Changes in doc/groups.dox [318:1e2d6ca80793:478:5a1e9fdcfd3a] in lemon
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r318 r478 3 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 2003-200 85 * Copyright (C) 2003-2009 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 … … 61 63 62 64 /** 65 @defgroup graph_adaptors Adaptor Classes for Graphs 66 @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 138 */ 139 140 /** 63 141 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs 64 142 @ingroup graphs … … 89 167 90 168 This group describes maps that are specifically designed to assign 91 values to the nodes and arcs of graphs. 169 values to the nodes and arcs/edges of graphs. 170 171 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap, 172 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts". 92 173 */ 93 174 … … 100 181 maps from other maps. 101 182 102 Most of them are \ref lemon::concepts::ReadMap "read-only maps".183 Most of them are \ref concepts::ReadMap "read-only maps". 103 184 They can make arithmetic and logical operations between one or two maps 104 185 (negation, shifting, addition, multiplication, logical 'and', 'or', … … 202 283 \brief Common graph search algorithms. 203 284 204 This group describes the common graph search algorithms like205 Breadth-First Search (BFS) and Depth-First Search (DFS).285 This group describes the common graph search algorithms, namely 286 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS). 206 287 */ 207 288 … … 211 292 \brief Algorithms for finding shortest paths. 212 293 213 This group describes the algorithms for finding shortest paths in graphs. 294 This group describes the algorithms for finding shortest paths in digraphs. 295 296 - \ref Dijkstra algorithm for finding shortest paths from a source node 297 when all arc lengths are non-negative. 298 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths 299 from a source node when arc lenghts can be either positive or negative, 300 but the digraph should not contain directed cycles with negative total 301 length. 302 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms 303 for solving the \e all-pairs \e shortest \e paths \e problem when arc 304 lenghts can be either positive or negative, but the digraph should 305 not contain directed cycles with negative total length. 306 - \ref Suurballe A successive shortest path algorithm for finding 307 arc-disjoint paths between two nodes having minimum total length. 214 308 */ 215 309 … … 222 316 feasible circulations. 223 317 224 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] 318 The \e maximum \e flow \e problem is to find a flow of maximum value between 319 a single source and a single target. Formally, there is a \f$G=(V,A)\f$ 320 digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and 321 \f$s, t \in V\f$ source and target nodes. 322 A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the 323 following optimization problem. 324 325 \f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f] 326 \f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a) 327 \qquad \forall v\in V\setminus\{s,t\} \f] 328 \f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f] 234 329 235 330 LEMON contains several algorithms for solving maximum flow problems: 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 the242 fastest method to compute the maximum flow. All impelementations243 provides functions to query the minimum cut, which is the dual linear244 pro gramming problem of the maximum flow.331 - \ref EdmondsKarp Edmonds-Karp algorithm. 332 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm. 333 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. 334 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees. 335 336 In most cases the \ref Preflow "Preflow" algorithm provides the 337 fastest method for computing a maximum flow. All implementations 338 provides functions to also query the minimum cut, which is the dual 339 problem of the maximum flow. 245 340 */ 246 341 … … 253 348 This group describes the algorithms for finding minimum cost flows and 254 349 circulations. 350 351 The \e minimum \e cost \e flow \e problem is to find a feasible flow of 352 minimum total cost from a set of supply nodes to a set of demand nodes 353 in a network with capacity constraints and arc costs. 354 Formally, let \f$G=(V,A)\f$ be a digraph, 355 \f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and 356 upper bounds for the flow values on the arcs, 357 \f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow 358 on the arcs, and 359 \f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values 360 of the nodes. 361 A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of 362 the following optimization problem. 