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r318 r1023 3 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 200320 085 * Copyright (C) 20032010 6 6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport 7 7 * (Egervary Research Group on Combinatorial Optimization, EGRES). … … 17 17 */ 18 18 19 namespace lemon { 20 19 21 /** 20 22 @defgroup datas Data Structures 21 This group describes the several data structures implemented in LEMON.23 This group contains the several data structures implemented in LEMON. 22 24 */ 23 25 … … 61 63 62 64 /** 63 @defgroup semi_adaptors SemiAdaptor Classes for Graphs65 @defgroup graph_adaptors Adaptor Classes for Graphs 64 66 @ingroup graphs 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 lightweight structures as the adaptors. 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 70 138 */ 71 139 … … 75 143 \brief Map structures implemented in LEMON. 76 144 77 This group describes the map structures implemented in LEMON.145 This group contains the map structures implemented in LEMON. 78 146 79 147 LEMON provides several special purpose maps and map adaptors that e.g. combine … … 88 156 \brief Special graphrelated maps. 89 157 90 This group describes maps that are specifically designed to assign 91 values to the nodes and arcs of graphs. 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". 92 163 */ 93 164 … … 97 168 \brief Tools to create new maps from existing ones 98 169 99 This group describes map adaptors that are used to create "implicit"170 This group contains map adaptors that are used to create "implicit" 100 171 maps from other maps. 101 172 102 Most of them are \ref lemon::concepts::ReadMap "readonly maps".173 Most of them are \ref concepts::ReadMap "readonly maps". 103 174 They can make arithmetic and logical operations between one or two maps 104 175 (negation, shifting, addition, multiplication, logical 'and', 'or', … … 156 227 157 228 /** 158 @defgroup matrices Matrices159 @ingroup datas160 \brief Two dimensional data storages implemented in LEMON.161 162 This group describes two dimensional data storages implemented in LEMON.163 */164 165 /**166 229 @defgroup paths Path Structures 167 230 @ingroup datas 168 231 \brief %Path structures implemented in LEMON. 169 232 170 This group describes the path structures implemented in LEMON.233 This group contains the path structures implemented in LEMON. 171 234 172 235 LEMON provides flexible data structures to work with paths. … … 176 239 any kind of path structure. 177 240 178 \sa lemon::concepts::Path 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" 179 263 */ 180 264 … … 184 268 \brief Auxiliary data structures implemented in LEMON. 185 269 186 This group describes some data structures implemented in LEMON in270 This group contains some data structures implemented in LEMON in 187 271 order to make it easier to implement combinatorial algorithms. 188 272 */ 189 273 190 274 /** 275 @defgroup geomdat Geometric Data Structures 276 @ingroup auxdat 277 \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 dimensional 282 vector with the usual operations. 283  \ref lemon::dim2::Box "dim2::Box" can be used to determine the 284 rectangular bounding box of a set of \ref lemon::dim2::Point 285 "dim2::Point"'s. 286 */ 287 288 /** 289 @defgroup matrices Matrices 290 @ingroup auxdat 291 \brief Two dimensional data storages implemented in LEMON. 292 293 This group contains two dimensional data storages implemented in LEMON. 294 */ 295 296 /** 191 297 @defgroup algs Algorithms 192 \brief This group describes the several algorithms298 \brief This group contains the several algorithms 193 299 implemented in LEMON. 194 300 195 This group describes the several algorithms301 This group contains the several algorithms 196 302 implemented in LEMON. 197 303 */ … … 202 308 \brief Common graph search algorithms. 203 309 204 This group describes the common graph search algorithms like 205 BreadthFirst Search (BFS) and DepthFirst Search (DFS). 310 This group contains the common graph search algorithms, namely 311 \e breadthfirst \e search (BFS) and \e depthfirst \e search (DFS) 312 \ref clrs01algorithms. 206 313 */ 207 314 … … 211 318 \brief Algorithms for finding shortest paths. 212 319 213 This group describes the algorithms for finding shortest paths in graphs. 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 nonnegative. 325  \ref BellmanFord "BellmanFord" 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 "FloydWarshall" and \ref Johnson "Johnson" algorithms 330 for solving the \e allpairs \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 arcdisjoint 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. 214 344 */ 215 345 … … 219 349 \brief Algorithms for finding maximum flows. 220 350 221 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] 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] 234 365 235 366 LEMON contains several algorithms for solving maximum flow problems: 236  \ref lemon::EdmondsKarp "EdmondsKarp" 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 367  \ref EdmondsKarp EdmondsKarp algorithm 368 \ref edmondskarp72theoretical. 