ref amo93networkflows. For more information about this 395 problem and its dual solution, see \ref min_cost_flow 396 "Minimum Cost Flow Problem". 397 398 LEMON contains several algorithms for this problem. 399 - \ref NetworkSimplex Primal Network Simplex algorithm with various 400 pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex. 401 - \ref CostScaling Cost Scaling algorithm based on push/augment and 402 relabel operations \ref goldberg90approximation, \ref goldberg97efficient, 403 \ref bunnagel98efficient. 404 - \ref CapacityScaling Capacity Scaling algorithm based on the successive 405 shortest path method \ref edmondskarp72theoretical. 406 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are 407 strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling. 408 409 In general, \ref NetworkSimplex and \ref CostScaling are the most efficient 410 implementations, but the other two algorithms could be faster in special cases. 411 For example, if the total supply and/or capacities are rather small, 412 \ref CapacityScaling is usually the fastest algorithm (without effective scaling). 253 This group describes the algorithms for finding minimum cost flows and 254 circulations. 413 255 */ 414 256 … … 419 261 \brief Algorithms for finding minimum cut in graphs. 420 262 421 This group contains the algorithms for finding minimum cut in graphs.422 423 The \e minimum \e cut \eproblem is to find a non-empty and non-complete424 \f$X\f$ subset of the nodes with minimum overall capacity on425 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a426 \f$c ap:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum263 This group describes the algorithms for finding minimum cut in graphs. 264 265 The minimum cut problem is to find a non-empty and non-complete 266 \f$X\f$ subset of the vertices with minimum overall capacity on 267 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an 268 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 427 269 cut is the \f$X\f$ solution of the next optimization problem: 428 270 429 271 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} 430 \sum_{uv\in A: u\in X, v\not\in X}cap(uv)\f]272 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f] 431 273 432 274 LEMON contains several algorithms related to minimum cut problems: 433 275 434 - \ref HaoOrlin "Hao-Orlin algorithm" for calculatingminimum cut435 in directed graphs .436 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for437 calculat ing minimum cut in undirected graphs.438 - \ref GomoryHu "Gomory-Hu tree computation" for calculating439 all-pairs minimum cut in undirected graphs.276 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut 277 in directed graphs 278 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to 279 calculate minimum cut in undirected graphs 280 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all 281 pairs minimum cut in undirected graphs 440 282 441 283 If you want to find minimum cut just between two distinict nodes, 442 see the \ref max_flow "maximum flow problem". 443 */ 444 445 /** 446 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms 447 @ingroup algs 448 \brief Algorithms for finding minimum mean cycles. 449 450 This group contains the algorithms for finding minimum mean cycles 451 \ref clrs01algorithms, \ref amo93networkflows. 452 453 The \e minimum \e mean \e cycle \e problem is to find a directed cycle 454 of minimum mean length (cost) in a digraph. 455 The mean length of a cycle is the average length of its arcs, i.e. the 456 ratio between the total length of the cycle and the number of arcs on it. 457 458 This problem has an important connection to \e conservative \e length 459 \e functions, too. A length function on the arcs of a digraph is called 460 conservative if and only if there is no directed cycle of negative total 461 length. For an arbitrary length function, the negative of the minimum 462 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the 463 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length 464 function. 465 466 LEMON contains three algorithms for solving the minimum mean cycle problem: 467 - \ref KarpMmc Karp's original algorithm \ref amo93networkflows, 468 \ref dasdan98minmeancycle. 469 - \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved 470 version of Karp's algorithm \ref dasdan98minmeancycle. 471 - \ref HowardMmc Howard's policy iteration algorithm 472 \ref dasdan98minmeancycle. 473 474 In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the 475 most efficient one, though the best known theoretical bound on its running 476 time is exponential. 477 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms 478 run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is 479 typically faster due to the applied early termination scheme. 284 please see the \ref max_flow "Maximum Flow page". 285 */ 286 287 /** 288 @defgroup graph_prop Connectivity and Other Graph Properties 289 @ingroup algs 290 \brief Algorithms for discovering the graph properties 291 292 This group describes the algorithms for discovering the graph properties 293 like connectivity, bipartiteness, euler property, simplicity etc. 294 295 \image html edge_biconnected_components.png 296 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth 297 */ 298 299 /** 300 @defgroup planar Planarity Embedding and Drawing 301 @ingroup algs 302 \brief Algorithms for planarity checking, embedding and drawing 303 304 This group describes the algorithms for planarity checking, 305 embedding and drawing. 