doc/groups.dox
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 09 Jan 2011 15:06:55 +0100
changeset 1204 dff32ce3db71
parent 1202 ef200e268af2
child 1206 a2d142bb5d3c
permissions -rw-r--r--
Make InsertionTsp much faster and improve docs (#386)
     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) 2003-2010
     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 paths Path Structures
   230 @ingroup datas
   231 \brief %Path structures implemented in LEMON.
   232 
   233 This group contains the path structures implemented in LEMON.
   234 
   235 LEMON provides flexible data structures to work with paths.
   236 All of them have similar interfaces and they can be copied easily with
   237 assignment operators and copy constructors. This makes it easy and
   238 efficient to have e.g. the Dijkstra algorithm to store its result in
   239 any kind of path structure.
   240 
   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 
   249 This group contains the heap structures implemented in LEMON.
   250 
   251 LEMON provides several heap classes. They are efficient implementations
   252 of the abstract data type \e priority \e queue. They store items with
   253 specified values called \e priorities in such a way that finding and
   254 removing the item with minimum priority are efficient.
   255 The basic operations are adding and erasing items, changing the priority
   256 of an item, etc.
   257 
   258 Heaps are crucial in several algorithms, such as Dijkstra and Prim.
   259 The heap implementations have the same interface, thus any of them can be
   260 used easily in such algorithms.
   261 
   262 \sa \ref concepts::Heap "Heap concept"
   263 */
   264 
   265 /**
   266 @defgroup auxdat Auxiliary Data Structures
   267 @ingroup datas
   268 \brief Auxiliary data structures implemented in LEMON.
   269 
   270 This group contains some data structures implemented in LEMON in
   271 order to make it easier to implement combinatorial algorithms.
   272 */
   273 
   274 /**
   275 @defgroup geomdat Geometric Data Structures
   276 @ingroup auxdat
   277 \brief Geometric data structures implemented in LEMON.
   278 
   279 This 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 /**
   289 @defgroup matrices Matrices
   290 @ingroup auxdat
   291 \brief Two dimensional data storages implemented in LEMON.
   292 
   293 This group contains two dimensional data storages implemented in LEMON.
   294 */
   295 
   296 /**
   297 @defgroup algs Algorithms
   298 \brief This group contains the several algorithms
   299 implemented in LEMON.
   300 
   301 This group contains the several algorithms
   302 implemented in LEMON.
   303 */
   304 
   305 /**
   306 @defgroup search Graph Search
   307 @ingroup algs
   308 \brief Common graph search algorithms.
   309 
   310 This group contains the common graph search algorithms, namely
   311 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
   312 \ref clrs01algorithms.
   313 */
   314 
   315 /**
   316 @defgroup shortest_path Shortest Path Algorithms
   317 @ingroup algs
   318 \brief Algorithms for finding shortest paths.
   319 
   320 This group contains the algorithms for finding shortest paths in digraphs
   321 \ref clrs01algorithms.
   322 
   323  - \ref Dijkstra algorithm for finding shortest paths from a source node
   324    when all arc lengths are non-negative.
   325  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   326    from a source node when arc lenghts can be either positive or negative,
   327    but the digraph should not contain directed cycles with negative total
   328    length.
   329  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   330    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   331    lenghts can be either positive or negative, but the digraph should
   332    not contain directed cycles with negative total length.
   333  - \ref Suurballe A successive shortest path algorithm for finding
   334    arc-disjoint paths between two nodes having minimum total length.
   335 */
   336 
   337 /**
   338 @defgroup spantree Minimum Spanning Tree Algorithms
   339 @ingroup algs
   340 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   341 
   342 This group contains the algorithms for finding minimum cost spanning
   343 trees and arborescences \ref clrs01algorithms.
   344 */
   345 
   346 /**
   347 @defgroup max_flow Maximum Flow Algorithms
   348 @ingroup algs
   349 \brief Algorithms for finding maximum flows.
   350 
   351 This group contains the algorithms for finding maximum flows and
   352 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
   353 
   354 The \e maximum \e flow \e problem is to find a flow of maximum value between
   355 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   356 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   357 \f$s, t \in V\f$ source and target nodes.
