doc/groups.dox
author Balazs Dezso <deba@inf.elte.hu>
Fri, 25 Sep 2009 21:51:36 +0200
changeset 948 636dadefe1e6
parent 757 f1fe0ddad6f7
child 953 d8ea85825e02
permissions -rw-r--r--
Add fractional matching algorithms (#314)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 namespace lemon {
    20 
    21 /**
    22 @defgroup datas Data Structures
    23 This group contains the several data structures implemented in LEMON.
    24 */
    25 
    26 /**
    27 @defgroup graphs Graph Structures
    28 @ingroup datas
    29 \brief Graph structures implemented in LEMON.
    30 
    31 The implementation of combinatorial algorithms heavily relies on
    32 efficient graph implementations. LEMON offers data structures which are
    33 planned to be easily used in an experimental phase of implementation studies,
    34 and thereafter the program code can be made efficient by small modifications.
    35 
    36 The most efficient implementation of diverse applications require the
    37 usage of different physical graph implementations. These differences
    38 appear in the size of graph we require to handle, memory or time usage
    39 limitations or in the set of operations through which the graph can be
    40 accessed.  LEMON provides several physical graph structures to meet
    41 the diverging requirements of the possible users.  In order to save on
    42 running time or on memory usage, some structures may fail to provide
    43 some graph features like arc/edge or node deletion.
    44 
    45 Alteration of standard containers need a very limited number of
    46 operations, these together satisfy the everyday requirements.
    47 In the case of graph structures, different operations are needed which do
    48 not alter the physical graph, but gives another view. If some nodes or
    49 arcs have to be hidden or the reverse oriented graph have to be used, then
    50 this is the case. It also may happen that in a flow implementation
    51 the residual graph can be accessed by another algorithm, or a node-set
    52 is to be shrunk for another algorithm.
    53 LEMON also provides a variety of graphs for these requirements called
    54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
    55 in conjunction with other graph representations.
    56 
    57 You are free to use the graph structure that fit your requirements
    58 the best, most graph algorithms and auxiliary data structures can be used
    59 with any graph structure.
    60 
    61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
    62 */
    63 
    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 /**
   141 @defgroup maps Maps
   142 @ingroup datas
   143 \brief Map structures implemented in LEMON.
   144 
   145 This group contains the map structures implemented in LEMON.
   146 
   147 LEMON provides several special purpose maps and map adaptors that e.g. combine
   148 new maps from existing ones.
   149 
   150 <b>See also:</b> \ref map_concepts "Map Concepts".
   151 */
   152 
   153 /**
   154 @defgroup graph_maps Graph Maps
   155 @ingroup maps
   156 \brief Special graph-related maps.
   157 
   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".
   163 */
   164 
   165 /**
   166 \defgroup map_adaptors Map Adaptors
   167 \ingroup maps
   168 \brief Tools to create new maps from existing ones
   169 
   170 This group contains map adaptors that are used to create "implicit"
   171 maps from other maps.
   172 
   173 Most of them are \ref concepts::ReadMap "read-only maps".
   174 They can make arithmetic and logical operations between one or two maps
   175 (negation, shifting, addition, multiplication, logical 'and', 'or',
   176 'not' etc.) or e.g. convert a map to another one of different Value type.
   177 
   178 The typical usage of this classes is passing implicit maps to
   179 algorithms.  If a function type algorithm is called then the function
   180 type map adaptors can be used comfortable. For example let's see the
   181 usage of map adaptors with the \c graphToEps() function.
   182 \code
   183   Color nodeColor(int deg) {
   184     if (deg >= 2) {
   185       return Color(0.5, 0.0, 0.5);
   186     } else if (deg == 1) {
   187       return Color(1.0, 0.5, 1.0);
   188     } else {
   189       return Color(0.0, 0.0, 0.0);
   190     }
   191   }
   192 
   193   Digraph::NodeMap<int> degree_map(graph);
   194 
   195   graphToEps(graph, "graph.eps")
   196     .coords(coords).scaleToA4().undirected()
   197     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
   198     .run();
   199 \endcode
   200 The \c functorToMap() function makes an \c int to \c Color map from the
   201 \c nodeColor() function. The \c composeMap() compose the \c degree_map
   202 and the previously created map. The composed map is a proper function to
   203 get the color of each node.
