doc/groups.dox
author Peter Kovacs <kpeter@inf.elte.hu>
Fri, 24 Jul 2009 10:27:40 +0200
changeset 760 4ac30454f1c1
parent 710 8b0df68370a4
child 761 98a30824fe36
permissions -rw-r--r--
Small doc improvements
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    18 
    19 namespace lemon {
    20 
    21 /**
    22 @defgroup datas Data Structures
    23 This group contains the several data structures implemented in LEMON.
    24 */
    25 
    26 /**
    27 @defgroup graphs Graph Structures
    28 @ingroup datas
    29 \brief Graph structures implemented in LEMON.
    30 
    31 The implementation of combinatorial algorithms heavily relies on
    32 efficient graph implementations. LEMON offers data structures which are
    33 planned to be easily used in an experimental phase of implementation studies,
    34 and thereafter the program code can be made efficient by small modifications.
    35 
    36 The most efficient implementation of diverse applications require the
    37 usage of different physical graph implementations. These differences
    38 appear in the size of graph we require to handle, memory or time usage
    39 limitations or in the set of operations through which the graph can be
    40 accessed.  LEMON provides several physical graph structures to meet
    41 the diverging requirements of the possible users.  In order to save on
    42 running time or on memory usage, some structures may fail to provide
    43 some graph features like arc/edge or node deletion.
    44 
    45 Alteration of standard containers need a very limited number of
    46 operations, these together satisfy the everyday requirements.
    47 In the case of graph structures, different operations are needed which do
    48 not alter the physical graph, but gives another view. If some nodes or
    49 arcs have to be hidden or the reverse oriented graph have to be used, then
    50 this is the case. It also may happen that in a flow implementation
    51 the residual graph can be accessed by another algorithm, or a node-set
    52 is to be shrunk for another algorithm.
    53 LEMON also provides a variety of graphs for these requirements called
    54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
    55 in conjunction with other graph representations.
    56 
    57 You are free to use the graph structure that fit your requirements
    58 the best, most graph algorithms and auxiliary data structures can be used
    59 with any graph structure.
    60 
    61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
    62 */
    63 
    64 /**
    65 @defgroup graph_adaptors Adaptor Classes for Graphs
    66 @ingroup graphs
    67 \brief Adaptor classes for digraphs and graphs
    68 
    69 This group contains several useful adaptor classes for digraphs and graphs.
    70 
    71 The main parts of LEMON are the different graph structures, generic
    72 graph algorithms, graph concepts, which couple them, and graph
    73 adaptors. While the previous notions are more or less clear, the
    74 latter one needs further explanation. Graph adaptors are graph classes
    75 which serve for considering graph structures in different ways.
    76 
    77 A short example makes this much clearer.  Suppose that we have an
    78 instance \c g of a directed graph type, say ListDigraph and an algorithm
    79 \code
    80 template <typename Digraph>
    81 int algorithm(const Digraph&);
    82 \endcode
    83 is needed to run on the reverse oriented graph.  It may be expensive
    84 (in time or in memory usage) to copy \c g with the reversed
    85 arcs.  In this case, an adaptor class is used, which (according
    86 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
    87 The adaptor uses the original digraph structure and digraph operations when
    88 methods of the reversed oriented graph are called.  This means that the adaptor
    89 have minor memory usage, and do not perform sophisticated algorithmic
    90 actions.  The purpose of it is to give a tool for the cases when a
    91 graph have to be used in a specific alteration.  If this alteration is
    92 obtained by a usual construction like filtering the node or the arc set or
    93 considering a new orientation, then an adaptor is worthwhile to use.
    94 To come back to the reverse oriented graph, in this situation
    95 \code
    96 template<typename Digraph> class ReverseDigraph;
    97 \endcode
    98 template class can be used. The code looks as follows
    99 \code
   100 ListDigraph g;
   101 ReverseDigraph<ListDigraph> rg(g);
   102 int result = algorithm(rg);
   103 \endcode
   104 During running the algorithm, the original digraph \c g is untouched.
   105 This techniques give rise to an elegant code, and based on stable
   106 graph adaptors, complex algorithms can be implemented easily.
