Alteration of standard containers need a very limited number of

 operations, these together satisfy the everyday requirements.

 In the case of graph structures, different operations are needed which do

 not alter the physical graph, but gives another view. If some nodes or

 arcs have to be hidden or the reverse oriented graph have to be used, then

 this is the case. It also may happen that in a flow implementation

 the residual graph can be accessed by another algorithm, or a node-set

 is to be shrunk for another algorithm.

 LEMON also provides a variety of graphs for these requirements called

 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only

 in conjunction with other graph representations.

 */

 /**

 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs

 @ingroup graphs

 \brief Graph types between real graphs and graph adaptors.

 This group describes some graph types between real graphs and graph adaptors.

 These classes wrap graphs to give new functionality as the adaptors do it.

 On the other hand they are not light-weight structures as the adaptors.

 @defgroup matrices Matrices

 @ingroup datas

 \brief Two dimensional data storages implemented in LEMON.

 This group describes two dimensional data storages implemented in LEMON.

 */

 /**

 @defgroup max_flow Maximum Flow algorithms

 @ingroup algs

 \brief Algorithms for finding maximum flows.

 This group describes the algorithms for finding maximum flows and

 feasible circulations.

 The maximum flow problem is to find a flow between a single source and

 a single target that is maximum. Formally, there is a \f$G=(V,A)\f$

 directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity

 function and given \f$s, t \in V\f$ source and target node. The

 maximum flow is the \f$f_a\f$ solution of the next optimization problem:

 \f[ 0 \le f_a \le c_a \f]

 \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv}

 \qquad \forall u \in V \setminus \{s,t\}\f]

 \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]

 LEMON contains several algorithms for solving maximum flow problems:

 - \ref lemon::EdmondsKarp "Edmonds-Karp"

 - \ref lemon::Preflow "Goldberg's Preflow algorithm"

 - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees"

 - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"

 In most cases the \ref lemon::Preflow "Preflow" algorithm provides the

 fastest method to compute the maximum flow. All impelementations

 provides functions to query the minimum cut, which is the dual linear

 programming problem of the maximum flow.

 */

 /**

 @defgroup min_cost_flow Minimum Cost Flow algorithms

 @ingroup algs

 \brief Algorithms for finding minimum cost flows and circulations.

 This group describes the algorithms for finding minimum cost flows and

 circulations.

 */

 /**

 @defgroup min_cut Minimum Cut algorithms

 @ingroup algs

 \brief Algorithms for finding minimum cut in graphs.

 This group describes the algorithms for finding minimum cut in graphs.

 The minimum cut problem is to find a non-empty and non-complete

 \f$X\f$ subset of the vertices with minimum overall capacity on

 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an

 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

 cut is the \f$X\f$ solution of the next optimization problem:

 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}

 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]

 LEMON contains several algorithms related to minimum cut problems:

 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut

   in directed graphs

 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to

   calculate minimum cut in undirected graphs

 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all

   pairs minimum cut in undirected graphs

 If you want to find minimum cut just between two distinict nodes,

 please see the \ref max_flow "Maximum Flow page".

 */

 /**

 @defgroup graph_prop Connectivity and other graph properties

 @ingroup algs

 \brief Algorithms for discovering the graph properties

 This group describes the algorithms for discovering the graph properties

 like connectivity, bipartiteness, euler property, simplicity etc.

 \image html edge_biconnected_components.png

 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth

 */

 /**

 @defgroup planar Planarity embedding and drawing

 @ingroup algs

 \brief Algorithms for planarity checking, embedding and drawing

 This group describes the algorithms for planarity checking,

 embedding and drawing.

 \image html planar.png

 \image latex planar.eps "Plane graph" width=\textwidth

 */

 /**

 @defgroup matching Matching algorithms

 @ingroup algs

 \brief Algorithms for finding matchings in graphs and bipartite graphs.

 This group contains algorithm objects and functions to calculate

 matchings in graphs and bipartite graphs. The general matching problem is

 finding a subset of the arcs which does not shares common endpoints.

 There are several different algorithms for calculate matchings in

 graphs.  The matching problems in bipartite graphs are generally

 easier than in general graphs. The goal of the matching optimization

 can be the finding maximum cardinality, maximum weight or minimum cost

 matching. The search can be constrained to find perfect or

 maximum cardinality matching.

 LEMON contains the next algorithms:

 - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp

   augmenting path algorithm for calculate maximum cardinality matching in

   bipartite graphs

 - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel

   algorithm for calculate maximum cardinality matching in bipartite graphs

 - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching"

   Successive shortest path algorithm for calculate maximum weighted matching

   and maximum weighted bipartite matching in bipartite graph

 - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching"

   Successive shortest path algorithm for calculate minimum cost maximum

   matching in bipartite graph

 - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm

   for calculate maximum cardinality matching in general graph

 - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom

   shrinking algorithm for calculate maximum weighted matching in general

   graph

 - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching"

   Edmond's blossom shrinking algorithm for calculate maximum weighted

   perfect matching in general graph

 \image html bipartite_matching.png

 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth

 */

 /**

 /**

 @defgroup auxalg Auxiliary algorithms

 @ingroup algs

 \brief Auxiliary algorithms implemented in LEMON.

 This group describes some algorithms implemented in LEMON

 in order to make it easier to implement complex algorithms.

 */

 /**

 @defgroup approx Approximation algorithms

 \brief Approximation algorithms.

 This group describes the approximation and heuristic algorithms

 implemented in LEMON.

 */

 /**

 @defgroup gen_opt_group General Optimization Tools

 \brief This group describes some general optimization frameworks

 implemented in LEMON.

 This group describes some general optimization frameworks

 implemented in LEMON.

 */

 /**

 @defgroup lp_group Lp and Mip solvers

 @ingroup gen_opt_group

 \brief Lp and Mip solver interfaces for LEMON.

 This group describes Lp and Mip solver interfaces for LEMON. The

 various LP solvers could be used in the same manner with this

 interface.

 */

 /**

 @defgroup lp_utils Tools for Lp and Mip solvers

 @ingroup lp_group

 \brief Helper tools to the Lp and Mip solvers.

 This group adds some helper tools to general optimization framework

 implemented in LEMON.

 */

 /**

 @defgroup metah Metaheuristics

 @ingroup gen_opt_group

 \brief Metaheuristics for LEMON library.

 This group describes some metaheuristic optimization tools.

 */

 @defgroup graphbits Tools for Graph Implementation

 @ingroup utils

 \brief Tools to make it easier to create graphs.

 This group describes the tools that makes it easier to create graphs and

 the maps that dynamically update with the graph changes.

 */

 /**

 /* --- Unused group

 @defgroup experimental Experimental Structures and Algorithms

 This group describes some Experimental structures and algorithms.

 The stuff here is subject to change.

 */

 /**

 @defgroup tools Standalone utility applications

 Some utility applications are listed here.

 The standard compilation procedure (<tt>./configure;make</tt>) will compile

 them, as well.

 */