author Peter Kovacs <>
Thu, 07 May 2009 02:07:59 +0200
changeset 698 3adf5e2d1e62
parent 687 6c408d864fa1
child 707 d9cf3b5858ae
permissions -rw-r--r--
Small doc improvements (#257)
     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  */
    19 namespace lemon {
    21 /**
    22 @defgroup datas Data Structures
    23 This group contains the several data structures implemented in LEMON.
    24 */
    26 /**
    27 @defgroup graphs Graph Structures
    28 @ingroup datas
    29 \brief Graph structures implemented in LEMON.
    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.
    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.
    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.
    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.
    61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
    62 */
    64 /**
    65 @defgroup graph_adaptors Adaptor Classes for Graphs
    66 @ingroup graphs
    67 \brief Adaptor classes for digraphs and graphs
    69 This group contains several useful adaptor classes for digraphs and graphs.
    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.
    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.
   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.
   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.
   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 */
   140 /**
   141 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs
   142 @ingroup graphs
   143 \brief Graph types between real graphs and graph adaptors.
   145 This group contains some graph types between real graphs and graph adaptors.
   146 These classes wrap graphs to give new functionality as the adaptors do it.
   147 On the other hand they are not light-weight structures as the adaptors.
   148 */
   150 /**
   151 @defgroup maps Maps
   152 @ingroup datas
   153 \brief Map structures implemented in LEMON.
   155 This group contains the map structures implemented in LEMON.
   157 LEMON provides several special purpose maps and map adaptors that e.g. combine
   158 new maps from existing ones.
   160 <b>See also:</b> \ref map_concepts "Map Concepts".
   161 */
   163 /**
   164 @defgroup graph_maps Graph Maps
   165 @ingroup maps
   166 \brief Special graph-related maps.
   168 This group contains maps that are specifically designed to assign
   169 values to the nodes and arcs/edges of graphs.
   171 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
   172 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
   173 */
   175 /**
   176 \defgroup map_adaptors Map Adaptors
   177 \ingroup maps
   178 \brief Tools to create new maps from existing ones
   180 This group contains map adaptors that are used to create "implicit"
   181 maps from other maps.
   183 Most of them are \ref concepts::ReadMap "read-only maps".
   184 They can make arithmetic and logical operations between one or two maps
   185 (negation, shifting, addition, multiplication, logical 'and', 'or',
   186 'not' etc.) or e.g. convert a map to another one of different Value type.
   188 The typical usage of this classes is passing implicit maps to
   189 algorithms.  If a function type algorithm is called then the function
   190 type map adaptors can be used comfortable. For example let's see the
   191 usage of map adaptors with the \c graphToEps() function.
   192 \code
   193   Color nodeColor(int deg) {
   194     if (deg >= 2) {
   195       return Color(0.5, 0.0, 0.5);
   196     } else if (deg == 1) {
   197       return Color(1.0, 0.5, 1.0);
   198     } else {
   199       return Color(0.0, 0.0, 0.0);
   200     }
   201   }
   203   Digraph::NodeMap<int> degree_map(graph);
   205   graphToEps(graph, "graph.eps")
   206     .coords(coords).scaleToA4().undirected()
   207     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
   208     .run();
   209 \endcode
   210 The \c functorToMap() function makes an \c int to \c Color map from the
   211 \c nodeColor() function. The \c composeMap() compose the \c degree_map
   212 and the previously created map. The composed map is a proper function to
   213 get the color of each node.
   215 The usage with class type algorithms is little bit harder. In this
   216 case the function type map adaptors can not be used, because the
   217 function map adaptors give back temporary objects.
   218 \code
   219   Digraph graph;
   221   typedef Digraph::ArcMap<double> DoubleArcMap;
   222   DoubleArcMap length(graph);
   223   DoubleArcMap speed(graph);
   225   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
   226   TimeMap time(length, speed);
   228   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
   229, target);
   230 \endcode
   231 We have a length map and a maximum speed map on the arcs of a digraph.
   232 The minimum time to pass the arc can be calculated as the division of
   233 the two maps which can be done implicitly with the \c DivMap template
   234 class. We use the implicit minimum time map as the length map of the
   235 \c Dijkstra algorithm.