   107 
   108 In flow, circulation and matching problems, the residual
   109 graph is of particular importance. Combining an adaptor implementing
   110 this with shortest path algorithms or minimum mean cycle algorithms,
   111 a range of weighted and cardinality optimization algorithms can be
   112 obtained. For other examples, the interested user is referred to the
   113 detailed documentation of particular adaptors.
   114 
   115 The behavior of graph adaptors can be very different. Some of them keep
   116 capabilities of the original graph while in other cases this would be
   117 meaningless. This means that the concepts that they meet depend
   118 on the graph adaptor, and the wrapped graph.
   119 For example, if an arc of a reversed digraph is deleted, this is carried
   120 out by deleting the corresponding arc of the original digraph, thus the
   121 adaptor modifies the original digraph.
   122 However in case of a residual digraph, this operation has no sense.
   123 
   124 Let us stand one more example here to simplify your work.
   125 ReverseDigraph has constructor
   126 \code
   127 ReverseDigraph(Digraph& digraph);
   128 \endcode
   129 This means that in a situation, when a <tt>const %ListDigraph&</tt>
   130 reference to a graph is given, then it have to be instantiated with
   131 <tt>Digraph=const %ListDigraph</tt>.
   132 \code
   133 int algorithm1(const ListDigraph& g) {
   134   ReverseDigraph<const ListDigraph> rg(g);
   135   return algorithm2(rg);
   136 }
   137 \endcode
   138 */
   139 
   140 /**
   141 @defgroup maps Maps
   142 @ingroup datas
   143 \brief Map structures implemented in LEMON.
   144 
   145 This group contains the map structures implemented in LEMON.
   146 
   147 LEMON provides several special purpose maps and map adaptors that e.g. combine
   148 new maps from existing ones.
   149 
   150 <b>See also:</b> \ref map_concepts "Map Concepts".
   151 */
   152 
   153 /**
   154 @defgroup graph_maps Graph Maps
   155 @ingroup maps
   156 \brief Special graph-related maps.
   157 
   158 This group contains maps that are specifically designed to assign
   159 values to the nodes and arcs/edges of graphs.
   160 
   161 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
   162 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
   163 */
   164 
   165 /**
   166 \defgroup map_adaptors Map Adaptors
   167 \ingroup maps
   168 \brief Tools to create new maps from existing ones
   169 
   170 This group contains map adaptors that are used to create "implicit"
   171 maps from other maps.
   172 
   173 Most of them are \ref concepts::ReadMap "read-only maps".
   174 They can make arithmetic and logical operations between one or two maps
   175 (negation, shifting, addition, multiplication, logical 'and', 'or',
   176 'not' etc.) or e.g. convert a map to another one of different Value type.
   177 
   178 The typical usage of this classes is passing implicit maps to
   179 algorithms.  If a function type algorithm is called then the function
   180 type map adaptors can be used comfortable. For example let's see the
   181 usage of map adaptors with the \c graphToEps() function.
   182 \code
   183   Color nodeColor(int deg) {
   184     if (deg >= 2) {
   185       return Color(0.5, 0.0, 0.5);
   186     } else if (deg == 1) {
   187       return Color(1.0, 0.5, 1.0);
   188     } else {
   189       return Color(0.0, 0.0, 0.0);
   190     }
   191   }
   192 
   193   Digraph::NodeMap<int> degree_map(graph);
   194 
   195   graphToEps(graph, "graph.eps")
   196     .coords(coords).scaleToA4().undirected()
   197     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
   198     .run();
   199 \endcode
   200 The \c functorToMap() function makes an \c int to \c Color map from the
   201 \c nodeColor() function. The \c composeMap() compose the \c degree_map
   202 and the previously created map. The composed map is a proper function to
   203 get the color of each node.