369  \ref Preflow GoldbergTarjan's preflow pushrelabel algorithm 370 \ref goldberg88newapproach. 371  \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees 372 \ref dinic70algorithm, \ref sleator83dynamic. 373  \ref GoldbergTarjan !Preflow pushrelabel 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 pushrelabel 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 249 389 @ingroup algs 250 390 251 391 \brief Algorithms for finding minimum cost flows and circulations. 252 392 253 This group describes the algorithms for finding minimum cost flows and 254 circulations. 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 CycleCanceling 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). 255 413 */ 256 414 … … 261 419 \brief Algorithms for finding minimum cut in graphs. 262 420 263 This group describes the algorithms for finding minimum cut in graphs.264 265 The minimum cutproblem is to find a nonempty and noncomplete266 \f$X\f$ subset of the vertices with minimum overall capacity on267 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an268 \f$c _a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum421 This group contains the algorithms for finding minimum cut in graphs. 422 423 The \e minimum \e cut \e problem is to find a nonempty and noncomplete 424 \f$X\f$ subset of the nodes with minimum overall capacity on 425 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a 426 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 269 427 cut is the \f$X\f$ solution of the next optimization problem: 270 428 271 429 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}} 272 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]430 \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f] 273 431 274 432 LEMON contains several algorithms related to minimum cut problems: 275 433 276  \ref lemon::HaoOrlin "HaoOrlin algorithm" to calculateminimum cut277 in directed graphs 278  \ref lemon::NagamochiIbaraki "NagamochiIbaraki algorithm" to279 calculat e minimum cut in undirected graphs280  \ref lemon::GomoryHuTree "GomoryHu tree computation" to calculate all281 pairs minimum cut in undirected graphs434  \ref HaoOrlin "HaoOrlin algorithm" for calculating minimum cut 435 in directed graphs. 436  \ref NagamochiIbaraki "NagamochiIbaraki algorithm" for 437 calculating minimum cut in undirected graphs. 438  \ref GomoryHu "GomoryHu tree computation" for calculating 439 allpairs minimum cut in undirected graphs. 282 440 283 441 If you want to find minimum cut just between two distinict nodes, 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 "biedgeconnected 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 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 HartmannOrlin'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 "HartmannOrlin" 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. 309 480 */ 310 481 … … 314 485 \brief Algorithms for finding matchings in graphs and bipartite graphs. 315 486 316 This group contains algorithm objects and functions to calculate487 This group contains the algorithms for calculating 317 488 matchings in graphs and bipartite graphs. The general matching problem is 318 finding a subset of the arcs which does not shares common endpoints. 489 finding a subset of the edges for which each node has at most one incident 490 edge. 319 491 320 492 There are several different algorithms for calculate matchings in 321 493 graphs. The matching problems in bipartite graphs are generally 322 494 easier than in general graphs. The goal of the matching optimization 323 can be thefinding maximum cardinality, maximum weight or minimum cost495 can be finding maximum cardinality, maximum weight or minimum cost 324 496 matching. The search can be constrained to find perfect or 325 497 maximum cardinality matching. 326 498 327 LEMON contains the next algorithms: 328  \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" HopcroftKarp 329 augmenting path algorithm for calculate maximum cardinality matching in 330 bipartite graphs 331  \ref lemon::PrBipartiteMatching "PrBipartiteMatching" PushRelabel 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 499 The matching algorithms implemented in LEMON: 500  \ref MaxBipartiteMatching HopcroftKarp augmenting path algorithm 501 for calculating maximum cardinality matching in bipartite graphs. 502  \ref PrBipartiteMatching Pushrelabel 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 Pushrelabel 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 555 @ingroup algs 556 \brief Approximation algorithms. 557 558 This group contains the approximation and heuristic algorithms 559 implemented in LEMON. 560 561 <b>Maximum Clique Problem</b> 562  \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of 563 Grosso, Locatelli, and Pullan. 359 564 */ 360 565 … … 364 569 \brief Auxiliary algorithms implemented in LEMON. 365 570 366 This group describes some algorithms implemented in LEMON571 This group contains some algorithms implemented in LEMON 367 572 in order to make it easier to implement complex algorithms. 368 573 */ 369 574 370 575 /** 371 @defgroup approx Approximation Algorithms 372 @ingroup algs 373 \brief Approximation algorithms. 