doc/groups.dox
author Alpar Juttner <alpar@cs.elte.hu>
Thu, 05 Nov 2009 08:39:49 +0100
changeset 817 432c54cec63c
parent 815 0a42883c8221
parent 802 134852d7fb0a
child 818 8452ca46e29a
permissions -rw-r--r--
Merge #179 (Port the min mean cycle algorithms)
     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 geomdat Geometric Data Structures
   284 @ingroup auxdat
   285 \brief Geometric data structures implemented in LEMON.
   286 
   287 This group contains geometric data structures implemented in LEMON.
   288 
   289  - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
   290    vector with the usual operations.
   291  - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
   292    rectangular bounding box of a set of \ref lemon::dim2::Point
   293    "dim2::Point"'s.
   294 */
   295 
   296 /**
   297 @defgroup matrices Matrices
   298 @ingroup auxdat
   299 \brief Two dimensional data storages implemented in LEMON.
   300 
   301 This group contains two dimensional data storages implemented in LEMON.
   302 */
   303 
   304 /**
   305 @defgroup algs Algorithms
   306 \brief This group contains the several algorithms
   307 implemented in LEMON.
   308 
   309 This group contains the several algorithms
   310 implemented in LEMON.
   311 */
   312 
   313 /**
   314 @defgroup search Graph Search
   315 @ingroup algs
   316 \brief Common graph search algorithms.
   317 
   318 This group contains the common graph search algorithms, namely
   319 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
   320 \ref clrs01algorithms.
   321 */
   322 
   323 /**
   324 @defgroup shortest_path Shortest Path Algorithms
   325 @ingroup algs
   326 \brief Algorithms for finding shortest paths.
   327 
   328 This group contains the algorithms for finding shortest paths in digraphs
   329 \ref clrs01algorithms.
   330 
   331  - \ref Dijkstra algorithm for finding shortest paths from a source node
   332    when all arc lengths are non-negative.
   333  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   334    from a source node when arc lenghts can be either positive or negative,
   335    but the digraph should not contain directed cycles with negative total
   336    length.
   337  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   338    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   339    lenghts can be either positive or negative, but the digraph should
   340    not contain directed cycles with negative total length.
   341  - \ref Suurballe A successive shortest path algorithm for finding
   342    arc-disjoint paths between two nodes having minimum total length.
   343 */
   344 
   345 /**
   346 @defgroup spantree Minimum Spanning Tree Algorithms
   347 @ingroup algs
   348 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   349 
   350 This group contains the algorithms for finding minimum cost spanning
   351 trees and arborescences \ref clrs01algorithms.
   352 */
   353 
   354 /**
   355 @defgroup max_flow Maximum Flow Algorithms
   356 @ingroup algs
   357 \brief Algorithms for finding maximum flows.
   358 
   359 This group contains the algorithms for finding maximum flows and
   360 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
   361 
   362 The \e maximum \e flow \e problem is to find a flow of maximum value between
   363 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   364 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   365 \f$s, t \in V\f$ source and target nodes.
   366 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   367 following optimization problem.
   368 
   369 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   370 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   371     \quad \forall u\in V\setminus\{s,t\} \f]
   372 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   373 
   374 LEMON contains several algorithms for solving maximum flow problems:
   375 - \ref EdmondsKarp Edmonds-Karp algorithm
   376   \ref edmondskarp72theoretical.
   377 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
   378   \ref goldberg88newapproach.
   379 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
   380   \ref dinic70algorithm, \ref sleator83dynamic.
   381 - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
   382   \ref goldberg88newapproach, \ref sleator83dynamic.
   383 
   384 In most cases the \ref Preflow algorithm provides the
   385 fastest method for computing a maximum flow. All implementations
   386 also provide functions to query the minimum cut, which is the dual
   387 problem of maximum flow.
   388 
   389 \ref Circulation is a preflow push-relabel algorithm implemented directly 
   390 for finding feasible circulations, which is a somewhat different problem,
   391 but it is strongly related to maximum flow.