   204 
   205 The usage with class type algorithms is little bit harder. In this
   206 case the function type map adaptors can not be used, because the
   207 function map adaptors give back temporary objects.
   208 \code
   209   Digraph graph;
   210 
   211   typedef Digraph::ArcMap<double> DoubleArcMap;
   212   DoubleArcMap length(graph);
   213   DoubleArcMap speed(graph);
   214 
   215   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
   216   TimeMap time(length, speed);
   217 
   218   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
   219   dijkstra.run(source, target);
   220 \endcode
   221 We have a length map and a maximum speed map on the arcs of a digraph.
   222 The minimum time to pass the arc can be calculated as the division of
   223 the two maps which can be done implicitly with the \c DivMap template
   224 class. We use the implicit minimum time map as the length map of the
   225 \c Dijkstra algorithm.
   226 */
   227 
   228 /**
   229 @defgroup matrices Matrices
   230 @ingroup datas
   231 \brief Two dimensional data storages implemented in LEMON.
   232 
   233 This group contains two dimensional data storages implemented in LEMON.
   234 */
   235 
   236 /**
   237 @defgroup paths Path Structures
   238 @ingroup datas
   239 \brief %Path structures implemented in LEMON.
   240 
   241 This group contains the path structures implemented in LEMON.
   242 
   243 LEMON provides flexible data structures to work with paths.
   244 All of them have similar interfaces and they can be copied easily with
   245 assignment operators and copy constructors. This makes it easy and
   246 efficient to have e.g. the Dijkstra algorithm to store its result in
   247 any kind of path structure.
   248 
   249 \sa lemon::concepts::Path
   250 */
   251 
   252 /**
   253 @defgroup auxdat Auxiliary Data Structures
   254 @ingroup datas
   255 \brief Auxiliary data structures implemented in LEMON.
   256 
   257 This group contains some data structures implemented in LEMON in
   258 order to make it easier to implement combinatorial algorithms.
   259 */
   260 
   261 /**
   262 @defgroup algs Algorithms
   263 \brief This group contains the several algorithms
   264 implemented in LEMON.
   265 
   266 This group contains the several algorithms
   267 implemented in LEMON.
   268 */
   269 
   270 /**
   271 @defgroup search Graph Search
   272 @ingroup algs
   273 \brief Common graph search algorithms.
   274 
   275 This group contains the common graph search algorithms, namely
   276 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
   277 */
   278 
   279 /**
   280 @defgroup shortest_path Shortest Path Algorithms
   281 @ingroup algs
   282 \brief Algorithms for finding shortest paths.
   283 
   284 This group contains the algorithms for finding shortest paths in digraphs.
   285 
   286  - \ref Dijkstra algorithm for finding shortest paths from a source node
   287    when all arc lengths are non-negative.
   288  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   289    from a source node when arc lenghts can be either positive or negative,
   290    but the digraph should not contain directed cycles with negative total
   291    length.
   292  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   293    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   294    lenghts can be either positive or negative, but the digraph should
   295    not contain directed cycles with negative total length.
   296  - \ref Suurballe A successive shortest path algorithm for finding
   297    arc-disjoint paths between two nodes having minimum total length.
   298 */
   299 
   300 /**
   301 @defgroup max_flow Maximum Flow Algorithms
   302 @ingroup algs
   303 \brief Algorithms for finding maximum flows.
   304 
   305 This group contains the algorithms for finding maximum flows and
   306 feasible circulations.
   307 
   308 The \e maximum \e flow \e problem is to find a flow of maximum value between
   309 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   310 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   311 \f$s, t \in V\f$ source and target nodes.
   312 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   313 following optimization problem.
   314 
   315 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   316 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   317     \quad \forall u\in V\setminus\{s,t\} \f]
   318 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   319 
   320 LEMON contains several algorithms for solving maximum flow problems:
   321 - \ref EdmondsKarp Edmonds-Karp algorithm.