   204 
   205 The usage with class type algorithms is little bit harder. In this
   206 case the function type map adaptors can not be used, because the
   207 function map adaptors give back temporary objects.
   208 \code
   209   Digraph graph;
   210 
   211   typedef Digraph::ArcMap<double> DoubleArcMap;
   212   DoubleArcMap length(graph);
   213   DoubleArcMap speed(graph);
   214 
   215   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
   216   TimeMap time(length, speed);
   217 
   218   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
   219   dijkstra.run(source, target);
   220 \endcode
   221 We have a length map and a maximum speed map on the arcs of a digraph.
   222 The minimum time to pass the arc can be calculated as the division of
   223 the two maps which can be done implicitly with the \c DivMap template
   224 class. We use the implicit minimum time map as the length map of the
   225 \c Dijkstra algorithm.
   226 */
   227 
   228 /**
   229 @defgroup paths Path Structures
   230 @ingroup datas
   231 \brief %Path structures implemented in LEMON.
   232 
   233 This group contains the path structures implemented in LEMON.
   234 
   235 LEMON provides flexible data structures to work with paths.
   236 All of them have similar interfaces and they can be copied easily with
   237 assignment operators and copy constructors. This makes it easy and
   238 efficient to have e.g. the Dijkstra algorithm to store its result in
   239 any kind of path structure.
   240 
   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"
   263 */
   264 
   265 /**
   266 @defgroup matrices Matrices
   267 @ingroup datas
   268 \brief Two dimensional data storages implemented in LEMON.
   269 
   270 This group contains two dimensional data storages implemented in LEMON.
   271 */
   272 
   273 /**
   274 @defgroup auxdat Auxiliary Data Structures
   275 @ingroup datas
   276 \brief Auxiliary data structures implemented in LEMON.
   277 
   278 This group contains some data structures implemented in LEMON in
   279 order to make it easier to implement combinatorial algorithms.
   280 */
   281 
   282 /**
   283 @defgroup algs Algorithms
   284 \brief This group contains the several algorithms
   285 implemented in LEMON.
   286 
   287 This group contains the several algorithms
   288 implemented in LEMON.
   289 */
   290 
   291 /**
   292 @defgroup search Graph Search
   293 @ingroup algs
   294 \brief Common graph search algorithms.
   295 
   296 This group contains the common graph search algorithms, namely
   297 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
   298 */
   299 
   300 /**
   301 @defgroup shortest_path Shortest Path Algorithms
   302 @ingroup algs
   303 \brief Algorithms for finding shortest paths.
   304 
   305 This group contains the algorithms for finding shortest paths in digraphs.
   306 
   307  - \ref Dijkstra algorithm for finding shortest paths from a source node
   308    when all arc lengths are non-negative.
   309  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   310    from a source node when arc lenghts can be either positive or negative,
   311    but the digraph should not contain directed cycles with negative total
   312    length.
   313  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   314    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   315    lenghts can be either positive or negative, but the digraph should
   316    not contain directed cycles with negative total length.
   317  - \ref Suurballe A successive shortest path algorithm for finding
   318    arc-disjoint paths between two nodes having minimum total length.
   319 */
   320 
   321 /**
   322 @defgroup max_flow Maximum Flow Algorithms
   323 @ingroup algs
   324 \brief Algorithms for finding maximum flows.
   325 
   326 This group contains the algorithms for finding maximum flows and
   327 feasible circulations.
   328 
   329 The \e maximum \e flow \e problem is to find a flow of maximum value between
   330 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   331 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   332 \f$s, t \in V\f$ source and target nodes.
   333 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   334 following optimization problem.