   236 */
   238 /**
   239 @defgroup matrices Matrices
   240 @ingroup datas
   241 \brief Two dimensional data storages implemented in LEMON.
   243 This group contains two dimensional data storages implemented in LEMON.
   244 */
   246 /**
   247 @defgroup paths Path Structures
   248 @ingroup datas
   249 \brief %Path structures implemented in LEMON.
   251 This group contains the path structures implemented in LEMON.
   253 LEMON provides flexible data structures to work with paths.
   254 All of them have similar interfaces and they can be copied easily with
   255 assignment operators and copy constructors. This makes it easy and
   256 efficient to have e.g. the Dijkstra algorithm to store its result in
   257 any kind of path structure.
   259 \sa lemon::concepts::Path
   260 */
   262 /**
   263 @defgroup auxdat Auxiliary Data Structures
   264 @ingroup datas
   265 \brief Auxiliary data structures implemented in LEMON.
   267 This group contains some data structures implemented in LEMON in
   268 order to make it easier to implement combinatorial algorithms.
   269 */
   271 /**
   272 @defgroup algs Algorithms
   273 \brief This group contains the several algorithms
   274 implemented in LEMON.
   276 This group contains the several algorithms
   277 implemented in LEMON.
   278 */
   280 /**
   281 @defgroup search Graph Search
   282 @ingroup algs
   283 \brief Common graph search algorithms.
   285 This group contains the common graph search algorithms, namely
   286 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
   287 */
   289 /**
   290 @defgroup shortest_path Shortest Path Algorithms
   291 @ingroup algs
   292 \brief Algorithms for finding shortest paths.
   294 This group contains the algorithms for finding shortest paths in digraphs.
   296  - \ref Dijkstra algorithm for finding shortest paths from a source node
   297    when all arc lengths are non-negative.
   298  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   299    from a source node when arc lenghts can be either positive or negative,
   300    but the digraph should not contain directed cycles with negative total
   301    length.
   302  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   303    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   304    lenghts can be either positive or negative, but the digraph should
   305    not contain directed cycles with negative total length.
   306  - \ref Suurballe A successive shortest path algorithm for finding
   307    arc-disjoint paths between two nodes having minimum total length.
   308 */
   310 /**
   311 @defgroup max_flow Maximum Flow Algorithms
   312 @ingroup algs
   313 \brief Algorithms for finding maximum flows.
   315 This group contains the algorithms for finding maximum flows and
   316 feasible circulations.
   318 The \e maximum \e flow \e problem is to find a flow of maximum value between
   319 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   320 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   321 \f$s, t \in V\f$ source and target nodes.
   322 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   323 following optimization problem.
   325 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   326 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   327     \quad \forall u\in V\setminus\{s,t\} \f]
   328 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   330 LEMON contains several algorithms for solving maximum flow problems:
   331 - \ref EdmondsKarp Edmonds-Karp algorithm.
   332 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
   333 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
   334 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
   336 In most cases the \ref Preflow "Preflow" algorithm provides the
   337 fastest method for computing a maximum flow. All implementations
   338 also provide functions to query the minimum cut, which is the dual
   339 problem of maximum flow.
   341 \ref Circulation is a preflow push-relabel algorithm implemented directly 
   342 for finding feasible circulations, which is a somewhat different problem,
   343 but it is strongly related to maximum flow.
   344 For more information, see \ref Circulation.
   345 */
   347 /**
   348 @defgroup min_cost_flow Minimum Cost Flow Algorithms
   349 @ingroup algs
   351 \brief Algorithms for finding minimum cost flows and circulations.
   353 This group contains the algorithms for finding minimum cost flows and
   354 circulations.
   356 The \e minimum \e cost \e flow \e problem is to find a feasible flow of
   357 minimum total cost from a set of supply nodes to a set of demand nodes
   358 in a network with capacity constraints (lower and upper bounds)
   359 and arc costs.
   360 Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
   361 \f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
   362 upper bounds for the flow values on the arcs, for which
   363 \f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
   364 \f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
   365 on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
   366 signed supply values of the nodes.