   322 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
   323 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
   324 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
   325 
   326 In most cases the \ref Preflow "Preflow" algorithm provides the
   327 fastest method for computing a maximum flow. All implementations
   328 also provide functions to query the minimum cut, which is the dual
   329 problem of maximum flow.
   330 
   331 \ref Circulation is a preflow push-relabel algorithm implemented directly 
   332 for finding feasible circulations, which is a somewhat different problem,
   333 but it is strongly related to maximum flow.
   334 For more information, see \ref Circulation.
   335 */
   336 
   337 /**
   338 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
   339 @ingroup algs
   340 
   341 \brief Algorithms for finding minimum cost flows and circulations.
   342 
   343 This group contains the algorithms for finding minimum cost flows and
   344 circulations. For more information about this problem and its dual
   345 solution see \ref min_cost_flow "Minimum Cost Flow Problem".
   346 
   347 LEMON contains several algorithms for this problem.
   348  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   349    pivot strategies.
   350  - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
   351    cost scaling.
   352  - \ref CapacityScaling Successive Shortest %Path algorithm with optional
   353    capacity scaling.
   354  - \ref CancelAndTighten The Cancel and Tighten algorithm.
   355  - \ref CycleCanceling Cycle-Canceling algorithms.
   356 
   357 In general NetworkSimplex is the most efficient implementation,
   358 but in special cases other algorithms could be faster.
   359 For example, if the total supply and/or capacities are rather small,
   360 CapacityScaling is usually the fastest algorithm (without effective scaling).
   361 */
   362 
   363 /**
   364 @defgroup min_cut Minimum Cut Algorithms
   365 @ingroup algs
   366 
   367 \brief Algorithms for finding minimum cut in graphs.
   368 
   369 This group contains the algorithms for finding minimum cut in graphs.
   370 
   371 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   372 \f$X\f$ subset of the nodes with minimum overall capacity on
   373 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   374 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   375 cut is the \f$X\f$ solution of the next optimization problem:
   376 
   377 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   378     \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
   379 
   380 LEMON contains several algorithms related to minimum cut problems:
   381 
   382 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   383   in directed graphs.
   384 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   385   calculating minimum cut in undirected graphs.
   386 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   387   all-pairs minimum cut in undirected graphs.
   388 
   389 If you want to find minimum cut just between two distinict nodes,
   390 see the \ref max_flow "maximum flow problem".
   391 */
   392 
   393 /**
   394 @defgroup graph_properties Connectivity and Other Graph Properties
   395 @ingroup algs
   396 \brief Algorithms for discovering the graph properties
   397 
   398 This group contains the algorithms for discovering the graph properties
   399 like connectivity, bipartiteness, euler property, simplicity etc.
   400 
   401 \image html connected_components.png
   402 \image latex connected_components.eps "Connected components" width=\textwidth
   403 */
   404 
   405 /**
   406 @defgroup planar Planarity Embedding and Drawing
   407 @ingroup algs
   408 \brief Algorithms for planarity checking, embedding and drawing
   409 
   410 This group contains the algorithms for planarity checking,
   411 embedding and drawing.
   412 
   413 \image html planar.png
   414 \image latex planar.eps "Plane graph" width=\textwidth
   415 */
   416 
   417 /**
   418 @defgroup matching Matching Algorithms
   419 @ingroup algs
   420 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   421 
   422 This group contains the algorithms for calculating
   423 matchings in graphs and bipartite graphs. The general matching problem is
   424 finding a subset of the edges for which each node has at most one incident
   425 edge.
   426 
   427 There are several different algorithms for calculate matchings in
   428 graphs.  The matching problems in bipartite graphs are generally
   429 easier than in general graphs. The goal of the matching optimization
   430 can be finding maximum cardinality, maximum weight or minimum cost
   431 matching. The search can be constrained to find perfect or
   432 maximum cardinality matching.