   335 
   336 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   337 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   338     \quad \forall u\in V\setminus\{s,t\} \f]
   339 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   340 
   341 LEMON contains several algorithms for solving maximum flow problems:
   342 - \ref EdmondsKarp Edmonds-Karp algorithm.
   343 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
   344 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
   345 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
   346 
   347 In most cases the \ref Preflow "Preflow" algorithm provides the
   348 fastest method for computing a maximum flow. All implementations
   349 also provide functions to query the minimum cut, which is the dual
   350 problem of maximum flow.
   351 
   352 \ref Circulation is a preflow push-relabel algorithm implemented directly
   353 for finding feasible circulations, which is a somewhat different problem,
   354 but it is strongly related to maximum flow.
   355 For more information, see \ref Circulation.
   356 */
   357 
   358 /**
   359 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
   360 @ingroup algs
   361 
   362 \brief Algorithms for finding minimum cost flows and circulations.
   363 
   364 This group contains the algorithms for finding minimum cost flows and
   365 circulations. For more information about this problem and its dual
   366 solution see \ref min_cost_flow "Minimum Cost Flow Problem".
   367 
   368 LEMON contains several algorithms for this problem.
   369  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   370    pivot strategies.
   371  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
   372    cost scaling.
   373  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
   374    capacity scaling.
   375  - \ref CancelAndTighten The Cancel and Tighten algorithm.
   376  - \ref CycleCanceling Cycle-Canceling algorithms.
   377 
   378 In general NetworkSimplex is the most efficient implementation,
   379 but in special cases other algorithms could be faster.
   380 For example, if the total supply and/or capacities are rather small,
   381 CapacityScaling is usually the fastest algorithm (without effective scaling).
   382 */
   383 
   384 /**
   385 @defgroup min_cut Minimum Cut Algorithms
   386 @ingroup algs
   387 
   388 \brief Algorithms for finding minimum cut in graphs.
   389 
   390 This group contains the algorithms for finding minimum cut in graphs.
   391 
   392 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   393 \f$X\f$ subset of the nodes with minimum overall capacity on
   394 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   395 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   396 cut is the \f$X\f$ solution of the next optimization problem:
   397 
   398 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   399     \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
   400 
   401 LEMON contains several algorithms related to minimum cut problems:
   402 
   403 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   404   in directed graphs.
   405 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   406   calculating minimum cut in undirected graphs.
   407 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   408   all-pairs minimum cut in undirected graphs.
   409 
   410 If you want to find minimum cut just between two distinict nodes,
   411 see the \ref max_flow "maximum flow problem".
   412 */
   413 
   414 /**
   415 @defgroup graph_properties Connectivity and Other Graph Properties
   416 @ingroup algs
   417 \brief Algorithms for discovering the graph properties
   418 
   419 This group contains the algorithms for discovering the graph properties
   420 like connectivity, bipartiteness, euler property, simplicity etc.
   421 
   422 \image html edge_biconnected_components.png
   423 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
   424 */
   425 
   426 /**
   427 @defgroup planar Planarity Embedding and Drawing
   428 @ingroup algs
   429 \brief Algorithms for planarity checking, embedding and drawing
   430 
   431 This group contains the algorithms for planarity checking,
   432 embedding and drawing.
   433 
   434 \image html planar.png
   435 \image latex planar.eps "Plane graph" width=\textwidth
   436 */
   437 
   438 /**
   439 @defgroup matching Matching Algorithms
   440 @ingroup algs
   441 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   442 
   443 This group contains the algorithms for calculating
   444 matchings in graphs and bipartite graphs. The general matching problem is
   445 finding a subset of the edges for which each node has at most one incident
   446 edge.
   447 
   448 There are several different algorithms for calculate matchings in
   449 graphs.  The matching problems in bipartite graphs are generally
   450 easier than in general graphs. The goal of the matching optimization
   451 can be finding maximum cardinality, maximum weight or minimum cost
   452 matching. The search can be constrained to find perfect or
   453 maximum cardinality matching.
   454 
   455 The matching algorithms implemented in LEMON:
   456 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   457   for calculating maximum cardinality matching in bipartite graphs.