   367 If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
   368 supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
   369 \f$-sup(u)\f$ demand.
   370 A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
   371 of the following optimization problem.
   373 \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
   374 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
   375     sup(u) \quad \forall u\in V \f]
   376 \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
   378 The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
   379 zero or negative in order to have a feasible solution (since the sum
   380 of the expressions on the left-hand side of the inequalities is zero).
   381 It means that the total demand must be greater or equal to the total
   382 supply and all the supplies have to be carried out from the supply nodes,
   383 but there could be demands that are not satisfied.
   384 If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
   385 constraints have to be satisfied with equality, i.e. all demands
   386 have to be satisfied and all supplies have to be used.
   388 If you need the opposite inequalities in the supply/demand constraints
   389 (i.e. the total demand is less than the total supply and all the demands
   390 have to be satisfied while there could be supplies that are not used),
   391 then you could easily transform the problem to the above form by reversing
   392 the direction of the arcs and taking the negative of the supply values
   393 (e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
   394 However \ref NetworkSimplex algorithm also supports this form directly
   395 for the sake of convenience.
   397 A feasible solution for this problem can be found using \ref Circulation.
   399 Note that the above formulation is actually more general than the usual
   400 definition of the minimum cost flow problem, in which strict equalities
   401 are required in the supply/demand contraints, i.e.
   403 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
   404     sup(u) \quad \forall u\in V. \f]
   406 However if the sum of the supply values is zero, then these two problems
   407 are equivalent. So if you need the equality form, you have to ensure this
   408 additional contraint for the algorithms.
   410 The dual solution of the minimum cost flow problem is represented by node 
   411 potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
   412 An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
   413 is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
   414 node potentials the following \e complementary \e slackness optimality
   415 conditions hold.
   417  - For all \f$uv\in A\f$ arcs:
   418    - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
   419    - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
   420    - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
   421  - For all \f$u\in V\f$ nodes:
   422    - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
   423      then \f$\pi(u)=0\f$.
   425 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
   426 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
   427 \f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
   429 All algorithms provide dual solution (node potentials) as well,
   430 if an optimal flow is found.
   432 LEMON contains several algorithms for solving minimum cost flow problems.
   433  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   434    pivot strategies.
   435  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
   436    cost scaling.
   437  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
   438    capacity scaling.
   439  - \ref CancelAndTighten The Cancel and Tighten algorithm.
   440  - \ref CycleCanceling Cycle-Canceling algorithms.
   442 Most of these implementations support the general inequality form of the
   443 minimum cost flow problem, but CancelAndTighten and CycleCanceling
   444 only support the equality form due to the primal method they use.
   446 In general NetworkSimplex is the most efficient implementation,
   447 but in special cases other algorithms could be faster.
   448 For example, if the total supply and/or capacities are rather small,
   449 CapacityScaling is usually the fastest algorithm (without effective scaling).
   450 */
   452 /**
   453 @defgroup min_cut Minimum Cut Algorithms
   454 @ingroup algs
   456 \brief Algorithms for finding minimum cut in graphs.
   458 This group contains the algorithms for finding minimum cut in graphs.
   460 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   461 \f$X\f$ subset of the nodes with minimum overall capacity on
   462 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   463 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   464 cut is the \f$X\f$ solution of the next optimization problem:
   466 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   467     \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
   469 LEMON contains several algorithms related to minimum cut problems:
   471 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   472   in directed graphs.
   473 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   474   calculating minimum cut in undirected graphs.
   475 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   476   all-pairs minimum cut in undirected graphs.
   478 If you want to find minimum cut just between two distinict nodes,
   479 see the \ref max_flow "maximum flow problem".
   480 */
   482 /**
   483 @defgroup graph_properties Connectivity and Other Graph Properties
   484 @ingroup algs
   485 \brief Algorithms for discovering the graph properties
   487 This group contains the algorithms for discovering the graph properties
   488 like connectivity, bipartiteness, euler property, simplicity etc.
