COIN-OR::LEMON - Graph Library

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    33 * This file is a part of LEMON, a generic C++ optimization library.
    44 *
    5  * Copyright (C) 2003-2008
     5 * Copyright (C) 2003-2010
    66 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
    77 * (Egervary Research Group on Combinatorial Optimization, EGRES).
     
    1717 */
    1818
     19namespace lemon {
     20
    1921/**
    2022@defgroup datas Data Structures
    21 This group describes the several data structures implemented in LEMON.
     23This group contains the several data structures implemented in LEMON.
    2224*/
    2325
     
    6163
    6264/**
    63 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs
     65@defgroup graph_adaptors Adaptor Classes for Graphs
    6466@ingroup graphs
    65 \brief Graph types between real graphs and graph adaptors.
    66 
    67 This group describes some graph types between real graphs and graph adaptors.
    68 These classes wrap graphs to give new functionality as the adaptors do it.
    69 On the other hand they are not light-weight structures as the adaptors.
     67\brief Adaptor classes for digraphs and graphs
     68
     69This group contains several useful adaptor classes for digraphs and graphs.
     70
     71The main parts of LEMON are the different graph structures, generic
     72graph algorithms, graph concepts, which couple them, and graph
     73adaptors. While the previous notions are more or less clear, the
     74latter one needs further explanation. Graph adaptors are graph classes
     75which serve for considering graph structures in different ways.
     76
     77A short example makes this much clearer.  Suppose that we have an
     78instance \c g of a directed graph type, say ListDigraph and an algorithm
     79\code
     80template <typename Digraph>
     81int algorithm(const Digraph&);
     82\endcode
     83is 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
     85arcs.  In this case, an adaptor class is used, which (according
     86to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
     87The adaptor uses the original digraph structure and digraph operations when
     88methods of the reversed oriented graph are called.  This means that the adaptor
     89have minor memory usage, and do not perform sophisticated algorithmic
     90actions.  The purpose of it is to give a tool for the cases when a
     91graph have to be used in a specific alteration.  If this alteration is
     92obtained by a usual construction like filtering the node or the arc set or
     93considering a new orientation, then an adaptor is worthwhile to use.
     94To come back to the reverse oriented graph, in this situation
     95\code
     96template<typename Digraph> class ReverseDigraph;
     97\endcode
     98template class can be used. The code looks as follows
     99\code
     100ListDigraph g;
     101ReverseDigraph<ListDigraph> rg(g);
     102int result = algorithm(rg);
     103\endcode
     104During running the algorithm, the original digraph \c g is untouched.
     105This techniques give rise to an elegant code, and based on stable
     106graph adaptors, complex algorithms can be implemented easily.
     107
     108In flow, circulation and matching problems, the residual
     109graph is of particular importance. Combining an adaptor implementing
     110this with shortest path algorithms or minimum mean cycle algorithms,
     111a range of weighted and cardinality optimization algorithms can be
     112obtained. For other examples, the interested user is referred to the
     113detailed documentation of particular adaptors.
     114
     115The behavior of graph adaptors can be very different. Some of them keep
     116capabilities of the original graph while in other cases this would be
     117meaningless. This means that the concepts that they meet depend
     118on the graph adaptor, and the wrapped graph.
     119For example, if an arc of a reversed digraph is deleted, this is carried
     120out by deleting the corresponding arc of the original digraph, thus the
     121adaptor modifies the original digraph.
     122However in case of a residual digraph, this operation has no sense.
     123
     124Let us stand one more example here to simplify your work.
     125ReverseDigraph has constructor
     126\code
     127ReverseDigraph(Digraph& digraph);
     128\endcode
     129This means that in a situation, when a <tt>const %ListDigraph&</tt>
     130reference to a graph is given, then it have to be instantiated with
     131<tt>Digraph=const %ListDigraph</tt>.
     132\code
     133int algorithm1(const ListDigraph& g) {
     134  ReverseDigraph<const ListDigraph> rg(g);
     135  return algorithm2(rg);
     136}
     137\endcode
    70138*/
    71139
     
    75143\brief Map structures implemented in LEMON.
    76144
    77 This group describes the map structures implemented in LEMON.
     145This group contains the map structures implemented in LEMON.
    78146
    79147LEMON provides several special purpose maps and map adaptors that e.g. combine
     
