author Peter Kovacs <>
Thu, 07 May 2009 02:05:12 +0200
changeset 843 189760a7cdd0
parent 687 6c408d864fa1
child 844 c01a98ce01fd
permissions -rw-r--r--
Remove references of missing tools (#257)
     1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
     2  *
     3  * This file is a part of LEMON, a generic C++ optimization library.
     4  *
     5  * Copyright (C) 2003-2009
     6  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
     7  * (Egervary Research Group on Combinatorial Optimization, EGRES).
     8  *
     9  * Permission to use, modify and distribute this software is granted
    10  * provided that this copyright notice appears in all copies. For
    11  * precise terms see the accompanying LICENSE file.
    12  *
    13  * This software is provided "AS IS" with no warranty of any kind,
    14  * express or implied, and with no claim as to its suitability for any
    15  * purpose.
    16  *
    17  */
    19 namespace lemon {
    21 /**
    22 @defgroup datas Data Structures
    23 This group contains the several data structures implemented in LEMON.
    24 */
    26 /**
    27 @defgroup graphs Graph Structures
    28 @ingroup datas
    29 \brief Graph structures implemented in LEMON.
    31 The implementation of combinatorial algorithms heavily relies on
    32 efficient graph implementations. LEMON offers data structures which are
    33 planned to be easily used in an experimental phase of implementation studies,
    34 and thereafter the program code can be made efficient by small modifications.
    36 The most efficient implementation of diverse applications require the
    37 usage of different physical graph implementations. These differences
    38 appear in the size of graph we require to handle, memory or time usage
    39 limitations or in the set of operations through which the graph can be
    40 accessed.  LEMON provides several physical graph structures to meet
    41 the diverging requirements of the possible users.  In order to save on
    42 running time or on memory usage, some structures may fail to provide
    43 some graph features like arc/edge or node deletion.
    45 Alteration of standard containers need a very limited number of
    46 operations, these together satisfy the everyday requirements.
    47 In the case of graph structures, different operations are needed which do
    48 not alter the physical graph, but gives another view. If some nodes or
    49 arcs have to be hidden or the reverse oriented graph have to be used, then
    50 this is the case. It also may happen that in a flow implementation
    51 the residual graph can be accessed by another algorithm, or a node-set
    52 is to be shrunk for another algorithm.
    53 LEMON also provides a variety of graphs for these requirements called
    54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
    55 in conjunction with other graph representations.
    57 You are free to use the graph structure that fit your requirements
    58 the best, most graph algorithms and auxiliary data structures can be used
    59 with any graph structure.
    61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
    62 */
    64 /**
    65 @defgroup graph_adaptors Adaptor Classes for Graphs
    66 @ingroup graphs
    67 \brief Adaptor classes for digraphs and graphs
    69 This group contains several useful adaptor classes for digraphs and graphs.
    71 The main parts of LEMON are the different graph structures, generic
    72 graph algorithms, graph concepts, which couple them, and graph
    73 adaptors. While the previous notions are more or less clear, the
    74 latter one needs further explanation. Graph adaptors are graph classes
    75 which serve for considering graph structures in different ways.
    77 A short example makes this much clearer.  Suppose that we have an
    78 instance \c g of a directed graph type, say ListDigraph and an algorithm
    79 \code
    80 template <typename Digraph>
    81 int algorithm(const Digraph&);
    82 \endcode
    83 is needed to run on the reverse oriented graph.  It may be expensive
    84 (in time or in memory usage) to copy \c g with the reversed
    85 arcs.  In this case, an adaptor class is used, which (according
    86 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
    87 The adaptor uses the original digraph structure and digraph operations when
    88 methods of the reversed oriented graph are called.  This means that the adaptor
    89 have minor memory usage, and do not perform sophisticated algorithmic
    90 actions.  The purpose of it is to give a tool for the cases when a
    91 graph have to be used in a specific alteration.  If this alteration is
    92 obtained by a usual construction like filtering the node or the arc set or
    93 considering a new orientation, then an adaptor is worthwhile to use.