   392 For more information, see \ref Circulation.
   393 */
   394 
   395 /**
   396 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
   397 @ingroup algs
   398 
   399 \brief Algorithms for finding minimum cost flows and circulations.
   400 
   401 This group contains the algorithms for finding minimum cost flows and
   402 circulations \ref amo93networkflows. For more information about this
   403 problem and its dual solution, see \ref min_cost_flow
   404 "Minimum Cost Flow Problem".
   405 
   406 LEMON contains several algorithms for this problem.
   407  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   408    pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
   409  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
   410    cost scaling \ref goldberg90approximation, \ref goldberg97efficient,
   411    \ref bunnagel98efficient.
   412  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
   413    capacity scaling \ref edmondskarp72theoretical.
   414  - \ref CancelAndTighten The Cancel and Tighten algorithm
   415    \ref goldberg89cyclecanceling.
   416  - \ref CycleCanceling Cycle-Canceling algorithms
   417    \ref klein67primal, \ref goldberg89cyclecanceling.
   418 
   419 In general NetworkSimplex is the most efficient implementation,
   420 but in special cases other algorithms could be faster.
   421 For example, if the total supply and/or capacities are rather small,
   422 CapacityScaling is usually the fastest algorithm (without effective scaling).
   423 */
   424 
   425 /**
   426 @defgroup min_cut Minimum Cut Algorithms
   427 @ingroup algs
   428 
   429 \brief Algorithms for finding minimum cut in graphs.
   430 
   431 This group contains the algorithms for finding minimum cut in graphs.
   432 
   433 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   434 \f$X\f$ subset of the nodes with minimum overall capacity on
   435 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   436 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   437 cut is the \f$X\f$ solution of the next optimization problem:
   438 
   439 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   440     \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
   441 
   442 LEMON contains several algorithms related to minimum cut problems:
   443 
   444 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   445   in directed graphs.
   446 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   447   calculating minimum cut in undirected graphs.
   448 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   449   all-pairs minimum cut in undirected graphs.
   450 
   451 If you want to find minimum cut just between two distinict nodes,
   452 see the \ref max_flow "maximum flow problem".
   453 */
   454 
   455 /**
   456 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
   457 @ingroup algs
   458 \brief Algorithms for finding minimum mean cycles.
   459 
   460 This group contains the algorithms for finding minimum mean cycles.
   461 
   462 The \e minimum \e mean \e cycle \e problem is to find a directed cycle
   463 of minimum mean length (cost) in a digraph.
   464 The mean length of a cycle is the average length of its arcs, i.e. the
   465 ratio between the total length of the cycle and the number of arcs on it.
   466 
   467 This problem has an important connection to \e conservative \e length
   468 \e functions, too. A length function on the arcs of a digraph is called
   469 conservative if and only if there is no directed cycle of negative total
   470 length. For an arbitrary length function, the negative of the minimum
   471 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
   472 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
   473 function.
   474 
   475 LEMON contains three algorithms for solving the minimum mean cycle problem:
   476 - \ref Karp "Karp"'s original algorithm.
   477 - \ref HartmannOrlin "Hartmann-Orlin"'s algorithm, which is an improved
   478   version of Karp's algorithm.
   479 - \ref Howard "Howard"'s policy iteration algorithm.
   480 
   481 In practice, the Howard algorithm proved to be by far the most efficient
   482 one, though the best known theoretical bound on its running time is
   483 exponential.
   484 Both Karp and HartmannOrlin algorithms run in time O(ne) and use space
   485 O(n<sup>2</sup>+e), but the latter one is typically faster due to the
   486 applied early termination scheme.
   487 */
   488 
   489 /**
   490 @defgroup matching Matching Algorithms
   491 @ingroup algs
   492 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   493 
   494 This group contains the algorithms for calculating
   495 matchings in graphs and bipartite graphs. The general matching problem is
   496 finding a subset of the edges for which each node has at most one incident
   497 edge.