    88156\brief Special graph-related maps.
    89157
    90 This group describes maps that are specifically designed to assign
    91 values to the nodes and arcs of graphs.
     158This group contains maps that are specifically designed to assign
     159values to the nodes and arcs/edges of graphs.
     160
     161If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
     162\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
    92163*/
    93164
     
    97168\brief Tools to create new maps from existing ones
    98169
    99 This group describes map adaptors that are used to create "implicit"
     170This group contains map adaptors that are used to create "implicit"
    100171maps from other maps.
    101172
    102 Most of them are \ref lemon::concepts::ReadMap "read-only maps".
     173Most of them are \ref concepts::ReadMap "read-only maps".
    103174They can make arithmetic and logical operations between one or two maps
    104175(negation, shifting, addition, multiplication, logical 'and', 'or',
     
    156227
    157228/**
    158 @defgroup matrices Matrices
    159 @ingroup datas
    160 \brief Two dimensional data storages implemented in LEMON.
    161 
    162 This group describes two dimensional data storages implemented in LEMON.
    163 */
    164 
    165 /**
    166229@defgroup paths Path Structures
    167230@ingroup datas
    168231\brief %Path structures implemented in LEMON.
    169232
    170 This group describes the path structures implemented in LEMON.
     233This group contains the path structures implemented in LEMON.
    171234
    172235LEMON provides flexible data structures to work with paths.
     
    176239any kind of path structure.
    177240
    178 \sa lemon::concepts::Path
     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
     249This group contains the heap structures implemented in LEMON.
     250
     251LEMON provides several heap classes. They are efficient implementations
     252of the abstract data type \e priority \e queue. They store items with
     253specified values called \e priorities in such a way that finding and
     254removing the item with minimum priority are efficient.
     255The basic operations are adding and erasing items, changing the priority
     256of an item, etc.
     257
     258Heaps are crucial in several algorithms, such as Dijkstra and Prim.
     259The heap implementations have the same interface, thus any of them can be
     260used easily in such algorithms.
     261
     262\sa \ref concepts::Heap "Heap concept"
    179263*/
    180264
     
    184268\brief Auxiliary data structures implemented in LEMON.
    185269
    186 This group describes some data structures implemented in LEMON in
     270This group contains some data structures implemented in LEMON in
    187271order to make it easier to implement combinatorial algorithms.
    188272*/
    189273
    190274/**
     275@defgroup geomdat Geometric Data Structures
     276@ingroup auxdat
     277\brief Geometric data structures implemented in LEMON.
     278
     279This group contains geometric data structures implemented in LEMON.
     280
     281 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
     282   vector with the usual operations.
     283 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
     284   rectangular bounding box of a set of \ref lemon::dim2::Point
     285   "dim2::Point"'s.
     286*/
     287
     288/**
    191289@defgroup algs Algorithms
    192 \brief This group describes the several algorithms
     290\brief This group contains the several algorithms
    193291implemented in LEMON.
    194292
    195 This group describes the several algorithms
     293This group contains the several algorithms
    196294implemented in LEMON.
    197295*/
     
    202300\brief Common graph search algorithms.
    203301
    204 This group describes the common graph search algorithms like
    205 Breadth-First Search (BFS) and Depth-First Search (DFS).
     302This group contains the common graph search algorithms, namely
     303\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
     304\ref clrs01algorithms.
    206305*/
    207306
     
    211310\brief Algorithms for finding shortest paths.
    212311
    213 This group describes the algorithms for finding shortest paths in graphs.
     312This group contains the algorithms for finding shortest paths in digraphs
     313\ref clrs01algorithms.
     314
     315 - \ref Dijkstra algorithm for finding shortest paths from a source node
     316   when all arc lengths are non-negative.
     317 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
     318   from a source node when arc lenghts can be either positive or negative,
     319   but the digraph should not contain directed cycles with negative total
     320   length.
     321 - \ref Suurballe A successive shortest path algorithm for finding
     322   arc-disjoint paths between two nodes having minimum total length.
     323*/
     324
     325/**
     326@defgroup spantree Minimum Spanning Tree Algorithms
     327@ingroup algs
     328\brief Algorithms for finding minimum cost spanning trees and arborescences.
     329
     330This group contains the algorithms for finding minimum cost spanning
     331trees and arborescences \ref clrs01algorithms.
    214332*/
    215333
     
