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) 2003-2009
    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"
     263*/
     264
     265/**
     266@defgroup matrices Matrices
     267@ingroup datas
     268\brief Two dimensional data storages implemented in LEMON.
     269
     270This group contains two dimensional data storages implemented in LEMON.
    179271*/
    180272
     
    184276\brief Auxiliary data structures implemented in LEMON.
    185277
    186 This group describes some data structures implemented in LEMON in
     278This group contains some data structures implemented in LEMON in
    187279order to make it easier to implement combinatorial algorithms.
    188280*/
    189281
    190282/**
     283@defgroup geomdat Geometric Data Structures
     284@ingroup auxdat
     285\brief Geometric data structures implemented in LEMON.
     286
     287This group contains geometric data structures implemented in LEMON.
     288
     289 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
     290   vector with the usual operations.
     291 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
     292   rectangular bounding box of a set of \ref lemon::dim2::Point
     293   "dim2::Point"'s.
     294*/
     295
     296/**
     297@defgroup matrices Matrices
     298@ingroup auxdat
     299\brief Two dimensional data storages implemented in LEMON.
     300
     301This group contains two dimensional data storages implemented in LEMON.
     302*/
     303
     304/**
    191305@defgroup algs Algorithms
    192 \brief This group describes the several algorithms
     306\brief This group contains the several algorithms
    193307implemented in LEMON.
    194308
    195 This group describes the several algorithms
     309This group contains the several algorithms
    196310implemented in LEMON.
    197311*/
     
    202316\brief Common graph search algorithms.
    203317
    204 This group describes the common graph search algorithms like
    205 Breadth-First Search (BFS) and Depth-First Search (DFS).
     318This group contains the common graph search algorithms, namely
     319\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
    206320*/
    207321
     
    211325\brief Algorithms for finding shortest paths.
    212326
    213 This group describes the algorithms for finding shortest paths in graphs.
     327This group contains the algorithms for finding shortest paths in digraphs.
     328
     329 - \ref Dijkstra algorithm for finding shortest paths from a source node
     330   when all arc lengths are non-negative.
     331 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
     332   from a source node when arc lenghts can be either positive or negative,
     333   but the digraph should not contain directed cycles with negative total
     334   length.
     335 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
     336   for solving the \e all-pairs \e shortest \e paths \e problem when arc
     337   lenghts can be either positive or negative, but the digraph should
     338   not contain directed cycles with negative total length.
     339 - \ref Suurballe A successive shortest path algorithm for finding
     340   arc-disjoint paths between two nodes having minimum total length.
     341*/
     342
     343/**
     344@defgroup spantree Minimum Spanning Tree Algorithms
     345@ingroup algs
     346\brief Algorithms for finding minimum cost spanning trees and arborescences.
     347
     348This group contains the algorithms for finding minimum cost spanning
     349trees and arborescences.
    214350*/
    215351
     
    219355\brief Algorithms for finding maximum flows.
    220356
    221 This group describes the algorithms for finding maximum flows and
     357This group contains the algorithms for finding maximum flows and
    222358feasible circulations.
    223359
    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]
     360The \e maximum \e flow \e problem is to find a flow of maximum value between
     361a single source and a single target. Formally, there is a \f$G=(V,A)\f$
     362digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
     363\f$s, t \in V\f$ source and target nodes.
     364A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
     365following optimization problem.
     366
     367\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
     368\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
     369    \quad \forall u\in V\setminus\{s,t\} \f]
     370\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
    234371
    235372LEMON 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
     373- \ref EdmondsKarp Edmonds-Karp algorithm.
     374- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
     375- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
     376- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
     377
     378In most cases the \ref Preflow "Preflow" algorithm provides the
     379fastest method for computing a maximum flow. All implementations
     380also provide functions to query the minimum cut, which is the dual
     381problem of maximum flow.
     382
     383\ref Circulation is a preflow push-relabel algorithm implemented directly
     384for finding feasible circulations, which is a somewhat different problem,
     385but it is strongly related to maximum flow.
     386For more information, see \ref Circulation.
     387*/
     388
     389/**
     390@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
    249391@ingroup algs
    250392
    251393\brief Algorithms for finding minimum cost flows and circulations.
    252394
    253 This group describes the algorithms for finding minimum cost flows and
    254 circulations.
     395This group contains the algorithms for finding minimum cost flows and
     396circulations. For more information about this problem and its dual
     397solution see \ref min_cost_flow "Minimum Cost Flow Problem".
     398
     399LEMON contains several algorithms for this problem.
     400 - \ref NetworkSimplex Primal Network Simplex algorithm with various
     401   pivot strategies.
     402 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
     403   cost scaling.
     404 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
     405   capacity scaling.
     406 - \ref CancelAndTighten The Cancel and Tighten algorithm.
     407 - \ref CycleCanceling Cycle-Canceling algorithms.
     408
     409In general NetworkSimplex is the most efficient implementation,
     410but in special cases other algorithms could be faster.
     411For example, if the total supply and/or capacities are rather small,
     412CapacityScaling is usually the fastest algorithm (without effective scaling).
    255413*/
    256414
     