   498 
   499 There are several different algorithms for calculate matchings in
   500 graphs.  The matching problems in bipartite graphs are generally
   501 easier than in general graphs. The goal of the matching optimization
   502 can be finding maximum cardinality, maximum weight or minimum cost
   503 matching. The search can be constrained to find perfect or
   504 maximum cardinality matching.
   505 
   506 The matching algorithms implemented in LEMON:
   507 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   508   for calculating maximum cardinality matching in bipartite graphs.
   509 - \ref PrBipartiteMatching Push-relabel algorithm
   510   for calculating maximum cardinality matching in bipartite graphs.
   511 - \ref MaxWeightedBipartiteMatching
   512   Successive shortest path algorithm for calculating maximum weighted
   513   matching and maximum weighted bipartite matching in bipartite graphs.
   514 - \ref MinCostMaxBipartiteMatching
   515   Successive shortest path algorithm for calculating minimum cost maximum
   516   matching in bipartite graphs.
   517 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   518   maximum cardinality matching in general graphs.
   519 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   520   maximum weighted matching in general graphs.
   521 - \ref MaxWeightedPerfectMatching
   522   Edmond's blossom shrinking algorithm for calculating maximum weighted
   523   perfect matching in general graphs.
   524 
   525 \image html bipartite_matching.png
   526 \image latex bipartite_matching.eps "Bipartite 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 Planarity 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 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 
   562 /**
   563 @defgroup auxalg Auxiliary Algorithms
   564 @ingroup algs
   565 \brief Auxiliary algorithms implemented in LEMON.
   566 
   567 This group contains some algorithms implemented in LEMON
   568 in order to make it easier to implement complex algorithms.
   569 */
   570 
   571 /**
   572 @defgroup gen_opt_group General Optimization Tools
   573 \brief This group contains some general optimization frameworks
   574 implemented in LEMON.
   575 
   576 This group contains some general optimization frameworks
   577 implemented in LEMON.
   578 */
   579 
   580 /**
   581 @defgroup lp_group LP and MIP Solvers
   582 @ingroup gen_opt_group
   583 \brief LP and MIP solver interfaces for LEMON.
   584 
   585 This group contains LP and MIP solver interfaces for LEMON.
   586 Various LP solvers could be used in the same manner with this
   587 high-level interface.
   588 
   589 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
   590 \ref cplex, \ref soplex.
   591 */
   592 
   593 /**
   594 @defgroup lp_utils Tools for Lp and Mip Solvers
   595 @ingroup lp_group
   596 \brief Helper tools to the Lp and Mip solvers.
   597 
   598 This group adds some helper tools to general optimization framework
   599 implemented in LEMON.
   600 */
   601 
   602 /**
   603 @defgroup metah Metaheuristics
   604 @ingroup gen_opt_group
   605 \brief Metaheuristics for LEMON library.
   606 
   607 This group contains some metaheuristic optimization tools.
   608 */
   609 
   610 /**
   611 @defgroup utils Tools and Utilities
   612 \brief Tools and utilities for programming in LEMON
   613 
   614 Tools and utilities for programming in LEMON.
   615 */
   616 
   617 /**
   618 @defgroup gutils Basic Graph Utilities
   619 @ingroup utils
   620 \brief Simple basic graph utilities.
   621 
   622 This group contains some simple basic graph utilities.
   623 */
   624 
   625 /**
   626 @defgroup misc Miscellaneous Tools
   627 @ingroup utils
   628 \brief Tools for development, debugging and testing.
   629 
   630 This group contains several useful tools for development,
   631 debugging and testing.
   632 */
   633 
   634 /**
   635 @defgroup timecount Time Measuring and Counting
   636 @ingroup misc
   637 \brief Simple tools for measuring the performance of algorithms.