    219337\brief Algorithms for finding maximum flows.
    220338
    221 This group describes the algorithms for finding maximum flows and
    222 feasible circulations.
    223 
    224 The maximum flow problem is to find a flow between a single source and
    225 a single target that is maximum. Formally, there is a \f$G=(V,A)\f$
    226 directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity
    227 function and given \f$s, t \in V\f$ source and target node. The
    228 maximum flow is the \f$f_a\f$ solution of the next optimization problem:
    229 
    230 \f[ 0 \le f_a \le c_a \f]
    231 \f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv}
    232 \qquad \forall u \in V \setminus \{s,t\}\f]
    233 \f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]
    234 
    235 LEMON contains several algorithms for solving maximum flow problems:
    236 - \ref lemon::EdmondsKarp "Edmonds-Karp"
    237 - \ref lemon::Preflow "Goldberg's Preflow algorithm"
    238 - \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic trees"
    239 - \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"
    240 
    241 In most cases the \ref lemon::Preflow "Preflow" algorithm provides the
    242 fastest method to compute the maximum flow. All impelementations
    243 provides functions to query the minimum cut, which is the dual linear
    244 programming problem of the maximum flow.
    245 */
    246 
    247 /**
    248 @defgroup min_cost_flow Minimum Cost Flow Algorithms
     339This group contains the algorithms for finding maximum flows and
     340feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
     341
     342The \e maximum \e flow \e problem is to find a flow of maximum value between
     343a single source and a single target. Formally, there is a \f$G=(V,A)\f$
     344digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
     345\f$s, t \in V\f$ source and target nodes.
     346A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
     347following optimization problem.
     348
     349\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
     350\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
     351    \quad \forall u\in V\setminus\{s,t\} \f]
     352\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
     353
     354\ref Preflow is an efficient implementation of Goldberg-Tarjan's
     355preflow push-relabel algorithm \ref goldberg88newapproach for finding
     356maximum flows. It also provides functions to query the minimum cut,
     357which is the dual problem of maximum flow.
     358
     359\ref Circulation is a preflow push-relabel algorithm implemented directly
     360for finding feasible circulations, which is a somewhat different problem,
     361but it is strongly related to maximum flow.
     362For more information, see \ref Circulation.
     363*/
     364
     365/**
     366@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
    249367@ingroup algs
    250368
    251369\brief Algorithms for finding minimum cost flows and circulations.
    252370
    253 This group describes the algorithms for finding minimum cost flows and
    254 circulations.
     371This group contains the algorithms for finding minimum cost flows and
     372circulations \ref amo93networkflows. For more information about this
     373problem and its dual solution, see \ref min_cost_flow
     374"Minimum Cost Flow Problem".
     375
     376LEMON contains several algorithms for this problem.
     377 - \ref NetworkSimplex Primal Network Simplex algorithm with various
     378   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
     379 - \ref CostScaling Cost Scaling algorithm based on push/augment and
     380   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
     381   \ref bunnagel98efficient.
     382 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
     383   shortest path method \ref edmondskarp72theoretical.
     384 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
     385   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
     386
     387In general NetworkSimplex is the most efficient implementation,
     388but in special cases other algorithms could be faster.
     389For example, if the total supply and/or capacities are rather small,
     390CapacityScaling is usually the fastest algorithm (without effective scaling).
    255391*/
    256392
     
