doc/groups.dox
author Alpar Juttner <alpar@cs.elte.hu>
Mon, 11 May 2009 16:38:21 +0100
changeset 662 4d3d1a2cd23d
parent 651 3adf5e2d1e62
child 663 8b0df68370a4
permissions -rw-r--r--
Merge
     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 matrices Matrices
   230 @ingroup datas
   231 \brief Two dimensional data storages implemented in LEMON.
   232 
   233 This group contains two dimensional data storages implemented in LEMON.
   234 */
   235 
   236 /**
   237 @defgroup paths Path Structures
   238 @ingroup datas
   239 \brief %Path structures implemented in LEMON.
   240 
   241 This group contains the path structures implemented in LEMON.
   242 
   243 LEMON provides flexible data structures to work with paths.
   244 All of them have similar interfaces and they can be copied easily with
   245 assignment operators and copy constructors. This makes it easy and
   246 efficient to have e.g. the Dijkstra algorithm to store its result in
   247 any kind of path structure.
   248 
   249 \sa lemon::concepts::Path
   250 */
   251 
   252 /**
   253 @defgroup auxdat Auxiliary Data Structures
   254 @ingroup datas
   255 \brief Auxiliary data structures implemented in LEMON.
   256 
   257 This group contains some data structures implemented in LEMON in
   258 order to make it easier to implement combinatorial algorithms.
   259 */
   260 
   261 /**
   262 @defgroup algs Algorithms
   263 \brief This group contains the several algorithms
   264 implemented in LEMON.
   265 
   266 This group contains the several algorithms
   267 implemented in LEMON.
   268 */
   269 
   270 /**
   271 @defgroup search Graph Search
   272 @ingroup algs
   273 \brief Common graph search algorithms.
   274 
   275 This group contains the common graph search algorithms, namely
   276 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
   277 */
   278 
   279 /**
   280 @defgroup shortest_path Shortest Path Algorithms
   281 @ingroup algs
   282 \brief Algorithms for finding shortest paths.
   283 
   284 This group contains the algorithms for finding shortest paths in digraphs.
   285 
   286  - \ref Dijkstra algorithm for finding shortest paths from a source node
   287    when all arc lengths are non-negative.
   288  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   289    from a source node when arc lenghts can be either positive or negative,
   290    but the digraph should not contain directed cycles with negative total
   291    length.
   292  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   293    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   294    lenghts can be either positive or negative, but the digraph should
   295    not contain directed cycles with negative total length.
   296  - \ref Suurballe A successive shortest path algorithm for finding
   297    arc-disjoint paths between two nodes having minimum total length.
   298 */
   299 
   300 /**
   301 @defgroup max_flow Maximum Flow Algorithms
   302 @ingroup algs
   303 \brief Algorithms for finding maximum flows.
   304 
   305 This group contains the algorithms for finding maximum flows and
   306 feasible circulations.
   307 
   308 The \e maximum \e flow \e problem is to find a flow of maximum value between
   309 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   310 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   311 \f$s, t \in V\f$ source and target nodes.
   312 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   313 following optimization problem.
   314 
   315 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   316 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   317     \quad \forall u\in V\setminus\{s,t\} \f]
   318 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   319 
   320 LEMON contains several algorithms for solving maximum flow problems:
   321 - \ref EdmondsKarp Edmonds-Karp algorithm.
   322 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
   323 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
   324 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
   325 
   326 In most cases the \ref Preflow "Preflow" algorithm provides the
   327 fastest method for computing a maximum flow. All implementations
   328 also provide functions to query the minimum cut, which is the dual
   329 problem of maximum flow.
   330 
   331 \ref Circulation is a preflow push-relabel algorithm implemented directly 
   332 for finding feasible circulations, which is a somewhat different problem,
   333 but it is strongly related to maximum flow.
   334 For more information, see \ref Circulation.
   335 */
   336 
   337 /**
   338 @defgroup min_cost_flow Minimum Cost Flow Algorithms
   339 @ingroup algs
   340 
   341 \brief Algorithms for finding minimum cost flows and circulations.
   342 
   343 This group contains the algorithms for finding minimum cost flows and
   344 circulations.
   345 
   346 The \e minimum \e cost \e flow \e problem is to find a feasible flow of
   347 minimum total cost from a set of supply nodes to a set of demand nodes
   348 in a network with capacity constraints (lower and upper bounds)
   349 and arc costs.