    94 To come back to the reverse oriented graph, in this situation
    95 \code
    96 template<typename Digraph> class ReverseDigraph;
    97 \endcode
    98 template class can be used. The code looks as follows
    99 \code
   100 ListDigraph g;
   101 ReverseDigraph<ListDigraph> rg(g);
   102 int result = algorithm(rg);
   103 \endcode
   104 During running the algorithm, the original digraph \c g is untouched.
   105 This techniques give rise to an elegant code, and based on stable
   106 graph adaptors, complex algorithms can be implemented easily.
   108 In flow, circulation and matching problems, the residual
   109 graph is of particular importance. Combining an adaptor implementing
   110 this with shortest path algorithms or minimum mean cycle algorithms,
   111 a range of weighted and cardinality optimization algorithms can be
   112 obtained. For other examples, the interested user is referred to the
   113 detailed documentation of particular adaptors.
   115 The behavior of graph adaptors can be very different. Some of them keep
   116 capabilities of the original graph while in other cases this would be
   117 meaningless. This means that the concepts that they meet depend
   118 on the graph adaptor, and the wrapped graph.
   119 For example, if an arc of a reversed digraph is deleted, this is carried
   120 out by deleting the corresponding arc of the original digraph, thus the
   121 adaptor modifies the original digraph.
   122 However in case of a residual digraph, this operation has no sense.
   124 Let us stand one more example here to simplify your work.
   125 ReverseDigraph has constructor
   126 \code
   127 ReverseDigraph(Digraph& digraph);
   128 \endcode
   129 This means that in a situation, when a <tt>const %ListDigraph&</tt>
   130 reference to a graph is given, then it have to be instantiated with
   131 <tt>Digraph=const %ListDigraph</tt>.
   132 \code
   133 int algorithm1(const ListDigraph& g) {
   134   ReverseDigraph<const ListDigraph> rg(g);
   135   return algorithm2(rg);
   136 }
   137 \endcode
   138 */
   140 /**
   141 @defgroup semi_adaptors Semi-Adaptor Classes for Graphs
   142 @ingroup graphs
   143 \brief Graph types between real graphs and graph adaptors.
   145 This group contains some graph types between real graphs and graph adaptors.
   146 These classes wrap graphs to give new functionality as the adaptors do it.
   147 On the other hand they are not light-weight structures as the adaptors.
   148 */
   150 /**
   151 @defgroup maps Maps
   152 @ingroup datas
   153 \brief Map structures implemented in LEMON.
   155 This group contains the map structures implemented in LEMON.
   157 LEMON provides several special purpose maps and map adaptors that e.g. combine
   158 new maps from existing ones.
   160 <b>See also:</b> \ref map_concepts "Map Concepts".
   161 */
   163 /**
   164 @defgroup graph_maps Graph Maps
   165 @ingroup maps
   166 \brief Special graph-related maps.
   168 This group contains maps that are specifically designed to assign
   169 values to the nodes and arcs/edges of graphs.
   171 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
   172 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
   173 */
   175 /**
   176 \defgroup map_adaptors Map Adaptors
   177 \ingroup maps
   178 \brief Tools to create new maps from existing ones
   180 This group contains map adaptors that are used to create "implicit"
   181 maps from other maps.
   183 Most of them are \ref concepts::ReadMap "read-only maps".
   184 They can make arithmetic and logical operations between one or two maps
   185 (negation, shifting, addition, multiplication, logical 'and', 'or',
   186 'not' etc.) or e.g. convert a map to another one of different Value type.
   188 The typical usage of this classes is passing implicit maps to
   189 algorithms.  If a function type algorithm is called then the function
   190 type map adaptors can be used comfortable. For example let's see the
   191 usage of map adaptors with the \c graphToEps() function.