    261397\brief Algorithms for finding minimum cut in graphs.
    262398
    263 This group describes the algorithms for finding minimum cut in graphs.
    264 
    265 The minimum cut problem is to find a non-empty and non-complete
    266 \f$X\f$ subset of the vertices with minimum overall capacity on
    267 outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an
    268 \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
     399This group contains the algorithms for finding minimum cut in graphs.
     400
     401The \e minimum \e cut \e problem is to find a non-empty and non-complete
     402\f$X\f$ subset of the nodes with minimum overall capacity on
     403outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
     404\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
    269405cut is the \f$X\f$ solution of the next optimization problem:
    270406
    271407\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
    272 \sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]
     408    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
    273409
    274410LEMON contains several algorithms related to minimum cut problems:
    275411
    276 - \ref lemon::HaoOrlin "Hao-Orlin algorithm" to calculate minimum cut
    277   in directed graphs
    278 - \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" to
    279   calculate minimum cut in undirected graphs
    280 - \ref lemon::GomoryHuTree "Gomory-Hu tree computation" to calculate all
    281   pairs minimum cut in undirected graphs
     412- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
     413  in directed graphs.
     414- \ref GomoryHu "Gomory-Hu tree computation" for calculating
     415  all-pairs minimum cut in undirected graphs.
    282416
    283417If you want to find minimum cut just between two distinict nodes,
    284 please see the \ref max_flow "Maximum Flow page".
    285 */
    286 
    287 /**
    288 @defgroup graph_prop Connectivity and Other Graph Properties
    289 @ingroup algs
    290 \brief Algorithms for discovering the graph properties
    291 
    292 This group describes the algorithms for discovering the graph properties
    293 like connectivity, bipartiteness, euler property, simplicity etc.
    294 
    295 \image html edge_biconnected_components.png
    296 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
    297 */
    298 
    299 /**
    300 @defgroup planar Planarity Embedding and Drawing
    301 @ingroup algs
    302 \brief Algorithms for planarity checking, embedding and drawing
    303 
    304 This group describes the algorithms for planarity checking,
    305 embedding and drawing.
    306 
    307 \image html planar.png
    308 \image latex planar.eps "Plane graph" width=\textwidth
     418see the \ref max_flow "maximum flow problem".
     419*/
     420
     421/**
     422@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
     423@ingroup algs
     424\brief Algorithms for finding minimum mean cycles.
     425
     426This group contains the algorithms for finding minimum mean cycles
     427\ref clrs01algorithms, \ref amo93networkflows.
     428
     429The \e minimum \e mean \e cycle \e problem is to find a directed cycle
     430of minimum mean length (cost) in a digraph.
     431The mean length of a cycle is the average length of its arcs, i.e. the
     432ratio between the total length of the cycle and the number of arcs on it.
     433
     434This problem has an important connection to \e conservative \e length
     435\e functions, too. A length function on the arcs of a digraph is called
     436conservative if and only if there is no directed cycle of negative total
     437length. For an arbitrary length function, the negative of the minimum
     438cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
     439arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
     440function.
     441
     442LEMON contains three algorithms for solving the minimum mean cycle problem:
     443- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
     444  \ref dasdan98minmeancycle.
     445- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
     446  version of Karp's algorithm \ref dasdan98minmeancycle.
     447- \ref HowardMmc Howard's policy iteration algorithm
     448  \ref dasdan98minmeancycle.
     449
     450In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
     451most efficient one, though the best known theoretical bound on its running
     452time is exponential.
     453Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
     454run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
     455typically faster due to the applied early termination scheme.
    309456*/
    310457
     
