Changes in doc/groups.dox [318:1e2d6ca80793:611:85cb3aa71cce] in lemon1.2
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r318 r611 3 3 * This file is a part of LEMON, a generic C++ optimization library. 4 4 * 5 * Copyright (C) 2003200 85 * Copyright (C) 20032009 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 /** 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 SemiAdaptor Classes for Graphs 64 142 @ingroup graphs 65 143 \brief Graph types between real graphs and graph adaptors. 66 144 67 This group describes some graph types between real graphs and graph adaptors.145 This group contains some graph types between real graphs and graph adaptors. 68 146 These classes wrap graphs to give new functionality as the adaptors do it. 69 147 On the other hand they are not lightweight structures as the adaptors. … … 75 153 \brief Map structures implemented in LEMON. 76 154 77 This group describes the map structures implemented in LEMON.155 This group contains the map structures implemented in LEMON. 78 156 79 157 LEMON provides several special purpose maps and map adaptors that e.g. combine … … 88 166 \brief Special graphrelated maps. 89 167 90 This group describes maps that are specifically designed to assign 91 values to the nodes and arcs of graphs. 168 This group contains maps that are specifically designed to assign 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 … … 97 178 \brief Tools to create new maps from existing ones 98 179 99 This group describes map adaptors that are used to create "implicit"180 This group contains map adaptors that are used to create "implicit" 100 181 maps from other maps. 101 182 102 Most of them are \ref lemon::concepts::ReadMap "readonly maps".183 Most of them are \ref concepts::ReadMap "readonly maps". 103 184 They can make arithmetic and logical operations between one or two maps 104 185 (negation, shifting, addition, multiplication, logical 'and', 'or', … … 160 241 \brief Two dimensional data storages implemented in LEMON. 161 242 162 This group describes two dimensional data storages implemented in LEMON.243 This group contains two dimensional data storages implemented in LEMON. 163 244 */ 164 245 … … 168 249 \brief %Path structures implemented in LEMON. 169 250 170 This group describes the path structures implemented in LEMON.251 This group contains the path structures implemented in LEMON. 171 252 172 253 LEMON provides flexible data structures to work with paths. … … 184 265 \brief Auxiliary data structures implemented in LEMON. 185 266 186 This group describes some data structures implemented in LEMON in267 This group contains some data structures implemented in LEMON in 187 268 order to make it easier to implement combinatorial algorithms. 188 269 */ … … 190 271 /** 191 272 @defgroup algs Algorithms 192 \brief This group describes the several algorithms273 \brief This group contains the several algorithms 193 274 implemented in LEMON. 194 275 195 This group describes the several algorithms276 This group contains the several algorithms 196 277 implemented in LEMON. 197 278 */ … … 202 283 \brief Common graph search algorithms. 203 284 204 This group describes the common graph search algorithms like205 BreadthFirst Search (BFS) and DepthFirst Search (DFS).285 This group contains the common graph search algorithms, namely 286 \e breadthfirst \e search (BFS) and \e depthfirst \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 contains 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 nonnegative. 298  \ref BellmanFord "BellmanFord" 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 "FloydWarshall" and \ref Johnson "Johnson" algorithms 303 for solving the \e allpairs \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 arcdisjoint paths between two nodes having minimum total length. 214 308 */ 215 309 … … 219 313 \brief Algorithms for finding maximum flows. 220 314 221 This group describes the algorithms for finding maximum flows and315 This group contains the algorithms for finding maximum flows and 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_{sv\in A} f(sv)  \sum_{vs\in A} f(vs) \f] 326 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu) 327 \quad \forall u\in V\setminus\{s,t\} \f] 328 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f] 234 329 235 330 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 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 EdmondsKarp algorithm. 332  \ref Preflow GoldbergTarjan's preflow pushrelabel algorithm. 333  \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees. 334  \ref GoldbergTarjan Preflow pushrelabel 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 … … 251 346 \brief Algorithms for finding minimum cost flows and circulations. 