   192 \code
   193   Color nodeColor(int deg) {
   194     if (deg >= 2) {
   195       return Color(0.5, 0.0, 0.5);
   196     } else if (deg == 1) {
   197       return Color(1.0, 0.5, 1.0);
   198     } else {
   199       return Color(0.0, 0.0, 0.0);
   200     }
   201   }
   203   Digraph::NodeMap<int> degree_map(graph);
   205   graphToEps(graph, "graph.eps")
   206     .coords(coords).scaleToA4().undirected()
   207     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
   208     .run();
   209 \endcode
   210 The \c functorToMap() function makes an \c int to \c Color map from the
   211 \c nodeColor() function. The \c composeMap() compose the \c degree_map
   212 and the previously created map. The composed map is a proper function to
   213 get the color of each node.
   215 The usage with class type algorithms is little bit harder. In this
   216 case the function type map adaptors can not be used, because the
   217 function map adaptors give back temporary objects.
   218 \code
   219   Digraph graph;
   221   typedef Digraph::ArcMap<double> DoubleArcMap;
   222   DoubleArcMap length(graph);
   223   DoubleArcMap speed(graph);
   225   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
   226   TimeMap time(length, speed);
   228   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
   229, target);
   230 \endcode
   231 We have a length map and a maximum speed map on the arcs of a digraph.
   232 The minimum time to pass the arc can be calculated as the division of
   233 the two maps which can be done implicitly with the \c DivMap template
   234 class. We use the implicit minimum time map as the length map of the
   235 \c Dijkstra algorithm.
   236 */
   238 /**
   239 @defgroup paths Path Structures
   240 @ingroup datas
   241 \brief %Path structures implemented in LEMON.
   243 This group contains the path structures implemented in LEMON.
   245 LEMON provides flexible data structures to work with paths.
   246 All of them have similar interfaces and they can be copied easily with
   247 assignment operators and copy constructors. This makes it easy and
   248 efficient to have e.g. the Dijkstra algorithm to store its result in
   249 any kind of path structure.
   251 \sa lemon::concepts::Path
   252 */
   254 /**
   255 @defgroup auxdat Auxiliary Data Structures
   256 @ingroup datas
   257 \brief Auxiliary data structures implemented in LEMON.
   259 This group contains some data structures implemented in LEMON in
   260 order to make it easier to implement combinatorial algorithms.
   261 */
   263 /**
   264 @defgroup algs Algorithms
   265 \brief This group contains the several algorithms
   266 implemented in LEMON.
   268 This group contains the several algorithms
   269 implemented in LEMON.
   270 */
   272 /**
   273 @defgroup search Graph Search
   274 @ingroup algs
   275 \brief Common graph search algorithms.
   277 This group contains the common graph search algorithms, namely
   278 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
   279 */
   281 /**
   282 @defgroup shortest_path Shortest Path Algorithms
   283 @ingroup algs
   284 \brief Algorithms for finding shortest paths.
   286 This group contains the algorithms for finding shortest paths in digraphs.
   288  - \ref Dijkstra Dijkstra's algorithm for finding shortest paths from a 
   289    source node when all arc lengths are non-negative.
   290  - \ref Suurballe A successive shortest path algorithm for finding
   291    arc-disjoint paths between two nodes having minimum total length.
   292 */
   294 /**
   295 @defgroup max_flow Maximum Flow Algorithms
   296 @ingroup algs
   297 \brief Algorithms for finding maximum flows.
   299 This group contains the algorithms for finding maximum flows and
   300 feasible circulations.
   302 The \e maximum \e flow \e problem is to find a flow of maximum value between
   303 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   304 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   305 \f$s, t \in V\f$ source and target nodes.
   306 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   307 following optimization problem.
   309 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   310 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   311     \quad \forall u\in V\setminus\{s,t\} \f]
   312 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   314 \ref Preflow implements the preflow push-relabel algorithm of Goldberg and
   315 Tarjan for solving this problem. It also provides functions to query the
   316 minimum cut, which is the dual problem of maximum flow.