   433 
   434 The matching algorithms implemented in LEMON:
   435 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   436   for calculating maximum cardinality matching in bipartite graphs.
   437 - \ref PrBipartiteMatching Push-relabel algorithm
   438   for calculating maximum cardinality matching in bipartite graphs.
   439 - \ref MaxWeightedBipartiteMatching
   440   Successive shortest path algorithm for calculating maximum weighted
   441   matching and maximum weighted bipartite matching in bipartite graphs.
   442 - \ref MinCostMaxBipartiteMatching
   443   Successive shortest path algorithm for calculating minimum cost maximum
   444   matching in bipartite graphs.
   445 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   446   maximum cardinality matching in general graphs.
   447 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   448   maximum weighted matching in general graphs.
   449 - \ref MaxWeightedPerfectMatching
   450   Edmond's blossom shrinking algorithm for calculating maximum weighted
   451   perfect matching in general graphs.
   452 
   453 \image html bipartite_matching.png
   454 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
   455 */
   456 
   457 /**
   458 @defgroup spantree Minimum Spanning Tree Algorithms
   459 @ingroup algs
   460 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   461 
   462 This group contains the algorithms for finding minimum cost spanning
   463 trees and arborescences.
   464 */
   465 
   466 /**
   467 @defgroup auxalg Auxiliary Algorithms
   468 @ingroup algs
   469 \brief Auxiliary algorithms implemented in LEMON.
   470 
   471 This group contains some algorithms implemented in LEMON
   472 in order to make it easier to implement complex algorithms.
   473 */
   474 
   475 /**
   476 @defgroup approx Approximation Algorithms
   477 @ingroup algs
   478 \brief Approximation algorithms.
   479 
   480 This group contains the approximation and heuristic algorithms
   481 implemented in LEMON.
   482 */
   483 
   484 /**
   485 @defgroup gen_opt_group General Optimization Tools
   486 \brief This group contains some general optimization frameworks
   487 implemented in LEMON.
   488 
   489 This group contains some general optimization frameworks
   490 implemented in LEMON.
   491 */
   492 
   493 /**
   494 @defgroup lp_group Lp and Mip Solvers
   495 @ingroup gen_opt_group
   496 \brief Lp and Mip solver interfaces for LEMON.
   497 
   498 This group contains Lp and Mip solver interfaces for LEMON. The
   499 various LP solvers could be used in the same manner with this
   500 interface.
   501 */
   502 
   503 /**
   504 @defgroup lp_utils Tools for Lp and Mip Solvers
   505 @ingroup lp_group
   506 \brief Helper tools to the Lp and Mip solvers.
   507 
   508 This group adds some helper tools to general optimization framework
   509 implemented in LEMON.
   510 */
   511 
   512 /**
   513 @defgroup metah Metaheuristics
   514 @ingroup gen_opt_group
   515 \brief Metaheuristics for LEMON library.
   516 
   517 This group contains some metaheuristic optimization tools.
   518 */
   519 
   520 /**
   521 @defgroup utils Tools and Utilities
   522 \brief Tools and utilities for programming in LEMON
   523 
   524 Tools and utilities for programming in LEMON.
   525 */
   526 
   527 /**
   528 @defgroup gutils Basic Graph Utilities
   529 @ingroup utils
   530 \brief Simple basic graph utilities.
   531 
   532 This group contains some simple basic graph utilities.
   533 */
   534 
   535 /**
   536 @defgroup misc Miscellaneous Tools
   537 @ingroup utils
   538 \brief Tools for development, debugging and testing.
   539 
   540 This group contains several useful tools for development,
   541 debugging and testing.
   542 */
   543 
   544 /**
   545 @defgroup timecount Time Measuring and Counting
   546 @ingroup misc
   547 \brief Simple tools for measuring the performance of algorithms.
   548 
   549 This group contains simple tools for measuring the performance
   550 of algorithms.