363 364 \f[ \min\sum_{a\in A} f(a) cost(a) \f] 365 \f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) = 366 supply(v) \qquad \forall v\in V \f] 367 \f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f] 368 369 LEMON contains several algorithms for solving minimum cost flow problems: 370 - \ref CycleCanceling Cycle-canceling algorithms. 371 - \ref CapacityScaling Successive shortest path algorithm with optional 372 capacity scaling. 373 - \ref CostScaling Push-relabel and augment-relabel algorithms based on 374 cost scaling. 375 - \ref NetworkSimplex Primal network simplex algorithm with various 376 pivot strategies. 255 377 */ 256 378 … … 263 385 This group describes the algorithms for finding minimum cut in graphs. 264 386 265 The minimum cutproblem is to find a non-empty and non-complete266 \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 minimum387 The \e minimum \e cut \e problem is to find a non-empty and non-complete 388 \f$X\f$ subset of the nodes with minimum overall capacity on 389 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a 390 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 269 391 cut is the \f$X\f$ solution of the next optimization problem: 270 392 271 393 \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]394 \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] 273 395 274 396 LEMON contains several algorithms related to minimum cut problems: 275 397 276 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculateminimum cut277 in directed graphs 278 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to279 calculat e minimum cut in undirected graphs280 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all281 pairs minimum cut in undirected graphs398 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut 399 in directed graphs. 400 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for 401 calculating minimum cut in undirected graphs. 402 - \ref GomoryHuTree "Gomory-Hu tree computation" for calculating 403 all-pairs minimum cut in undirected graphs. 282 404 283 405 If you want to find minimum cut just between two distinict nodes, 284 please see the \ref max_flow "Maximum Flow page".406 see the \ref max_flow "maximum flow problem". 285 407 */ 286 408 … … 321 443 graphs. The matching problems in bipartite graphs are generally 322 444 easier than in general graphs. The goal of the matching optimization 323 can be thefinding maximum cardinality, maximum weight or minimum cost445 can be finding maximum cardinality, maximum weight or minimum cost 324 446 matching. The search can be constrained to find perfect or 325 447 maximum cardinality matching. 326 448 327 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 449 The matching algorithms implemented in LEMON: 450 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm 451 for calculating maximum cardinality matching in bipartite graphs. 452 - \ref PrBipartiteMatching Push-relabel algorithm 453 for calculating maximum cardinality matching in bipartite graphs. 454 - \ref MaxWeightedBipartiteMatching 455 Successive shortest path algorithm for calculating maximum weighted 456 matching and maximum weighted bipartite matching in bipartite graphs. 457 - \ref MinCostMaxBipartiteMatching 458 Successive shortest path algorithm for calculating minimum cost maximum 459 matching in bipartite graphs. 460 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating 461 maximum cardinality matching in general graphs. 462 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating 463 maximum weighted matching in general graphs. 464 - \ref MaxWeightedPerfectMatching 465 Edmond's blossom shrinking algorithm for calculating maximum weighted 466 perfect matching in general graphs. 347 467 348 468 \image html bipartite_matching.png … … 356 476 357 477 This group describes the algorithms for finding a minimum cost spanning 358 tree in a graph 478 tree in a graph. 359 479 */ 360 480 … … 465 585 466 586 /** 467 @defgroup lemon_io LEMON Input-Output587 @defgroup lemon_io LEMON Graph Format 468 588 @ingroup io_group 469 589 \brief Reading and writing LEMON Graph Format. … … 480 600 This group describes general \c EPS drawing methods and special 481 601 graph exporting tools. 602 */ 603 604 /** 605 @defgroup dimacs_group DIMACS format 606 @ingroup io_group 607 \brief Read and write files in DIMACS format 608 609 Tools to read a digraph from or write it to a file in DIMACS format data. 610 */ 611 612 /** 613 @defgroup nauty_group NAUTY Format 614 @ingroup io_group 615 \brief Read \e Nauty format 616 617 Tool to read graphs from \e Nauty format data. 482 618 */ 483 619 … … 531 667 \anchor demoprograms 532 668 533 @defgroup demos Demo programs669 @defgroup demos Demo Programs 534 670 535 671 Some demo programs are listed here. Their full source codes can be found in … … 541 677 542 678 /** 543 @defgroup tools Standalone utility applications679 @defgroup tools Standalone Utility Applications 544 680 545 681 Some utility applications are listed here. … … 549 685 */ 550 686 687 }
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