306 307 \image html planar.png 308 \image latex planar.eps "Plane graph" width=\textwidth 480 309 */ 481 310 … … 485 314 \brief Algorithms for finding matchings in graphs and bipartite graphs. 486 315 487 This group contains the algorithms for calculating316 This group contains algorithm objects and functions to calculate 488 317 matchings in graphs and bipartite graphs. The general matching problem is 489 finding a subset of the edges for which each node has at most one incident 490 edge. 318 finding a subset of the arcs which does not shares common endpoints. 491 319 492 320 There are several different algorithms for calculate matchings in 493 321 graphs. The matching problems in bipartite graphs are generally 494 322 easier than in general graphs. The goal of the matching optimization 495 can be finding maximum cardinality, maximum weight or minimum cost323 can be the finding maximum cardinality, maximum weight or minimum cost 496 324 matching. The search can be constrained to find perfect or 497 325 maximum cardinality matching. 498 326 499 The matching algorithms implemented in LEMON: 500 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm 501 for calculating maximum cardinality matching in bipartite graphs. 502 - \ref PrBipartiteMatching Push-relabel algorithm 503 for calculating maximum cardinality matching in bipartite graphs. 504 - \ref MaxWeightedBipartiteMatching 505 Successive shortest path algorithm for calculating maximum weighted 506 matching and maximum weighted bipartite matching in bipartite graphs. 507 - \ref MinCostMaxBipartiteMatching 508 Successive shortest path algorithm for calculating minimum cost maximum 509 matching in bipartite graphs. 510 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating 511 maximum cardinality matching in general graphs. 512 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating 513 maximum weighted matching in general graphs. 514 - \ref MaxWeightedPerfectMatching 515 Edmond's blossom shrinking algorithm for calculating maximum weighted 516 perfect matching in general graphs. 517 - \ref MaxFractionalMatching Push-relabel algorithm for calculating 518 maximum cardinality fractional matching in general graphs. 519 - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating 520 maximum weighted fractional matching in general graphs. 521 - \ref MaxWeightedPerfectFractionalMatching 522 Augmenting path algorithm for calculating maximum weighted 523 perfect fractional matching in general graphs. 524 525 \image html matching.png 526 \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth 527 */ 528 529 /** 530 @defgroup graph_properties Connectivity and Other Graph Properties 531 @ingroup algs 532 \brief Algorithms for discovering the graph properties 533 534 This group contains the algorithms for discovering the graph properties 535 like connectivity, bipartiteness, euler property, simplicity etc. 536 537 \image html connected_components.png 538 \image latex connected_components.eps "Connected components" width=\textwidth 539 */ 540 541 /** 542 @defgroup planar Planar Embedding and Drawing 543 @ingroup algs 544 \brief Algorithms for planarity checking, embedding and drawing 545 546 This group contains the algorithms for planarity checking, 547 embedding and drawing. 548 549 \image html planar.png 550 \image latex planar.eps "Plane graph" width=\textwidth 551 */ 552 553 /** 554 @defgroup approx_algs Approximation Algorithms 327 LEMON contains the next algorithms: 328 - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp 329 augmenting path algorithm for calculate maximum cardinality matching in 330 bipartite graphs 331 - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel 332 algorithm for calculate maximum cardinality matching in bipartite graphs 333 - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching" 334 Successive shortest path algorithm for calculate maximum weighted matching 335 and maximum weighted bipartite matching in bipartite graph 336 - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching" 337 Successive shortest path algorithm for calculate minimum cost maximum 338 matching in bipartite graph 339 - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm 340 for calculate maximum cardinality matching in general graph 341 - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom 342 shrinking algorithm for calculate maximum weighted matching in general 343 graph 344 - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching" 345 Edmond's blossom shrinking algorithm for calculate maximum weighted 346 perfect matching in general graph 347 348 \image html bipartite_matching.png 349 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth 350 */ 351 352 /** 353 @defgroup spantree Minimum Spanning Tree Algorithms 354 @ingroup algs 355 \brief Algorithms for finding a minimum cost spanning tree in a graph. 356 357 This group describes the algorithms for finding a minimum cost spanning 358 tree in a graph 359 */ 360 361 /** 362 @defgroup auxalg Auxiliary Algorithms 363 @ingroup algs 364 \brief Auxiliary algorithms implemented in LEMON. 365 366 This group describes some algorithms implemented in LEMON 367 in order to make it easier to implement complex algorithms. 368 */ 369 370 /** 371 @defgroup approx Approximation Algorithms 555 372 @ingroup algs 556 373 \brief Approximation algorithms. 557 374 558 This group contains the approximation and heuristic algorithms375 This group describes the approximation and heuristic algorithms 559 376 implemented in LEMON. 