    314461\brief Algorithms for finding matchings in graphs and bipartite graphs.
    315462
    316 This group contains algorithm objects and functions to calculate
     463This group contains the algorithms for calculating
    317464matchings in graphs and bipartite graphs. The general matching problem is
    318 finding a subset of the arcs which does not shares common endpoints.
     465finding a subset of the edges for which each node has at most one incident
     466edge.
    319467
    320468There are several different algorithms for calculate matchings in
    321469graphs.  The matching problems in bipartite graphs are generally
    322470easier than in general graphs. The goal of the matching optimization
    323 can be the finding maximum cardinality, maximum weight or minimum cost
     471can be finding maximum cardinality, maximum weight or minimum cost
    324472matching. The search can be constrained to find perfect or
    325473maximum cardinality matching.
    326474
    327 LEMON contains the next algorithms:
    328 - \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp
    329   augmenting path algorithm for calculate maximum cardinality matching in
    330   bipartite graphs
    331 - \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel
    332   algorithm for calculate maximum cardinality matching in bipartite graphs
    333 - \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching"
    334   Successive shortest path algorithm for calculate maximum weighted matching
    335   and maximum weighted bipartite matching in bipartite graph
    336 - \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching"
    337   Successive shortest path algorithm for calculate minimum cost maximum
    338   matching in bipartite graph
    339 - \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm
    340   for calculate maximum cardinality matching in general graph
    341 - \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom
    342   shrinking algorithm for calculate maximum weighted matching in general
    343   graph
    344 - \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching"
    345   Edmond's blossom shrinking algorithm for calculate maximum weighted
    346   perfect matching in general graph
    347 
    348 \image html bipartite_matching.png
    349 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
    350 */
    351 
    352 /**
    353 @defgroup spantree Minimum Spanning Tree Algorithms
    354 @ingroup algs
    355 \brief Algorithms for finding a minimum cost spanning tree in a graph.
    356 
    357 This group describes the algorithms for finding a minimum cost spanning
    358 tree in a graph
     475The matching algorithms implemented in LEMON:
     476- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
     477  maximum cardinality matching in general graphs.
     478- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
     479  maximum weighted matching in general graphs.
     480- \ref MaxWeightedPerfectMatching
     481  Edmond's blossom shrinking algorithm for calculating maximum weighted
     482  perfect matching in general graphs.
     483- \ref MaxFractionalMatching Push-relabel algorithm for calculating
     484  maximum cardinality fractional matching in general graphs.
     485- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
     486  maximum weighted fractional matching in general graphs.
     487- \ref MaxWeightedPerfectFractionalMatching
     488  Augmenting path algorithm for calculating maximum weighted
     489  perfect fractional matching in general graphs.
     490
     491\image html matching.png
     492\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
     493*/
     494
     495/**
     496@defgroup graph_properties Connectivity and Other Graph Properties
     497@ingroup algs
     498\brief Algorithms for discovering the graph properties
     499
     500This group contains the algorithms for discovering the graph properties
     501like connectivity, bipartiteness, euler property, simplicity etc.
     502
     503\image html connected_components.png
     504\image latex connected_components.eps "Connected components" width=\textwidth
     505*/
     506
     507/**
     508@defgroup planar Planarity Embedding and Drawing
     509@ingroup algs
     510\brief Algorithms for planarity checking, embedding and drawing
     511
     512This group contains the algorithms for planarity checking,
     513embedding and drawing.
     514
     515\image html planar.png
     516\image latex planar.eps "Plane graph" width=\textwidth
    359517*/
    360518
     
    364522\brief Auxiliary algorithms implemented in LEMON.
    365523
    366 This group describes some algorithms implemented in LEMON
     524This group contains some algorithms implemented in LEMON
    367525in order to make it easier to implement complex algorithms.
    368526*/
    369527
    370528/**
    371 @defgroup approx Approximation Algorithms
    372 @ingroup algs
    373 \brief Approximation algorithms.
    374 
    375 This group describes the approximation and heuristic algorithms
     529@defgroup gen_opt_group General Optimization Tools
     530\brief This group contains some general optimization frameworks
    376531implemented in LEMON.
    377 */
    378 
    379 /**
    380 @defgroup gen_opt_group General Optimization Tools
    381 \brief This group describes some general optimization frameworks
     532
     533This group contains some general optimization frameworks
    382534implemented in LEMON.
    383 
    384 This group describes some general optimization frameworks
    385 implemented in LEMON.
    386 */
    387 
    388 /**
    389 @defgroup lp_group Lp and Mip Solvers
     535*/
     536
     537/**
     538@defgroup lp_group LP and MIP Solvers
    390539@ingroup gen_opt_group
    391 \brief Lp and Mip solver interfaces for LEMON.
    392 
    393 This group describes Lp and Mip solver interfaces for LEMON. The
    394 various LP solvers could be used in the same manner with this
    395 interface.
    396 */
    397 
    398 /**
    399 @defgroup lp_utils Tools for Lp and Mip Solvers
    400 @ingroup lp_group
    401 \brief Helper tools to the Lp and Mip solvers.
    402 
    403 This group adds some helper tools to general optimization framework
    404 implemented in LEMON.
    405 */
    406 
    407 /**
    408 @defgroup metah Metaheuristics
    409 @ingroup gen_opt_group
    410 \brief Metaheuristics for LEMON library.
    411 
    412 This group describes some metaheuristic optimization tools.
     540\brief LP and MIP solver interfaces for LEMON.
     541
     542This group contains LP and MIP solver interfaces for LEMON.
     543Various LP solvers could be used in the same manner with this
     544high-level interface.
     545
     546The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
     547\ref cplex, \ref soplex.
    413548*/
    414549
     