   318 \ref Circulation is a preflow push-relabel algorithm implemented directly 
   319 for finding feasible circulations, which is a somewhat different problem,
   320 but it is strongly related to maximum flow.
   321 For more information, see \ref Circulation.
   322 */
   324 /**
   325 @defgroup min_cost_flow Minimum Cost Flow Algorithms
   326 @ingroup algs
   328 \brief Algorithms for finding minimum cost flows and circulations.
   330 This group contains the algorithms for finding minimum cost flows and
   331 circulations.
   333 The \e minimum \e cost \e flow \e problem is to find a feasible flow of
   334 minimum total cost from a set of supply nodes to a set of demand nodes
   335 in a network with capacity constraints (lower and upper bounds)
   336 and arc costs.
   337 Formally, let \f$G=(V,A)\f$ be a digraph, \f$lower: A\rightarrow\mathbf{Z}\f$,
   338 \f$upper: A\rightarrow\mathbf{Z}\cup\{+\infty\}\f$ denote the lower and
   339 upper bounds for the flow values on the arcs, for which
   340 \f$lower(uv) \leq upper(uv)\f$ must hold for all \f$uv\in A\f$,
   341 \f$cost: A\rightarrow\mathbf{Z}\f$ denotes the cost per unit flow
   342 on the arcs and \f$sup: V\rightarrow\mathbf{Z}\f$ denotes the
   343 signed supply values of the nodes.
   344 If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$
   345 supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with
   346 \f$-sup(u)\f$ demand.
   347 A minimum cost flow is an \f$f: A\rightarrow\mathbf{Z}\f$ solution
   348 of the following optimization problem.
   350 \f[ \min\sum_{uv\in A} f(uv) \cdot cost(uv) \f]
   351 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq
   352     sup(u) \quad \forall u\in V \f]
   353 \f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]
   355 The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be
   356 zero or negative in order to have a feasible solution (since the sum
   357 of the expressions on the left-hand side of the inequalities is zero).
   358 It means that the total demand must be greater or equal to the total
   359 supply and all the supplies have to be carried out from the supply nodes,
   360 but there could be demands that are not satisfied.
   361 If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand
   362 constraints have to be satisfied with equality, i.e. all demands
   363 have to be satisfied and all supplies have to be used.
   365 If you need the opposite inequalities in the supply/demand constraints
   366 (i.e. the total demand is less than the total supply and all the demands
   367 have to be satisfied while there could be supplies that are not used),
   368 then you could easily transform the problem to the above form by reversing
   369 the direction of the arcs and taking the negative of the supply values
   370 (e.g. using \ref ReverseDigraph and \ref NegMap adaptors).
   371 However \ref NetworkSimplex algorithm also supports this form directly
   372 for the sake of convenience.
   374 A feasible solution for this problem can be found using \ref Circulation.
   376 Note that the above formulation is actually more general than the usual
   377 definition of the minimum cost flow problem, in which strict equalities
   378 are required in the supply/demand contraints, i.e.
   380 \f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =
   381     sup(u) \quad \forall u\in V. \f]
   383 However if the sum of the supply values is zero, then these two problems
   384 are equivalent. So if you need the equality form, you have to ensure this
   385 additional contraint for the algorithms.
   387 The dual solution of the minimum cost flow problem is represented by node 
   388 potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.
   389 An \f$f: A\rightarrow\mathbf{Z}\f$ feasible solution of the problem
   390 is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$
   391 node potentials the following \e complementary \e slackness optimality
   392 conditions hold.
   394  - For all \f$uv\in A\f$ arcs:
   395    - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;
   396    - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;
   397    - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.
   398  - For all \f$u\in V\f$ nodes:
   399    - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,
   400      then \f$\pi(u)=0\f$.
   402 Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc
   403 \f$uv\in A\f$ with respect to the potential function \f$\pi\f$, i.e.