   350 Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
   351 \f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
   352 upper bounds for the flow values on the arcs, for which
   353 \f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
   354 \f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
   355 on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
   356 signed supply values of the nodes.
   357 If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
   358 supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
   359 \f$-sup(u)\f$ demand.
   360 A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
   361 of the following optimization problem.
   362 
   363 \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
   364 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
   365     sup(u) \quad \forall u\in V \f]
   366 \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
   367 
   368 The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
   369 zero or negative in order to have a feasible solution (since the sum
   370 of the expressions on the left-hand side of the inequalities is zero).
   371 It means that the total demand must be greater or equal to the total
   372 supply and all the supplies have to be carried out from the supply nodes,
   373 but there could be demands that are not satisfied.
   374 If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
   375 constraints have to be satisfied with equality, i.e. all demands
   376 have to be satisfied and all supplies have to be used.
   377 
   378 If you need the opposite inequalities in the supply/demand constraints
   379 (i.e. the total demand is less than the total supply and all the demands
   380 have to be satisfied while there could be supplies that are not used),
   381 then you could easily transform the problem to the above form by reversing
   382 the direction of the arcs and taking the negative of the supply values
   383 (e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
   384 However \ref NetworkSimplex algorithm also supports this form directly
   385 for the sake of convenience.
   386 
   387 A feasible solution for this problem can be found using \ref Circulation.
   388 
   389 Note that the above formulation is actually more general than the usual
   390 definition of the minimum cost flow problem, in which strict equalities
   391 are required in the supply/demand contraints, i.e.
   392 
   393 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
   394     sup(u) \quad \forall u\in V. \f]
   395 
   396 However if the sum of the supply values is zero, then these two problems
   397 are equivalent. So if you need the equality form, you have to ensure this
   398 additional contraint for the algorithms.
   399 
   400 The dual solution of the minimum cost flow problem is represented by node 
   401 potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
   402 An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
   403 is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
   404 node potentials the following \e complementary \e slackness optimality
   405 conditions hold.
   406 
   407  - For all \f$uv\in A\f$ arcs:
   408    - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
   409    - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
   410    - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
   411  - For all \f$u\in V\f$ nodes:
   412    - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
   413      then \f$\pi(u)=0\f$.
   414  
   415 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
   416 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
   417 \f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
   418 
   419 All algorithms provide dual solution (node potentials) as well,
   420 if an optimal flow is found.
   421 
   422 LEMON contains several algorithms for solving minimum cost flow problems.
   423  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   424    pivot strategies.
   425  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
   426    cost scaling.
   427  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
   428    capacity scaling.
   429  - \ref CancelAndTighten The Cancel and Tighten algorithm.
   430  - \ref CycleCanceling Cycle-Canceling algorithms.
   431 
   432 Most of these implementations support the general inequality form of the
   433 minimum cost flow problem, but CancelAndTighten and CycleCanceling
   434 only support the equality form due to the primal method they use.
   435 
   436 In general NetworkSimplex is the most efficient implementation,
   437 but in special cases other algorithms could be faster.
   438 For example, if the total supply and/or capacities are rather small,
   439 CapacityScaling is usually the fastest algorithm (without effective scaling).
   440 */
   441 
   442 /**
   443 @defgroup min_cut Minimum Cut Algorithms
   444 @ingroup algs
   445 
   446 \brief Algorithms for finding minimum cut in graphs.
   447 
   448 This group contains the algorithms for finding minimum cut in graphs.
   449 
   450 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   451 \f$X\f$ subset of the nodes with minimum overall capacity on
   452 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   453 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   454 cut is the \f$X\f$ solution of the next optimization problem:
   455 
   456 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   457     \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
   458 
   459 LEMON contains several algorithms related to minimum cut problems:
   460 
   461 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   462   in directed graphs.
   463 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   464   calculating minimum cut in undirected graphs.
   465 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   466   all-pairs minimum cut in undirected graphs.
   467 
   468 If you want to find minimum cut just between two distinict nodes,
   469 see the \ref max_flow "maximum flow problem".
   470 */
   471 
   472 /**
   473 @defgroup graph_properties Connectivity and Other Graph Properties
   474 @ingroup algs
   475 \brief Algorithms for discovering the graph properties
   476 
   477 This group contains the algorithms for discovering the graph properties
   478 like connectivity, bipartiteness, euler property, simplicity etc.