   458 - \ref PrBipartiteMatching Push-relabel algorithm
   459   for calculating maximum cardinality matching in bipartite graphs.
   460 - \ref MaxWeightedBipartiteMatching
   461   Successive shortest path algorithm for calculating maximum weighted
   462   matching and maximum weighted bipartite matching in bipartite graphs.
   463 - \ref MinCostMaxBipartiteMatching
   464   Successive shortest path algorithm for calculating minimum cost maximum
   465   matching in bipartite graphs.
   466 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   467   maximum cardinality matching in general graphs.
   468 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   469   maximum weighted matching in general graphs.
   470 - \ref MaxWeightedPerfectMatching
   471   Edmond's blossom shrinking algorithm for calculating maximum weighted
   472   perfect matching in general graphs.
   473 - \ref MaxFractionalMatching Push-relabel algorithm for calculating
   474   maximum cardinality fractional matching in general graphs.
   475 - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
   476   maximum weighted fractional matching in general graphs.
   477 - \ref MaxWeightedPerfectFractionalMatching
   478   Augmenting path algorithm for calculating maximum weighted
   479   perfect fractional matching in general graphs.
   480 
   481 \image html bipartite_matching.png
   482 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
   483 */
   484 
   485 /**
   486 @defgroup spantree Minimum Spanning Tree Algorithms
   487 @ingroup algs
   488 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   489 
   490 This group contains the algorithms for finding minimum cost spanning
   491 trees and arborescences.
   492 */
   493 
   494 /**
   495 @defgroup auxalg Auxiliary Algorithms
   496 @ingroup algs
   497 \brief Auxiliary algorithms implemented in LEMON.
   498 
   499 This group contains some algorithms implemented in LEMON
   500 in order to make it easier to implement complex algorithms.
   501 */
   502 
   503 /**
   504 @defgroup approx Approximation Algorithms
   505 @ingroup algs
   506 \brief Approximation algorithms.
   507 
   508 This group contains the approximation and heuristic algorithms
   509 implemented in LEMON.
   510 */
   511 
   512 /**
   513 @defgroup gen_opt_group General Optimization Tools
   514 \brief This group contains some general optimization frameworks
   515 implemented in LEMON.
   516 
   517 This group contains some general optimization frameworks
   518 implemented in LEMON.
   519 */
   520 
   521 /**
   522 @defgroup lp_group Lp and Mip Solvers
   523 @ingroup gen_opt_group
   524 \brief Lp and Mip solver interfaces for LEMON.
   525 
   526 This group contains Lp and Mip solver interfaces for LEMON. The
   527 various LP solvers could be used in the same manner with this
   528 interface.
   529 */
   530 
   531 /**
   532 @defgroup lp_utils Tools for Lp and Mip Solvers
   533 @ingroup lp_group
   534 \brief Helper tools to the Lp and Mip solvers.
   535 
   536 This group adds some helper tools to general optimization framework
   537 implemented in LEMON.
   538 */
   539 
   540 /**
   541 @defgroup metah Metaheuristics
   542 @ingroup gen_opt_group
   543 \brief Metaheuristics for LEMON library.
   544 
   545 This group contains some metaheuristic optimization tools.
   546 */
   547 
   548 /**
   549 @defgroup utils Tools and Utilities
   550 \brief Tools and utilities for programming in LEMON
   551 
   552 Tools and utilities for programming in LEMON.
   553 */
   554 
   555 /**
   556 @defgroup gutils Basic Graph Utilities
   557 @ingroup utils
   558 \brief Simple basic graph utilities.
   559 
   560 This group contains some simple basic graph utilities.
   561 */
   562 
   563 /**
   564 @defgroup misc Miscellaneous Tools
   565 @ingroup utils
   566 \brief Tools for development, debugging and testing.
   567 
   568 This group contains several useful tools for development,
   569 debugging and testing.
   570 */
   571 
   572 /**
   573 @defgroup timecount Time Measuring and Counting
   574 @ingroup misc
   575 \brief Simple tools for measuring the performance of algorithms.