374 375 This group describes the approximation and heuristic algorithms 576 @defgroup gen_opt_group General Optimization Tools 577 \brief This group contains some general optimization frameworks 376 578 implemented in LEMON. 377 */ 378 379 /** 380 @defgroup gen_opt_group General Optimization Tools 381 \brief This group describes some general optimization frameworks 579 580 This group contains some general optimization frameworks 382 581 implemented in LEMON. 383 384 This group describes some general optimization frameworks 385 implemented in LEMON. 386 */ 387 388 /** 389 @defgroup lp_group Lp and Mip Solvers 582 */ 583 584 /** 585 @defgroup lp_group LP and MIP Solvers 390 586 @ingroup gen_opt_group 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. 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 highlevel interface. 592 593 The currently supported solvers are \ref glpk, \ref clp, \ref cbc, 594 \ref cplex, \ref soplex. 396 595 */ 397 596 … … 410 609 \brief Metaheuristics for LEMON library. 411 610 412 This group describes some metaheuristic optimization tools.611 This group contains some metaheuristic optimization tools. 413 612 */ 414 613 … … 425 624 \brief Simple basic graph utilities. 426 625 427 This group describes some simple basic graph utilities.626 This group contains some simple basic graph utilities. 428 627 */ 429 628 … … 433 632 \brief Tools for development, debugging and testing. 434 633 435 This group describes several useful tools for development,634 This group contains several useful tools for development, 436 635 debugging and testing. 437 636 */ … … 442 641 \brief Simple tools for measuring the performance of algorithms. 443 642 444 This group describes simple tools for measuring the performance643 This group contains simple tools for measuring the performance 445 644 of algorithms. 446 645 */ … … 451 650 \brief Exceptions defined in LEMON. 452 651 453 This group describes the exceptions defined in LEMON.652 This group contains the exceptions defined in LEMON. 454 653 */ 455 654 … … 458 657 \brief Graph InputOutput methods 459 658 460 This group describes the tools for importing and exporting graphs659 This group contains the tools for importing and exporting graphs 461 660 and graph related data. Now it supports the \ref lgfformat 462 661 "LEMON Graph Format", the \c DIMACS format and the encapsulated … … 465 664 466 665 /** 467 @defgroup lemon_io LEMON InputOutput666 @defgroup lemon_io LEMON Graph Format 468 667 @ingroup io_group 469 668 \brief Reading and writing LEMON Graph Format. 470 669 471 This group describes methods for reading and writing670 This group contains methods for reading and writing 472 671 \ref lgfformat "LEMON Graph Format". 473 672 */ … … 478 677 \brief General \c EPS drawer and graph exporter 479 678 480 This group describes general \c EPS drawing methods and special679 This group contains general \c EPS drawing methods and special 481 680 graph exporting tools. 681 */ 682 683 /** 684 @defgroup dimacs_group DIMACS Format 685 @ingroup io_group 686 \brief Read and write files in DIMACS format 687 688 Tools to read a digraph from or write it to a file in DIMACS format data. 689 */ 690 691 /** 692 @defgroup nauty_group NAUTY Format 693 @ingroup io_group 694 \brief Read \e Nauty format 695 696 Tool to read graphs from \e Nauty format data. 482 697 */ 483 698 … … 486 701 \brief Skeleton classes and concept checking classes 487 702 488 This group describes the data/algorithm skeletons and concept checking703 This group contains the data/algorithm skeletons and concept checking 489 704 classes implemented in LEMON. 490 705 … … 516 731 \brief Skeleton and concept checking classes for graph structures 517 732 518 This group describes the skeletons and concept checking classes of LEMON's519 graph structures and helper classes used to implement these.733 This group contains the skeletons and concept checking classes of 734 graph structures. 520 735 */ 521 736 … … 525 740 \brief Skeleton and concept checking classes for maps 526 741 527 This group describes the skeletons and concept checking classes of maps. 742 This group contains the skeletons and concept checking classes of maps. 743 */ 744 745 /** 746 @defgroup tools Standalone Utility Applications 747 748 Some utility applications are listed here. 749 750 The standard compilation procedure (<tt>./configure;make</tt>) will compile 751 them, as well. 528 752 */ 529 753 … … 531 755 \anchor demoprograms 532 756 533 @defgroup demos Demo programs757 @defgroup demos Demo Programs 534 758 535 759 Some demo programs are listed here. Their full source codes can be found in 536 760 the \c demo subdirectory of the source tree. 537 761 538 It order to compile them, use <tt>enabledemo</tt> configure option when 539 build the library. 540 */ 541 542 /** 543 @defgroup tools Standalone utility applications 544 545 Some utility applications are listed here. 546 547 The standard compilation procedure (<tt>./configure;make</tt>) will compile 548 them, as well. 549 */ 550 762 In order to compile them, use the <tt>make demo</tt> or the 763 <tt>make check</tt> commands. 764 */ 765 766 }
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