560 561 <b>Maximum Clique Problem</b>562 - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of563 Grosso, Locatelli, and Pullan.564 */565 566 /**567 @defgroup auxalg Auxiliary Algorithms568 @ingroup algs569 \brief Auxiliary algorithms implemented in LEMON.570 571 This group contains some algorithms implemented in LEMON572 in order to make it easier to implement complex algorithms.573 377 */ 574 378 575 379 /** 576 380 @defgroup gen_opt_group General Optimization Tools 577 \brief This group contains some general optimization frameworks381 \brief This group describes some general optimization frameworks 578 382 implemented in LEMON. 579 383 580 This group contains some general optimization frameworks384 This group describes some general optimization frameworks 581 385 implemented in LEMON. 582 386 */ 583 387 584 388 /** 585 @defgroup lp_group L P and MIPSolvers389 @defgroup lp_group Lp and Mip Solvers 586 390 @ingroup gen_opt_group 587 \brief LP and MIP solver interfaces for LEMON. 588 589 This group contains LP and MIP solver interfaces for LEMON. 590 Various LP solvers could be used in the same manner with this 591 high-level interface. 592 593 The currently supported solvers are \ref glpk, \ref clp, \ref cbc, 594 \ref cplex, \ref soplex. 391 \brief Lp and Mip solver interfaces for LEMON. 392 393 This group describes Lp and Mip solver interfaces for LEMON. The 394 various LP solvers could be used in the same manner with this 395 interface. 595 396 */ 596 397 … … 609 410 \brief Metaheuristics for LEMON library. 610 411 611 This group contains some metaheuristic optimization tools.412 This group describes some metaheuristic optimization tools. 612 413 */ 613 414 … … 624 425 \brief Simple basic graph utilities. 625 426 626 This group contains some simple basic graph utilities.427 This group describes some simple basic graph utilities. 627 428 */ 628 429 … … 632 433 \brief Tools for development, debugging and testing. 633 434 634 This group contains several useful tools for development,435 This group describes several useful tools for development, 635 436 debugging and testing. 636 437 */ … … 641 442 \brief Simple tools for measuring the performance of algorithms. 642 443 643 This group contains simple tools for measuring the performance444 This group describes simple tools for measuring the performance 644 445 of algorithms. 645 446 */ … … 650 451 \brief Exceptions defined in LEMON. 651 452 652 This group contains the exceptions defined in LEMON.453 This group describes the exceptions defined in LEMON. 653 454 */ 654 455 … … 657 458 \brief Graph Input-Output methods 658 459 659 This group contains the tools for importing and exporting graphs460 This group describes the tools for importing and exporting graphs 660 461 and graph related data. Now it supports the \ref lgf-format 661 462 "LEMON Graph Format", the \c DIMACS format and the encapsulated … … 664 465 665 466 /** 666 @defgroup lemon_io LEMON Graph Format467 @defgroup lemon_io LEMON Input-Output 667 468 @ingroup io_group 668 469 \brief Reading and writing LEMON Graph Format. 669 470 670 This group contains methods for reading and writing471 This group describes methods for reading and writing 671 472 \ref lgf-format "LEMON Graph Format". 672 473 */ … … 677 478 \brief General \c EPS drawer and graph exporter 678 479 679 This group contains general \c EPS drawing methods and special480 This group describes general \c EPS drawing methods and special 680 481 graph exporting tools. 681 */682 683 /**684 @defgroup dimacs_group DIMACS Format685 @ingroup io_group686 \brief Read and write files in DIMACS format687 688 Tools to read a digraph from or write it to a file in DIMACS format data.689 */690 691 /**692 @defgroup nauty_group NAUTY Format693 @ingroup io_group694 \brief Read \e Nauty format695 696 Tool to read graphs from \e Nauty format data.697 482 */ 698 483 … … 701 486 \brief Skeleton classes and concept checking classes 702 487 703 This group contains the data/algorithm skeletons and concept checking488 This group describes the data/algorithm skeletons and concept checking 704 489 classes implemented in LEMON. 705 490 … … 731 516 \brief Skeleton and concept checking classes for graph structures 732 517 733 This group contains the skeletons and concept checking classes of734 graph structures .518 This group describes the skeletons and concept checking classes of LEMON's 519 graph structures and helper classes used to implement these. 735 520 */ 736 521 … … 740 525 \brief Skeleton and concept checking classes for maps 741 526 742 This group contains the skeletons and concept checking classes of maps. 743 */ 744 745 /** 746 @defgroup tools Standalone Utility Applications 527 This group describes the skeletons and concept checking classes of maps. 528 */ 529 530 /** 531 \anchor demoprograms 532 533 @defgroup demos Demo programs 534 535 Some demo programs are listed here. Their full source codes can be found in 536 the \c demo subdirectory of the source tree. 537 538 It order to compile them, use <tt>--enable-demo</tt> configure option when 539 build the library. 540 */ 541 542 /** 543 @defgroup tools Standalone utility applications 747 544 748 545 Some utility applications are listed here. … … 752 549 */ 753 550 754 /**755 \anchor demoprograms756 757 @defgroup demos Demo Programs758 759 Some demo programs are listed here. Their full source codes can be found in760 the \c demo subdirectory of the source tree.761 762 In order to compile them, use the <tt>make demo</tt> or the763 <tt>make check</tt> commands.764 */765 766 }
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