    261419\brief Algorithms for finding minimum cut in graphs.
    262420
    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
     421This group contains the algorithms for finding minimum cut in graphs.
     422
     423The \e minimum \e cut \e problem is to find a non-empty and non-complete
     424\f$X\f$ subset of the nodes with minimum overall capacity on
     425outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
     426\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
    269427cut is the \f$X\f$ solution of the next optimization problem:
    270428
    271429\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]
     430    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
    273431
    274432LEMON contains several algorithms related to minimum cut problems:
    275433
    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
     434- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
     435  in directed graphs.
     436- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
     437  calculating minimum cut in undirected graphs.
     438- \ref GomoryHu "Gomory-Hu tree computation" for calculating
     439  all-pairs minimum cut in undirected graphs.
    282440
    283441If 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
     442see the \ref max_flow "maximum flow problem".
    309443*/
    310444
     
    314448\brief Algorithms for finding matchings in graphs and bipartite graphs.
    315449
    316 This group contains algorithm objects and functions to calculate
     450This group contains the algorithms for calculating
    317451matchings in graphs and bipartite graphs. The general matching problem is
    318 finding a subset of the arcs which does not shares common endpoints.
     452finding a subset of the edges for which each node has at most one incident
     453edge.
    319454
    320455There are several different algorithms for calculate matchings in
    321456graphs.  The matching problems in bipartite graphs are generally
    322457easier than in general graphs. The goal of the matching optimization
    323 can be the finding maximum cardinality, maximum weight or minimum cost
     458can be finding maximum cardinality, maximum weight or minimum cost
    324459matching. The search can be constrained to find perfect or
    325460maximum cardinality matching.
    326461
    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
     462The matching algorithms implemented in LEMON:
     463- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
     464  for calculating maximum cardinality matching in bipartite graphs.
     465- \ref PrBipartiteMatching Push-relabel algorithm
     466  for calculating maximum cardinality matching in bipartite graphs.
     467- \ref MaxWeightedBipartiteMatching
     468  Successive shortest path algorithm for calculating maximum weighted
     469  matching and maximum weighted bipartite matching in bipartite graphs.
     470- \ref MinCostMaxBipartiteMatching
     471  Successive shortest path algorithm for calculating minimum cost maximum
     472  matching in bipartite graphs.
     473- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
     474  maximum cardinality matching in general graphs.
     475- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
     476  maximum weighted matching in general graphs.
     477- \ref MaxWeightedPerfectMatching
     478  Edmond's blossom shrinking algorithm for calculating maximum weighted
     479  perfect matching in general graphs.
    347480
    348481\image html bipartite_matching.png
     
    351484
    352485/**
    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
     486@defgroup graph_properties Connectivity and Other Graph Properties
     487@ingroup algs
     488\brief Algorithms for discovering the graph properties
     489
     490This group contains the algorithms for discovering the graph properties
     491like connectivity, bipartiteness, euler property, simplicity etc.
     492
     493\image html connected_components.png
     494\image latex connected_components.eps "Connected components" width=\textwidth
     495*/
     496
     497/**
     498@defgroup planar Planarity Embedding and Drawing
     499@ingroup algs
     500\brief Algorithms for planarity checking, embedding and drawing
     501
     502This group contains the algorithms for planarity checking,
     503embedding and drawing.
     504
     505\image html planar.png
     506\image latex planar.eps "Plane graph" width=\textwidth
     507*/
     508
     509/**
     510@defgroup approx Approximation Algorithms
     511@ingroup algs
     512\brief Approximation algorithms.
     513
     514This group contains the approximation and heuristic algorithms
     515implemented in LEMON.
    359516*/
    360517
     