   404 \f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]
   406 \ref NetworkSimplex is an efficient implementation of the primal Network
   407 Simplex algorithm for finding minimum cost flows. It also provides dual
   408 solution (node potentials), if an optimal flow is found.
   409 */
   411 /**
   412 @defgroup min_cut Minimum Cut Algorithms
   413 @ingroup algs
   415 \brief Algorithms for finding minimum cut in graphs.
   417 This group contains the algorithms for finding minimum cut in graphs.
   419 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   420 \f$X\f$ subset of the nodes with minimum overall capacity on
   421 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   422 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   423 cut is the \f$X\f$ solution of the next optimization problem:
   425 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   426     \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
   428 LEMON contains several algorithms related to minimum cut problems:
   430 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   431   in directed graphs.
   432 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   433   all-pairs minimum cut in undirected graphs.
   435 If you want to find minimum cut just between two distinict nodes,
   436 see the \ref max_flow "maximum flow problem".
   437 */
   439 /**
   440 @defgroup graph_properties Connectivity and Other Graph Properties
   441 @ingroup algs
   442 \brief Algorithms for discovering the graph properties
   444 This group contains the algorithms for discovering the graph properties
   445 like connectivity, bipartiteness, euler property, simplicity etc.
   447 \image html edge_biconnected_components.png
   448 \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
   449 */
   451 /**
   452 @defgroup matching Matching Algorithms
   453 @ingroup algs
   454 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   456 This group contains the algorithms for calculating matchings in graphs.
   457 The general matching problem is finding a subset of the edges for which
   458 each node has at most one incident edge.
   460 There are several different algorithms for calculate matchings in
   461 graphs. The goal of the matching optimization
   462 can be finding maximum cardinality, maximum weight or minimum cost
   463 matching. The search can be constrained to find perfect or
   464 maximum cardinality matching.
   466 The matching algorithms implemented in LEMON:
   467 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   468   maximum cardinality matching in general graphs.
   469 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   470   maximum weighted matching in general graphs.
   471 - \ref MaxWeightedPerfectMatching
   472   Edmond's blossom shrinking algorithm for calculating maximum weighted
   473   perfect matching in general graphs.
   475 \image html bipartite_matching.png
   476 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
   477 */
   479 /**
   480 @defgroup spantree Minimum Spanning Tree Algorithms
   481 @ingroup algs
   482 \brief Algorithms for finding a minimum cost spanning tree in a graph.
   484 This group contains the algorithms for finding a minimum cost spanning
   485 tree in a graph.
   486 */
   488 /**
   489 @defgroup auxalg Auxiliary Algorithms
   490 @ingroup algs
   491 \brief Auxiliary algorithms implemented in LEMON.
   493 This group contains some algorithms implemented in LEMON
   494 in order to make it easier to implement complex algorithms.
   495 */
   497 /**
   498 @defgroup gen_opt_group General Optimization Tools
   499 \brief This group contains some general optimization frameworks
   500 implemented in LEMON.
   502 This group contains some general optimization frameworks
   503 implemented in LEMON.
   504 */
   506 /**
   507 @defgroup lp_group Lp and Mip Solvers
   508 @ingroup gen_opt_group
   509 \brief Lp and Mip solver interfaces for LEMON.
   511 This group contains Lp and Mip solver interfaces for LEMON. The
   512 various LP solvers could be used in the same manner with this
   513 interface.
   514 */
   516 /**
   517 @defgroup utils Tools and Utilities
   518 \brief Tools and utilities for programming in LEMON
   520 Tools and utilities for programming in LEMON.
   521 */
   523 /**
   524 @defgroup gutils Basic Graph Utilities
   525 @ingroup utils
   526 \brief Simple basic graph utilities.
   528 This group contains some simple basic graph utilities.
   529 */
   531 /**
   532 @defgroup misc Miscellaneous Tools
   533 @ingroup utils
   534 \brief Tools for development, debugging and testing.