252 347 253 This group describes the algorithms for finding minimum cost flows and348 This group contains 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 (lower and upper bounds) 354 and arc costs. 355 Formally, let \f$G=(V,A)\f$ be a digraph, 356 \f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and 357 upper bounds for the flow values on the arcs, for which 358 \f$0 \leq lower(uv) \leq upper(uv)\f$ holds for all \f$uv\in A\f$. 359 \f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow 360 on the arcs, and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the 361 signed supply values of the nodes. 362 If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$ 363 supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with 364 \f$sup(u)\f$ demand. 365 A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}^+_0\f$ solution 366 of the following optimization problem. 367 368 \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f] 369 \f[ \sum_{uv\in A} f(uv)  \sum_{vu\in A} f(vu) \geq 370 sup(u) \quad \forall u\in V \f] 371 \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f] 372 373 The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be 374 zero or negative in order to have a feasible solution (since the sum 375 of the expressions on the lefthand side of the inequalities is zero). 376 It means that the total demand must be greater or equal to the total 377 supply and all the supplies have to be carried out from the supply nodes, 378 but there could be demands that are not satisfied. 379 If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand 380 constraints have to be satisfied with equality, i.e. all demands 381 have to be satisfied and all supplies have to be used. 382 383 If you need the opposite inequalities in the supply/demand constraints 384 (i.e. the total demand is less than the total supply and all the demands 385 have to be satisfied while there could be supplies that are not used), 386 then you could easily transform the problem to the above form by reversing 387 the direction of the arcs and taking the negative of the supply values 388 (e.g. using \ref ReverseDigraph and \ref NegMap adaptors). 389 However \ref NetworkSimplex algorithm also supports this form directly 390 for the sake of convenience. 391 392 A feasible solution for this problem can be found using \ref Circulation. 393 394 Note that the above formulation is actually more general than the usual 395 definition of the minimum cost flow problem, in which strict equalities 396 are required in the supply/demand contraints, i.e. 397 398 \f[ \sum_{uv\in A} f(uv)  \sum_{vu\in A} f(vu) = 399 sup(u) \quad \forall u\in V. \f] 400 401 However if the sum of the supply values is zero, then these two problems 402 are equivalent. So if you need the equality form, you have to ensure this 403 additional contraint for the algorithms. 404 405 The dual solution of the minimum cost flow problem is represented by node 406 potentials \f$\pi: V\rightarrow\mathbf{Z}\f$. 407 An \f$f: A\rightarrow\mathbf{Z}^+_0\f$ feasible solution of the problem 408 is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$ 409 node potentials the following \e complementary \e slackness optimality 410 conditions hold. 411 412  For all \f$uv\in A\f$ arcs: 413  if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$; 414  if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$; 415  if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$. 416  For all \f$u\in V\f$: 417  if \f$\sum_{uv\in A} f(uv)  \sum_{vu\in A} f(vu) \neq sup(u)\f$, 418 then \f$\pi(u)=0\f$. 419 420 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc 421 \f$uv\in A\f$ with respect to the node potentials \f$\pi\f$, i.e. 422 \f[ cost^\pi(uv) = cost(uv) + \pi(u)  \pi(v).\f] 423 424 All algorithms provide dual solution (node potentials) as well 425 if an optimal flow is found. 426 427 LEMON contains several algorithms for solving minimum cost flow problems. 428  \ref NetworkSimplex Primal Network Simplex algorithm with various 429 pivot strategies. 430  \ref CostScaling PushRelabel and AugmentRelabel algorithms based on 431 cost scaling. 432  \ref CapacityScaling Successive Shortest %Path algorithm with optional 433 capacity scaling. 434  \ref CancelAndTighten The Cancel and Tighten algorithm. 435  \ref CycleCanceling CycleCanceling algorithms. 436 437 Most of these implementations support the general inequality form of the 438 minimum cost flow problem, but CancelAndTighten and CycleCanceling 439 only support the equality form due to the primal method they use. 440 441 In general NetworkSimplex is the most efficient implementation, 442 but in special cases other algorithms could be faster. 443 For example, if the total supply and/or capacities are rather small, 444 CapacityScaling is usually the fastest algorithm (without effective scaling). 