    364521\brief Auxiliary algorithms implemented in LEMON.
    365522
    366 This group describes some algorithms implemented in LEMON
     523This group contains some algorithms implemented in LEMON
    367524in order to make it easier to implement complex algorithms.
    368525*/
    369526
    370527/**
    371 @defgroup approx Approximation Algorithms
    372 @ingroup algs
    373 \brief Approximation algorithms.
    374 
    375 This group describes the approximation and heuristic algorithms
     528@defgroup gen_opt_group General Optimization Tools
     529\brief This group contains some general optimization frameworks
    376530implemented in LEMON.
    377 */
    378 
    379 /**
    380 @defgroup gen_opt_group General Optimization Tools
    381 \brief This group describes some general optimization frameworks
    382 implemented in LEMON.
    383 
    384 This group describes some general optimization frameworks
     531
     532This group contains some general optimization frameworks
    385533implemented in LEMON.
    386534*/
     
    391539\brief Lp and Mip solver interfaces for LEMON.
    392540
    393 This group describes Lp and Mip solver interfaces for LEMON. The
     541This group contains Lp and Mip solver interfaces for LEMON. The
    394542various LP solvers could be used in the same manner with this
    395543interface.
     
    410558\brief Metaheuristics for LEMON library.
    411559
    412 This group describes some metaheuristic optimization tools.
     560This group contains some metaheuristic optimization tools.
    413561*/
    414562
     
    425573\brief Simple basic graph utilities.
    426574
    427 This group describes some simple basic graph utilities.
     575This group contains some simple basic graph utilities.
    428576*/
    429577
     
    433581\brief Tools for development, debugging and testing.
    434582
    435 This group describes several useful tools for development,
     583This group contains several useful tools for development,
    436584debugging and testing.
    437585*/
     
    442590\brief Simple tools for measuring the performance of algorithms.
    443591
    444 This group describes simple tools for measuring the performance
     592This group contains simple tools for measuring the performance
    445593of algorithms.
    446594*/
     
    451599\brief Exceptions defined in LEMON.
    452600
    453 This group describes the exceptions defined in LEMON.
     601This group contains the exceptions defined in LEMON.
    454602*/
    455603
     
    458606\brief Graph Input-Output methods
    459607
    460 This group describes the tools for importing and exporting graphs
     608This group contains the tools for importing and exporting graphs
    461609and graph related data. Now it supports the \ref lgf-format
    462610"LEMON Graph Format", the \c DIMACS format and the encapsulated
     
    465613
    466614/**
    467 @defgroup lemon_io LEMON Input-Output
     615@defgroup lemon_io LEMON Graph Format
    468616@ingroup io_group
    469617\brief Reading and writing LEMON Graph Format.
    470618
    471 This group describes methods for reading and writing
     619This group contains methods for reading and writing
    472620\ref lgf-format "LEMON Graph Format".
    473621*/
     
    478626\brief General \c EPS drawer and graph exporter
    479627
    480 This group describes general \c EPS drawing methods and special
     628This group contains general \c EPS drawing methods and special
    481629graph exporting tools.
     630*/
     631
     632/**
     633@defgroup dimacs_group DIMACS Format
     634@ingroup io_group
     635\brief Read and write files in DIMACS format
     636
     637Tools to read a digraph from or write it to a file in DIMACS format data.
     638*/
     639
     640/**
     641@defgroup nauty_group NAUTY Format
     642@ingroup io_group
     643\brief Read \e Nauty format
     644
     645Tool to read graphs from \e Nauty format data.
    482646*/
    483647
     
    486650\brief Skeleton classes and concept checking classes
    487651
    488 This group describes the data/algorithm skeletons and concept checking
     652This group contains the data/algorithm skeletons and concept checking
    489653classes implemented in LEMON.
    490654
     
    516680\brief Skeleton and concept checking classes for graph structures
    517681
    518 This group describes the skeletons and concept checking classes of LEMON's
    519 graph structures and helper classes used to implement these.
     682This group contains the skeletons and concept checking classes of
     683graph structures.
    520684*/
    521685
     
    525689\brief Skeleton and concept checking classes for maps
    526690
    527 This group describes the skeletons and concept checking classes of maps.
     691This group contains the skeletons and concept checking classes of maps.
     692*/
     693
     694/**
     695@defgroup tools Standalone Utility Applications
     696
     697Some utility applications are listed here.
     698
     699The standard compilation procedure (<tt>./configure;make</tt>) will compile
     700them, as well.
    528701*/
    529702
     
    531704\anchor demoprograms
    532705
    533 @defgroup demos Demo programs
     706@defgroup demos Demo Programs
    534707
    535708Some demo programs are listed here. Their full source codes can be found in
    536709the \c demo subdirectory of the source tree.
    537710
    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 
     711In order to compile them, use the <tt>make demo</tt> or the
     712<tt>make check</tt> commands.
     713*/
     714
     715}
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