   551 */
   552 
   553 /**
   554 @defgroup exceptions Exceptions
   555 @ingroup utils
   556 \brief Exceptions defined in LEMON.
   557 
   558 This group contains the exceptions defined in LEMON.
   559 */
   560 
   561 /**
   562 @defgroup io_group Input-Output
   563 \brief Graph Input-Output methods
   564 
   565 This group contains the tools for importing and exporting graphs
   566 and graph related data. Now it supports the \ref lgf-format
   567 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   568 postscript (EPS) format.
   569 */
   570 
   571 /**
   572 @defgroup lemon_io LEMON Graph Format
   573 @ingroup io_group
   574 \brief Reading and writing LEMON Graph Format.
   575 
   576 This group contains methods for reading and writing
   577 \ref lgf-format "LEMON Graph Format".
   578 */
   579 
   580 /**
   581 @defgroup eps_io Postscript Exporting
   582 @ingroup io_group
   583 \brief General \c EPS drawer and graph exporter
   584 
   585 This group contains general \c EPS drawing methods and special
   586 graph exporting tools.
   587 */
   588 
   589 /**
   590 @defgroup dimacs_group DIMACS format
   591 @ingroup io_group
   592 \brief Read and write files in DIMACS format
   593 
   594 Tools to read a digraph from or write it to a file in DIMACS format data.
   595 */
   596 
   597 /**
   598 @defgroup nauty_group NAUTY Format
   599 @ingroup io_group
   600 \brief Read \e Nauty format
   601 
   602 Tool to read graphs from \e Nauty format data.
   603 */
   604 
   605 /**
   606 @defgroup concept Concepts
   607 \brief Skeleton classes and concept checking classes
   608 
   609 This group contains the data/algorithm skeletons and concept checking
   610 classes implemented in LEMON.
   611 
   612 The purpose of the classes in this group is fourfold.
   613 
   614 - These classes contain the documentations of the %concepts. In order
   615   to avoid document multiplications, an implementation of a concept
   616   simply refers to the corresponding concept class.
   617 
   618 - These classes declare every functions, <tt>typedef</tt>s etc. an
   619   implementation of the %concepts should provide, however completely
   620   without implementations and real data structures behind the
   621   interface. On the other hand they should provide nothing else. All
   622   the algorithms working on a data structure meeting a certain concept
   623   should compile with these classes. (Though it will not run properly,
   624   of course.) In this way it is easily to check if an algorithm
   625   doesn't use any extra feature of a certain implementation.
   626 
   627 - The concept descriptor classes also provide a <em>checker class</em>
   628   that makes it possible to check whether a certain implementation of a
   629   concept indeed provides all the required features.
   630 
   631 - Finally, They can serve as a skeleton of a new implementation of a concept.
   632 */
   633 
   634 /**
   635 @defgroup graph_concepts Graph Structure Concepts
   636 @ingroup concept
   637 \brief Skeleton and concept checking classes for graph structures
   638 
   639 This group contains the skeletons and concept checking classes of LEMON's
   640 graph structures and helper classes used to implement these.
   641 */
   642 
   643 /**
   644 @defgroup map_concepts Map Concepts
   645 @ingroup concept
   646 \brief Skeleton and concept checking classes for maps
   647 
   648 This group contains the skeletons and concept checking classes of maps.
   649 */
   650 
   651 /**
   652 \anchor demoprograms
   653 
   654 @defgroup demos Demo Programs
   655 
   656 Some demo programs are listed here. Their full source codes can be found in
   657 the \c demo subdirectory of the source tree.
   658 
   659 In order to compile them, use the <tt>make demo</tt> or the
   660 <tt>make check</tt> commands.
   661 */
   662 
   663 /**
   664 @defgroup tools Standalone Utility Applications
   665 
   666 Some utility applications are listed here.
   667 
   668 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   669 them, as well.
   670 */
   671 
   672 }