   536 This group contains several useful tools for development,
   537 debugging and testing.
   538 */
   540 /**
   541 @defgroup timecount Time Measuring and Counting
   542 @ingroup misc
   543 \brief Simple tools for measuring the performance of algorithms.
   545 This group contains simple tools for measuring the performance
   546 of algorithms.
   547 */
   549 /**
   550 @defgroup exceptions Exceptions
   551 @ingroup utils
   552 \brief Exceptions defined in LEMON.
   554 This group contains the exceptions defined in LEMON.
   555 */
   557 /**
   558 @defgroup io_group Input-Output
   559 \brief Graph Input-Output methods
   561 This group contains the tools for importing and exporting graphs
   562 and graph related data. Now it supports the \ref lgf-format
   563 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   564 postscript (EPS) format.
   565 */
   567 /**
   568 @defgroup lemon_io LEMON Graph Format
   569 @ingroup io_group
   570 \brief Reading and writing LEMON Graph Format.
   572 This group contains methods for reading and writing
   573 \ref lgf-format "LEMON Graph Format".
   574 */
   576 /**
   577 @defgroup eps_io Postscript Exporting
   578 @ingroup io_group
   579 \brief General \c EPS drawer and graph exporter
   581 This group contains general \c EPS drawing methods and special
   582 graph exporting tools.
   583 */
   585 /**
   586 @defgroup dimacs_group DIMACS format
   587 @ingroup io_group
   588 \brief Read and write files in DIMACS format
   590 Tools to read a digraph from or write it to a file in DIMACS format data.
   591 */
   593 /**
   594 @defgroup nauty_group NAUTY Format
   595 @ingroup io_group
   596 \brief Read \e Nauty format
   598 Tool to read graphs from \e Nauty format data.
   599 */
   601 /**
   602 @defgroup concept Concepts
   603 \brief Skeleton classes and concept checking classes
   605 This group contains the data/algorithm skeletons and concept checking
   606 classes implemented in LEMON.
   608 The purpose of the classes in this group is fourfold.
   610 - These classes contain the documentations of the %concepts. In order
   611   to avoid document multiplications, an implementation of a concept
   612   simply refers to the corresponding concept class.
   614 - These classes declare every functions, <tt>typedef</tt>s etc. an
   615   implementation of the %concepts should provide, however completely
   616   without implementations and real data structures behind the
   617   interface. On the other hand they should provide nothing else. All
   618   the algorithms working on a data structure meeting a certain concept
   619   should compile with these classes. (Though it will not run properly,
   620   of course.) In this way it is easily to check if an algorithm
   621   doesn't use any extra feature of a certain implementation.
   623 - The concept descriptor classes also provide a <em>checker class</em>
   624   that makes it possible to check whether a certain implementation of a
   625   concept indeed provides all the required features.
   627 - Finally, They can serve as a skeleton of a new implementation of a concept.
   628 */
   630 /**
   631 @defgroup graph_concepts Graph Structure Concepts
   632 @ingroup concept
   633 \brief Skeleton and concept checking classes for graph structures
   635 This group contains the skeletons and concept checking classes of LEMON's
   636 graph structures and helper classes used to implement these.
   637 */
   639 /**
   640 @defgroup map_concepts Map Concepts
   641 @ingroup concept
   642 \brief Skeleton and concept checking classes for maps
   644 This group contains the skeletons and concept checking classes of maps.
   645 */
   647 /**
   648 \anchor demoprograms
   650 @defgroup demos Demo Programs
   652 Some demo programs are listed here. Their full source codes can be found in
   653 the \c demo subdirectory of the source tree.
   655 In order to compile them, use the <tt>make demo</tt> or the
   656 <tt>make check</tt> commands.
   657 */
   659 /**
   660 @defgroup tools Standalone Utility Applications
   662 Some utility applications are listed here.
   664 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   665 them, as well.
   666 */
   668 }