   490 \image html edge_biconnected_components.png
   491 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
   492 */
   494 /**
   495 @defgroup planar Planarity Embedding and Drawing
   496 @ingroup algs
   497 \brief Algorithms for planarity checking, embedding and drawing
   499 This group contains the algorithms for planarity checking,
   500 embedding and drawing.
   502 \image html planar.png
   503 \image latex planar.eps "Plane graph" width=\textwidth
   504 */
   506 /**
   507 @defgroup matching Matching Algorithms
   508 @ingroup algs
   509 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   511 This group contains the algorithms for calculating
   512 matchings in graphs and bipartite graphs. The general matching problem is
   513 finding a subset of the edges for which each node has at most one incident
   514 edge.
   516 There are several different algorithms for calculate matchings in
   517 graphs.  The matching problems in bipartite graphs are generally
   518 easier than in general graphs. The goal of the matching optimization
   519 can be finding maximum cardinality, maximum weight or minimum cost
   520 matching. The search can be constrained to find perfect or
   521 maximum cardinality matching.
   523 The matching algorithms implemented in LEMON:
   524 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   525   for calculating maximum cardinality matching in bipartite graphs.
   526 - \ref PrBipartiteMatching Push-relabel algorithm
   527   for calculating maximum cardinality matching in bipartite graphs.
   528 - \ref MaxWeightedBipartiteMatching
   529   Successive shortest path algorithm for calculating maximum weighted
   530   matching and maximum weighted bipartite matching in bipartite graphs.
   531 - \ref MinCostMaxBipartiteMatching
   532   Successive shortest path algorithm for calculating minimum cost maximum
   533   matching in bipartite graphs.
   534 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   535   maximum cardinality matching in general graphs.
   536 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   537   maximum weighted matching in general graphs.
   538 - \ref MaxWeightedPerfectMatching
   539   Edmond's blossom shrinking algorithm for calculating maximum weighted
   540   perfect matching in general graphs.
   542 \image html bipartite_matching.png
   543 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
   544 */
   546 /**
   547 @defgroup spantree Minimum Spanning Tree Algorithms
   548 @ingroup algs
   549 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   551 This group contains the algorithms for finding minimum cost spanning
   552 trees and arborescences.
   553 */
   555 /**
   556 @defgroup auxalg Auxiliary Algorithms
   557 @ingroup algs
   558 \brief Auxiliary algorithms implemented in LEMON.
   560 This group contains some algorithms implemented in LEMON
   561 in order to make it easier to implement complex algorithms.
   562 */
   564 /**
   565 @defgroup approx Approximation Algorithms
   566 @ingroup algs
   567 \brief Approximation algorithms.
   569 This group contains the approximation and heuristic algorithms
   570 implemented in LEMON.
   571 */
   573 /**
   574 @defgroup gen_opt_group General Optimization Tools
   575 \brief This group contains some general optimization frameworks
   576 implemented in LEMON.
   578 This group contains some general optimization frameworks
   579 implemented in LEMON.
   580 */
   582 /**
   583 @defgroup lp_group Lp and Mip Solvers
   584 @ingroup gen_opt_group
   585 \brief Lp and Mip solver interfaces for LEMON.
   587 This group contains Lp and Mip solver interfaces for LEMON. The
   588 various LP solvers could be used in the same manner with this
   589 interface.
   590 */
   592 /**
   593 @defgroup lp_utils Tools for Lp and Mip Solvers
   594 @ingroup lp_group
   595 \brief Helper tools to the Lp and Mip solvers.
   597 This group adds some helper tools to general optimization framework
   598 implemented in LEMON.
   599 */
   601 /**
   602 @defgroup metah Metaheuristics
   603 @ingroup gen_opt_group
   604 \brief Metaheuristics for LEMON library.
   606 This group contains some metaheuristic optimization tools.
   607 */
   609 /**
   610 @defgroup utils Tools and Utilities
   611 \brief Tools and utilities for programming in LEMON
   613 Tools and utilities for programming in LEMON.
   614 */
   616 /**
   617 @defgroup gutils Basic Graph Utilities
   618 @ingroup utils
   619 \brief Simple basic graph utilities.