255 445 */ 256 446 … … 261 451 \brief Algorithms for finding minimum cut in graphs. 262 452 263 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 minimum453 This group contains the algorithms for finding minimum cut in graphs. 454 455 The \e minimum \e cut \e problem is to find a nonempty and noncomplete 456 \f$X\f$ subset of the nodes with minimum overall capacity on 457 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a 458 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum 269 459 cut is the \f$X\f$ solution of the next optimization problem: 270 460 271 461 \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]462 \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f] 273 463 274 464 LEMON contains several algorithms related to minimum cut problems: 275 465 276  \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 graphs466  \ref HaoOrlin "HaoOrlin algorithm" for calculating minimum cut 467 in directed graphs. 468  \ref NagamochiIbaraki "NagamochiIbaraki algorithm" for 469 calculating minimum cut in undirected graphs. 470  \ref GomoryHu "GomoryHu tree computation" for calculating 471 allpairs minimum cut in undirected graphs. 282 472 283 473 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 Properties474 see the \ref max_flow "maximum flow problem". 475 */ 476 477 /** 478 @defgroup graph_properties Connectivity and Other Graph Properties 289 479 @ingroup algs 290 480 \brief Algorithms for discovering the graph properties 291 481 292 This group describes the algorithms for discovering the graph properties482 This group contains the algorithms for discovering the graph properties 293 483 like connectivity, bipartiteness, euler property, simplicity etc. 294 484 … … 302 492 \brief Algorithms for planarity checking, embedding and drawing 303 493 304 This group describes the algorithms for planarity checking,494 This group contains the algorithms for planarity checking, 305 495 embedding and drawing. 306 496 … … 314 504 \brief Algorithms for finding matchings in graphs and bipartite graphs. 315 505 316 This group contains algorithm objects and functions to calculate506 This group contains the algorithms for calculating 317 507 matchings in graphs and bipartite graphs. The general matching problem is 318 finding a subset of the arcs which does not shares common endpoints. 508 finding a subset of the edges for which each node has at most one incident 509 edge. 319 510 320 511 There are several different algorithms for calculate matchings in 321 512 graphs. The matching problems in bipartite graphs are generally 322 513 easier than in general graphs. The goal of the matching optimization 323 can be thefinding maximum cardinality, maximum weight or minimum cost514 can be finding maximum cardinality, maximum weight or minimum cost 324 515 matching. The search can be constrained to find perfect or 325 516 maximum cardinality matching. 326 517 327 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 518 The matching algorithms implemented in LEMON: 519  \ref MaxBipartiteMatching HopcroftKarp augmenting path algorithm 520 for calculating maximum cardinality matching in bipartite graphs. 521  \ref PrBipartiteMatching Pushrelabel algorithm 522 for calculating maximum cardinality matching in bipartite graphs. 523  \ref MaxWeightedBipartiteMatching 524 Successive shortest path algorithm for calculating maximum weighted 525 matching and maximum weighted bipartite matching in bipartite graphs. 526  \ref MinCostMaxBipartiteMatching 527 Successive shortest path algorithm for calculating minimum cost maximum 528 matching in bipartite graphs. 529  \ref MaxMatching Edmond's blossom shrinking algorithm for calculating 530 maximum cardinality matching in general graphs. 531  \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating 532 maximum weighted matching in general graphs. 533  \ref MaxWeightedPerfectMatching 534 Edmond's blossom shrinking algorithm for calculating maximum weighted 535 perfect matching in general graphs. 347 536 348 537 \image html bipartite_matching.png … … 355 544 \brief Algorithms for finding a minimum cost spanning tree in a graph. 356 545 357 This group describes the algorithms for finding a minimum cost spanning358 tree in a graph 546 This group contains the algorithms for finding a minimum cost spanning 547 tree in a graph. 359 548 */ 360 549 … … 364 553 \brief Auxiliary algorithms implemented in LEMON. 365 554 366 This group describes some algorithms implemented in LEMON555 This group contains some algorithms implemented in LEMON 367 556 in order to make it easier to implement complex algorithms. 368 557 */ … … 373 562 \brief Approximation algorithms. 