   638 
   639 This group contains simple tools for measuring the performance
   640 of algorithms.
   641 */
   642 
   643 /**
   644 @defgroup exceptions Exceptions
   645 @ingroup utils
   646 \brief Exceptions defined in LEMON.
   647 
   648 This group contains the exceptions defined in LEMON.
   649 */
   650 
   651 /**
   652 @defgroup io_group Input-Output
   653 \brief Graph Input-Output methods
   654 
   655 This group contains the tools for importing and exporting graphs
   656 and graph related data. Now it supports the \ref lgf-format
   657 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   658 postscript (EPS) format.
   659 */
   660 
   661 /**
   662 @defgroup lemon_io LEMON Graph Format
   663 @ingroup io_group
   664 \brief Reading and writing LEMON Graph Format.
   665 
   666 This group contains methods for reading and writing
   667 \ref lgf-format "LEMON Graph Format".
   668 */
   669 
   670 /**
   671 @defgroup eps_io Postscript Exporting
   672 @ingroup io_group
   673 \brief General \c EPS drawer and graph exporter
   674 
   675 This group contains general \c EPS drawing methods and special
   676 graph exporting tools.
   677 */
   678 
   679 /**
   680 @defgroup dimacs_group DIMACS Format
   681 @ingroup io_group
   682 \brief Read and write files in DIMACS format
   683 
   684 Tools to read a digraph from or write it to a file in DIMACS format data.
   685 */
   686 
   687 /**
   688 @defgroup nauty_group NAUTY Format
   689 @ingroup io_group
   690 \brief Read \e Nauty format
   691 
   692 Tool to read graphs from \e Nauty format data.
   693 */
   694 
   695 /**
   696 @defgroup concept Concepts
   697 \brief Skeleton classes and concept checking classes
   698 
   699 This group contains the data/algorithm skeletons and concept checking
   700 classes implemented in LEMON.
   701 
   702 The purpose of the classes in this group is fourfold.
   703 
   704 - These classes contain the documentations of the %concepts. In order
   705   to avoid document multiplications, an implementation of a concept
   706   simply refers to the corresponding concept class.
   707 
   708 - These classes declare every functions, <tt>typedef</tt>s etc. an
   709   implementation of the %concepts should provide, however completely
   710   without implementations and real data structures behind the
   711   interface. On the other hand they should provide nothing else. All
   712   the algorithms working on a data structure meeting a certain concept
   713   should compile with these classes. (Though it will not run properly,
   714   of course.) In this way it is easily to check if an algorithm
   715   doesn't use any extra feature of a certain implementation.
   716 
   717 - The concept descriptor classes also provide a <em>checker class</em>
   718   that makes it possible to check whether a certain implementation of a
   719   concept indeed provides all the required features.
   720 
   721 - Finally, They can serve as a skeleton of a new implementation of a concept.
   722 */
   723 
   724 /**
   725 @defgroup graph_concepts Graph Structure Concepts
   726 @ingroup concept
   727 \brief Skeleton and concept checking classes for graph structures
   728 
   729 This group contains the skeletons and concept checking classes of
   730 graph structures.
   731 */
   732 
   733 /**
   734 @defgroup map_concepts Map Concepts
   735 @ingroup concept
   736 \brief Skeleton and concept checking classes for maps
   737 
   738 This group contains the skeletons and concept checking classes of maps.
   739 */
   740 
   741 /**
   742 @defgroup tools Standalone Utility Applications
   743 
   744 Some utility applications are listed here.
   745 
   746 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   747 them, as well.
   748 */
   749 
   750 /**
   751 \anchor demoprograms
   752 
   753 @defgroup demos Demo Programs
   754 
   755 Some demo programs are listed here. Their full source codes can be found in
   756 the \c demo subdirectory of the source tree.
   757 
   758 In order to compile them, use the <tt>make demo</tt> or the
   759 <tt>make check</tt> commands.
   760 */
   761 
   762 }