   621 This group contains some simple basic graph utilities.
   622 */
   624 /**
   625 @defgroup misc Miscellaneous Tools
   626 @ingroup utils
   627 \brief Tools for development, debugging and testing.
   629 This group contains several useful tools for development,
   630 debugging and testing.
   631 */
   633 /**
   634 @defgroup timecount Time Measuring and Counting
   635 @ingroup misc
   636 \brief Simple tools for measuring the performance of algorithms.
   638 This group contains simple tools for measuring the performance
   639 of algorithms.
   640 */
   642 /**
   643 @defgroup exceptions Exceptions
   644 @ingroup utils
   645 \brief Exceptions defined in LEMON.
   647 This group contains the exceptions defined in LEMON.
   648 */
   650 /**
   651 @defgroup io_group Input-Output
   652 \brief Graph Input-Output methods
   654 This group contains the tools for importing and exporting graphs
   655 and graph related data. Now it supports the \ref lgf-format
   656 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   657 postscript (EPS) format.
   658 */
   660 /**
   661 @defgroup lemon_io LEMON Graph Format
   662 @ingroup io_group
   663 \brief Reading and writing LEMON Graph Format.
   665 This group contains methods for reading and writing
   666 \ref lgf-format "LEMON Graph Format".
   667 */
   669 /**
   670 @defgroup eps_io Postscript Exporting
   671 @ingroup io_group
   672 \brief General \c EPS drawer and graph exporter
   674 This group contains general \c EPS drawing methods and special
   675 graph exporting tools.
   676 */
   678 /**
   679 @defgroup dimacs_group DIMACS format
   680 @ingroup io_group
   681 \brief Read and write files in DIMACS format
   683 Tools to read a digraph from or write it to a file in DIMACS format data.
   684 */
   686 /**
   687 @defgroup nauty_group NAUTY Format
   688 @ingroup io_group
   689 \brief Read \e Nauty format
   691 Tool to read graphs from \e Nauty format data.
   692 */
   694 /**
   695 @defgroup concept Concepts
   696 \brief Skeleton classes and concept checking classes
   698 This group contains the data/algorithm skeletons and concept checking
   699 classes implemented in LEMON.
   701 The purpose of the classes in this group is fourfold.
   703 - These classes contain the documentations of the %concepts. In order
   704   to avoid document multiplications, an implementation of a concept
   705   simply refers to the corresponding concept class.
   707 - These classes declare every functions, <tt>typedef</tt>s etc. an
   708   implementation of the %concepts should provide, however completely
   709   without implementations and real data structures behind the
   710   interface. On the other hand they should provide nothing else. All
   711   the algorithms working on a data structure meeting a certain concept
   712   should compile with these classes. (Though it will not run properly,
   713   of course.) In this way it is easily to check if an algorithm
   714   doesn't use any extra feature of a certain implementation.
   716 - The concept descriptor classes also provide a <em>checker class</em>
   717   that makes it possible to check whether a certain implementation of a
   718   concept indeed provides all the required features.
   720 - Finally, They can serve as a skeleton of a new implementation of a concept.
   721 */
   723 /**
   724 @defgroup graph_concepts Graph Structure Concepts
   725 @ingroup concept
   726 \brief Skeleton and concept checking classes for graph structures
   728 This group contains the skeletons and concept checking classes of LEMON's
   729 graph structures and helper classes used to implement these.
   730 */
   732 /**
   733 @defgroup map_concepts Map Concepts
   734 @ingroup concept
   735 \brief Skeleton and concept checking classes for maps
   737 This group contains the skeletons and concept checking classes of maps.
   738 */
   740 /**
   741 \anchor demoprograms
   743 @defgroup demos Demo Programs
   745 Some demo programs are listed here. Their full source codes can be found in
   746 the \c demo subdirectory of the source tree.
   748 In order to compile them, use the <tt>make demo</tt> or the
   749 <tt>make check</tt> commands.
   750 */
   752 /**
   753 @defgroup tools Standalone Utility Applications
   755 Some utility applications are listed here.
   757 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   758 them, as well.
   759 */
   761 }