374 563 375 This group describes the approximation and heuristic algorithms564 This group contains the approximation and heuristic algorithms 376 565 implemented in LEMON. 377 566 */ … … 379 568 /** 380 569 @defgroup gen_opt_group General Optimization Tools 381 \brief This group describes some general optimization frameworks570 \brief This group contains some general optimization frameworks 382 571 implemented in LEMON. 383 572 384 This group describes some general optimization frameworks573 This group contains some general optimization frameworks 385 574 implemented in LEMON. 386 575 */ … … 391 580 \brief Lp and Mip solver interfaces for LEMON. 392 581 393 This group describes Lp and Mip solver interfaces for LEMON. The582 This group contains Lp and Mip solver interfaces for LEMON. The 394 583 various LP solvers could be used in the same manner with this 395 584 interface. … … 410 599 \brief Metaheuristics for LEMON library. 411 600 412 This group describes some metaheuristic optimization tools.601 This group contains some metaheuristic optimization tools. 413 602 */ 414 603 … … 425 614 \brief Simple basic graph utilities. 426 615 427 This group describes some simple basic graph utilities.616 This group contains some simple basic graph utilities. 428 617 */ 429 618 … … 433 622 \brief Tools for development, debugging and testing. 434 623 435 This group describes several useful tools for development,624 This group contains several useful tools for development, 436 625 debugging and testing. 437 626 */ … … 442 631 \brief Simple tools for measuring the performance of algorithms. 443 632 444 This group describes simple tools for measuring the performance633 This group contains simple tools for measuring the performance 445 634 of algorithms. 446 635 */ … … 451 640 \brief Exceptions defined in LEMON. 452 641 453 This group describes the exceptions defined in LEMON.642 This group contains the exceptions defined in LEMON. 454 643 */ 455 644 … … 458 647 \brief Graph InputOutput methods 459 648 460 This group describes the tools for importing and exporting graphs649 This group contains the tools for importing and exporting graphs 461 650 and graph related data. Now it supports the \ref lgfformat 462 651 "LEMON Graph Format", the \c DIMACS format and the encapsulated … … 465 654 466 655 /** 467 @defgroup lemon_io LEMON InputOutput656 @defgroup lemon_io LEMON Graph Format 468 657 @ingroup io_group 469 658 \brief Reading and writing LEMON Graph Format. 470 659 471 This group describes methods for reading and writing660 This group contains methods for reading and writing 472 661 \ref lgfformat "LEMON Graph Format". 473 662 */ … … 478 667 \brief General \c EPS drawer and graph exporter 479 668 480 This group describes general \c EPS drawing methods and special669 This group contains general \c EPS drawing methods and special 481 670 graph exporting tools. 671 */ 672 673 /** 674 @defgroup dimacs_group DIMACS format 675 @ingroup io_group 676 \brief Read and write files in DIMACS format 677 678 Tools to read a digraph from or write it to a file in DIMACS format data. 679 */ 680 681 /** 682 @defgroup nauty_group NAUTY Format 683 @ingroup io_group 684 \brief Read \e Nauty format 685 686 Tool to read graphs from \e Nauty format data. 482 687 */ 483 688 … … 486 691 \brief Skeleton classes and concept checking classes 487 692 488 This group describes the data/algorithm skeletons and concept checking693 This group contains the data/algorithm skeletons and concept checking 489 694 classes implemented in LEMON. 490 695 … … 516 721 \brief Skeleton and concept checking classes for graph structures 517 722 518 This group describes the skeletons and concept checking classes of LEMON's723 This group contains the skeletons and concept checking classes of LEMON's 519 724 graph structures and helper classes used to implement these. 520 725 */ … … 525 730 \brief Skeleton and concept checking classes for maps 526 731 527 This group describes the skeletons and concept checking classes of maps.732 This group contains the skeletons and concept checking classes of maps. 528 733 */ 529 734 … … 531 736 \anchor demoprograms 532 737 533 @defgroup demos Demo programs738 @defgroup demos Demo Programs 534 739 535 740 Some demo programs are listed here. Their full source codes can be found in 536 741 the \c demo subdirectory of the source tree. 537 742 538 I t order to compile them, use <tt>enabledemo</tt> configure option when539 build the library.540 */ 541 542 /** 543 @defgroup tools Standalone utility applications743 In order to compile them, use the <tt>make demo</tt> or the 744 <tt>make check</tt> commands. 745 */ 746 747 /** 748 @defgroup tools Standalone Utility Applications 544 749 545 750 Some utility applications are listed here. … … 549 754 */ 550 755 756 }
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