    425560\brief Simple basic graph utilities.
    426561
    427 This group describes some simple basic graph utilities.
     562This group contains some simple basic graph utilities.
    428563*/
    429564
     
    433568\brief Tools for development, debugging and testing.
    434569
    435 This group describes several useful tools for development,
     570This group contains several useful tools for development,
    436571debugging and testing.
    437572*/
     
    442577\brief Simple tools for measuring the performance of algorithms.
    443578
    444 This group describes simple tools for measuring the performance
     579This group contains simple tools for measuring the performance
    445580of algorithms.
    446581*/
     
    451586\brief Exceptions defined in LEMON.
    452587
    453 This group describes the exceptions defined in LEMON.
     588This group contains the exceptions defined in LEMON.
    454589*/
    455590
     
    458593\brief Graph Input-Output methods
    459594
    460 This group describes the tools for importing and exporting graphs
     595This group contains the tools for importing and exporting graphs
    461596and graph related data. Now it supports the \ref lgf-format
    462597"LEMON Graph Format", the \c DIMACS format and the encapsulated
     
    465600
    466601/**
    467 @defgroup lemon_io LEMON Input-Output
     602@defgroup lemon_io LEMON Graph Format
    468603@ingroup io_group
    469604\brief Reading and writing LEMON Graph Format.
    470605
    471 This group describes methods for reading and writing
     606This group contains methods for reading and writing
    472607\ref lgf-format "LEMON Graph Format".
    473608*/
     
    478613\brief General \c EPS drawer and graph exporter
    479614
    480 This group describes general \c EPS drawing methods and special
     615This group contains general \c EPS drawing methods and special
    481616graph exporting tools.
     617*/
     618
     619/**
     620@defgroup dimacs_group DIMACS Format
     621@ingroup io_group
     622\brief Read and write files in DIMACS format
     623
     624Tools to read a digraph from or write it to a file in DIMACS format data.
     625*/
     626
     627/**
     628@defgroup nauty_group NAUTY Format
     629@ingroup io_group
     630\brief Read \e Nauty format
     631
     632Tool to read graphs from \e Nauty format data.
    482633*/
    483634
     
    486637\brief Skeleton classes and concept checking classes
    487638
    488 This group describes the data/algorithm skeletons and concept checking
     639This group contains the data/algorithm skeletons and concept checking
    489640classes implemented in LEMON.
    490641
     
    516667\brief Skeleton and concept checking classes for graph structures
    517668
    518 This group describes the skeletons and concept checking classes of LEMON's
    519 graph structures and helper classes used to implement these.
     669This group contains the skeletons and concept checking classes of
     670graph structures.
    520671*/
    521672
     
    525676\brief Skeleton and concept checking classes for maps
    526677
    527 This group describes the skeletons and concept checking classes of maps.
     678This group contains the skeletons and concept checking classes of maps.
     679*/
     680
     681/**
     682@defgroup tools Standalone Utility Applications
     683
     684Some utility applications are listed here.
     685
     686The standard compilation procedure (<tt>./configure;make</tt>) will compile
     687them, as well.
    528688*/
    529689
     
    531691\anchor demoprograms
    532692
    533 @defgroup demos Demo programs
     693@defgroup demos Demo Programs
    534694
    535695Some demo programs are listed here. Their full source codes can be found in
    536696the \c demo subdirectory of the source tree.
    537697
    538 It order to compile them, use <tt>--enable-demo</tt> configure option when
    539 build the library.
    540 */
    541 
    542 /**
    543 @defgroup tools Standalone utility applications
    544 
    545 Some utility applications are listed here.
    546 
    547 The standard compilation procedure (<tt>./configure;make</tt>) will compile
    548 them, as well.
    549 */
    550 
     698In order to compile them, use the <tt>make demo</tt> or the
     699<tt>make check</tt> commands.
     700*/
     701
     702}
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