   479 
   480 \image html edge_biconnected_components.png
   481 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
   482 */
   483 
   484 /**
   485 @defgroup planar Planarity Embedding and Drawing
   486 @ingroup algs
   487 \brief Algorithms for planarity checking, embedding and drawing
   488 
   489 This group contains the algorithms for planarity checking,
   490 embedding and drawing.
   491 
   492 \image html planar.png
   493 \image latex planar.eps "Plane graph" width=\textwidth
   494 */
   495 
   496 /**
   497 @defgroup matching Matching Algorithms
   498 @ingroup algs
   499 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   500 
   501 This group contains the algorithms for calculating
   502 matchings in graphs and bipartite graphs. The general matching problem is
   503 finding a subset of the edges for which each node has at most one incident
   504 edge.
   505 
   506 There are several different algorithms for calculate matchings in
   507 graphs.  The matching problems in bipartite graphs are generally
   508 easier than in general graphs. The goal of the matching optimization
   509 can be finding maximum cardinality, maximum weight or minimum cost
   510 matching. The search can be constrained to find perfect or
   511 maximum cardinality matching.
   512 
   513 The matching algorithms implemented in LEMON:
   514 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   515   for calculating maximum cardinality matching in bipartite graphs.
   516 - \ref PrBipartiteMatching Push-relabel algorithm
   517   for calculating maximum cardinality matching in bipartite graphs.
   518 - \ref MaxWeightedBipartiteMatching
   519   Successive shortest path algorithm for calculating maximum weighted
   520   matching and maximum weighted bipartite matching in bipartite graphs.
   521 - \ref MinCostMaxBipartiteMatching
   522   Successive shortest path algorithm for calculating minimum cost maximum
   523   matching in bipartite graphs.
   524 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   525   maximum cardinality matching in general graphs.
   526 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   527   maximum weighted matching in general graphs.
   528 - \ref MaxWeightedPerfectMatching
   529   Edmond's blossom shrinking algorithm for calculating maximum weighted
   530   perfect matching in general graphs.
   531 
   532 \image html bipartite_matching.png
   533 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
   534 */
   535 
   536 /**
   537 @defgroup spantree Minimum Spanning Tree Algorithms
   538 @ingroup algs
   539 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   540 
   541 This group contains the algorithms for finding minimum cost spanning
   542 trees and arborescences.
   543 */
   544 
   545 /**
   546 @defgroup auxalg Auxiliary Algorithms
   547 @ingroup algs
   548 \brief Auxiliary algorithms implemented in LEMON.
   549 
   550 This group contains some algorithms implemented in LEMON
   551 in order to make it easier to implement complex algorithms.
   552 */
   553 
   554 /**
   555 @defgroup approx Approximation Algorithms
   556 @ingroup algs
   557 \brief Approximation algorithms.
   558 
   559 This group contains the approximation and heuristic algorithms
   560 implemented in LEMON.
   561 */
   562 
   563 /**
   564 @defgroup gen_opt_group General Optimization Tools
   565 \brief This group contains some general optimization frameworks
   566 implemented in LEMON.
   567 
   568 This group contains some general optimization frameworks
   569 implemented in LEMON.
   570 */
   571 
   572 /**
   573 @defgroup lp_group Lp and Mip Solvers
   574 @ingroup gen_opt_group
   575 \brief Lp and Mip solver interfaces for LEMON.
   576 
   577 This group contains Lp and Mip solver interfaces for LEMON. The
   578 various LP solvers could be used in the same manner with this
   579 interface.
   580 */
   581 
   582 /**
   583 @defgroup lp_utils Tools for Lp and Mip Solvers
   584 @ingroup lp_group
   585 \brief Helper tools to the Lp and Mip solvers.
   586 
   587 This group adds some helper tools to general optimization framework
   588 implemented in LEMON.
   589 */
   590 
   591 /**
   592 @defgroup metah Metaheuristics
   593 @ingroup gen_opt_group
   594 \brief Metaheuristics for LEMON library.
   595 
   596 This group contains some metaheuristic optimization tools.
   597 */
   598 
   599 /**
   600 @defgroup utils Tools and Utilities
   601 \brief Tools and utilities for programming in LEMON
   602 
   603 Tools and utilities for programming in LEMON.
   604 */
   605 
   606 /**
   607 @defgroup gutils Basic Graph Utilities
   608 @ingroup utils
   609 \brief Simple basic graph utilities.