   576 
   577 This group contains simple tools for measuring the performance
   578 of algorithms.
   579 */
   580 
   581 /**
   582 @defgroup exceptions Exceptions
   583 @ingroup utils
   584 \brief Exceptions defined in LEMON.
   585 
   586 This group contains the exceptions defined in LEMON.
   587 */
   588 
   589 /**
   590 @defgroup io_group Input-Output
   591 \brief Graph Input-Output methods
   592 
   593 This group contains the tools for importing and exporting graphs
   594 and graph related data. Now it supports the \ref lgf-format
   595 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   596 postscript (EPS) format.
   597 */
   598 
   599 /**
   600 @defgroup lemon_io LEMON Graph Format
   601 @ingroup io_group
   602 \brief Reading and writing LEMON Graph Format.
   603 
   604 This group contains methods for reading and writing
   605 \ref lgf-format "LEMON Graph Format".
   606 */
   607 
   608 /**
   609 @defgroup eps_io Postscript Exporting
   610 @ingroup io_group
   611 \brief General \c EPS drawer and graph exporter
   612 
   613 This group contains general \c EPS drawing methods and special
   614 graph exporting tools.
   615 */
   616 
   617 /**
   618 @defgroup dimacs_group DIMACS format
   619 @ingroup io_group
   620 \brief Read and write files in DIMACS format
   621 
   622 Tools to read a digraph from or write it to a file in DIMACS format data.
   623 */
   624 
   625 /**
   626 @defgroup nauty_group NAUTY Format
   627 @ingroup io_group
   628 \brief Read \e Nauty format
   629 
   630 Tool to read graphs from \e Nauty format data.
   631 */
   632 
   633 /**
   634 @defgroup concept Concepts
   635 \brief Skeleton classes and concept checking classes
   636 
   637 This group contains the data/algorithm skeletons and concept checking
   638 classes implemented in LEMON.
   639 
   640 The purpose of the classes in this group is fourfold.
   641 
   642 - These classes contain the documentations of the %concepts. In order
   643   to avoid document multiplications, an implementation of a concept
   644   simply refers to the corresponding concept class.
   645 
   646 - These classes declare every functions, <tt>typedef</tt>s etc. an
   647   implementation of the %concepts should provide, however completely
   648   without implementations and real data structures behind the
   649   interface. On the other hand they should provide nothing else. All
   650   the algorithms working on a data structure meeting a certain concept
   651   should compile with these classes. (Though it will not run properly,
   652   of course.) In this way it is easily to check if an algorithm
   653   doesn't use any extra feature of a certain implementation.
   654 
   655 - The concept descriptor classes also provide a <em>checker class</em>
   656   that makes it possible to check whether a certain implementation of a
   657   concept indeed provides all the required features.
   658 
   659 - Finally, They can serve as a skeleton of a new implementation of a concept.
   660 */
   661 
   662 /**
   663 @defgroup graph_concepts Graph Structure Concepts
   664 @ingroup concept
   665 \brief Skeleton and concept checking classes for graph structures
   666 
   667 This group contains the skeletons and concept checking classes of LEMON's
   668 graph structures and helper classes used to implement these.
   669 */
   670 
   671 /**
   672 @defgroup map_concepts Map Concepts
   673 @ingroup concept
   674 \brief Skeleton and concept checking classes for maps
   675 
   676 This group contains the skeletons and concept checking classes of maps.
   677 */
   678 
   679 /**
   680 \anchor demoprograms
   681 
   682 @defgroup demos Demo Programs
   683 
   684 Some demo programs are listed here. Their full source codes can be found in
   685 the \c demo subdirectory of the source tree.
   686 
   687 In order to compile them, use the <tt>make demo</tt> or the
   688 <tt>make check</tt> commands.
   689 */
   690 
   691 /**
   692 @defgroup tools Standalone Utility Applications
   693 
   694 Some utility applications are listed here.
   695 
   696 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   697 them, as well.
   698 */
   699 
   700 }