   610 
   611 This group contains some simple basic graph utilities.
   612 */
   613 
   614 /**
   615 @defgroup misc Miscellaneous Tools
   616 @ingroup utils
   617 \brief Tools for development, debugging and testing.
   618 
   619 This group contains several useful tools for development,
   620 debugging and testing.
   621 */
   622 
   623 /**
   624 @defgroup timecount Time Measuring and Counting
   625 @ingroup misc
   626 \brief Simple tools for measuring the performance of algorithms.
   627 
   628 This group contains simple tools for measuring the performance
   629 of algorithms.
   630 */
   631 
   632 /**
   633 @defgroup exceptions Exceptions
   634 @ingroup utils
   635 \brief Exceptions defined in LEMON.
   636 
   637 This group contains the exceptions defined in LEMON.
   638 */
   639 
   640 /**
   641 @defgroup io_group Input-Output
   642 \brief Graph Input-Output methods
   643 
   644 This group contains the tools for importing and exporting graphs
   645 and graph related data. Now it supports the \ref lgf-format
   646 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   647 postscript (EPS) format.
   648 */
   649 
   650 /**
   651 @defgroup lemon_io LEMON Graph Format
   652 @ingroup io_group
   653 \brief Reading and writing LEMON Graph Format.
   654 
   655 This group contains methods for reading and writing
   656 \ref lgf-format "LEMON Graph Format".
   657 */
   658 
   659 /**
   660 @defgroup eps_io Postscript Exporting
   661 @ingroup io_group
   662 \brief General \c EPS drawer and graph exporter
   663 
   664 This group contains general \c EPS drawing methods and special
   665 graph exporting tools.
   666 */
   667 
   668 /**
   669 @defgroup dimacs_group DIMACS format
   670 @ingroup io_group
   671 \brief Read and write files in DIMACS format
   672 
   673 Tools to read a digraph from or write it to a file in DIMACS format data.
   674 */
   675 
   676 /**
   677 @defgroup nauty_group NAUTY Format
   678 @ingroup io_group
   679 \brief Read \e Nauty format
   680 
   681 Tool to read graphs from \e Nauty format data.
   682 */
   683 
   684 /**
   685 @defgroup concept Concepts
   686 \brief Skeleton classes and concept checking classes
   687 
   688 This group contains the data/algorithm skeletons and concept checking
   689 classes implemented in LEMON.
   690 
   691 The purpose of the classes in this group is fourfold.
   692 
   693 - These classes contain the documentations of the %concepts. In order
   694   to avoid document multiplications, an implementation of a concept
   695   simply refers to the corresponding concept class.
   696 
   697 - These classes declare every functions, <tt>typedef</tt>s etc. an
   698   implementation of the %concepts should provide, however completely
   699   without implementations and real data structures behind the
   700   interface. On the other hand they should provide nothing else. All
   701   the algorithms working on a data structure meeting a certain concept
   702   should compile with these classes. (Though it will not run properly,
   703   of course.) In this way it is easily to check if an algorithm
   704   doesn't use any extra feature of a certain implementation.
   705 
   706 - The concept descriptor classes also provide a <em>checker class</em>
   707   that makes it possible to check whether a certain implementation of a
   708   concept indeed provides all the required features.
   709 
   710 - Finally, They can serve as a skeleton of a new implementation of a concept.
   711 */
   712 
   713 /**
   714 @defgroup graph_concepts Graph Structure Concepts
   715 @ingroup concept
   716 \brief Skeleton and concept checking classes for graph structures
   717 
   718 This group contains the skeletons and concept checking classes of LEMON's
   719 graph structures and helper classes used to implement these.
   720 */
   721 
   722 /**
   723 @defgroup map_concepts Map Concepts
   724 @ingroup concept
   725 \brief Skeleton and concept checking classes for maps
   726 
   727 This group contains the skeletons and concept checking classes of maps.
   728 */
   729 
   730 /**
   731 \anchor demoprograms
   732 
   733 @defgroup demos Demo Programs
   734 
   735 Some demo programs are listed here. Their full source codes can be found in
   736 the \c demo subdirectory of the source tree.
   737 
   738 In order to compile them, use the <tt>make demo</tt> or the
   739 <tt>make check</tt> commands.
   740 */
   741 
   742 /**
   743 @defgroup tools Standalone Utility Applications
   744 
   745 Some utility applications are listed here.
   746 
   747 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   748 them, as well.
   749 */
   750 
   751 }