   358 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   359 following optimization problem.
   360 
   361 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   362 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   363     \quad \forall u\in V\setminus\{s,t\} \f]
   364 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   365 
   366 LEMON contains several algorithms for solving maximum flow problems:
   367 - \ref EdmondsKarp Edmonds-Karp algorithm
   368   \ref edmondskarp72theoretical.
   369 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
   370   \ref goldberg88newapproach.
   371 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
   372   \ref dinic70algorithm, \ref sleator83dynamic.
   373 - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
   374   \ref goldberg88newapproach, \ref sleator83dynamic.
   375 
   376 In most cases the \ref Preflow algorithm provides the
   377 fastest method for computing a maximum flow. All implementations
   378 also provide functions to query the minimum cut, which is the dual
   379 problem of maximum flow.
   380 
   381 \ref Circulation is a preflow push-relabel algorithm implemented directly
   382 for finding feasible circulations, which is a somewhat different problem,
   383 but it is strongly related to maximum flow.
   384 For more information, see \ref Circulation.
   385 */
   386 
   387 /**
   388 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
   389 @ingroup algs
   390 
   391 \brief Algorithms for finding minimum cost flows and circulations.
   392 
   393 This group contains the algorithms for finding minimum cost flows and
   394 circulations \ref amo93networkflows. For more information about this
   395 problem and its dual solution, see \ref min_cost_flow
   396 "Minimum Cost Flow Problem".
   397 
   398 LEMON contains several algorithms for this problem.
   399  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   400    pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
   401  - \ref CostScaling Cost Scaling algorithm based on push/augment and
   402    relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
   403    \ref bunnagel98efficient.
   404  - \ref CapacityScaling Capacity Scaling algorithm based on the successive
   405    shortest path method \ref edmondskarp72theoretical.
   406  - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
   407    strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
   408 
   409 In general NetworkSimplex is the most efficient implementation,
   410 but in special cases other algorithms could be faster.
   411 For example, if the total supply and/or capacities are rather small,
   412 CapacityScaling is usually the fastest algorithm (without effective scaling).
   413 */
   414 
   415 /**
   416 @defgroup min_cut Minimum Cut Algorithms
   417 @ingroup algs
   418 
   419 \brief Algorithms for finding minimum cut in graphs.
   420 
   421 This group contains the algorithms for finding minimum cut in graphs.
   422 
   423 The \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
   425 outgoing 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
   427 cut is the \f$X\f$ solution of the next optimization problem:
   428 
   429 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   430     \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
   431 
   432 LEMON contains several algorithms related to minimum cut problems:
   433 
   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.
   440 
   441 If you want to find minimum cut just between two distinict nodes,
   442 see the \ref max_flow "maximum flow problem".
   443 */
   444 
   445 /**
   446 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
   447 @ingroup algs
   448 \brief Algorithms for finding minimum mean cycles.
   449 
   450 This group contains the algorithms for finding minimum mean cycles
   451 \ref clrs01algorithms, \ref amo93networkflows.
   452 
   453 The \e minimum \e mean \e cycle \e problem is to find a directed cycle
   454 of minimum mean length (cost) in a digraph.
   455 The mean length of a cycle is the average length of its arcs, i.e. the
   456 ratio between the total length of the cycle and the number of arcs on it.
   457 
   458 This problem has an important connection to \e conservative \e length
   459 \e functions, too. A length function on the arcs of a digraph is called
   460 conservative if and only if there is no directed cycle of negative total
   461 length. For an arbitrary length function, the negative of the minimum
   462 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
   463 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
   464 function.
   465 
   466 LEMON contains three algorithms for solving the minimum mean cycle problem:
   467 - \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
   468   \ref dasdan98minmeancycle.
   469 - \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
   470   version of Karp's algorithm \ref dasdan98minmeancycle.
   471 - \ref HowardMmc Howard's policy iteration algorithm
   472   \ref dasdan98minmeancycle.
   473 
   474 In practice, the \ref HowardMmc "Howard" algorithm proved to be by far the
   475 most efficient one, though the best known theoretical bound on its running
   476 time is exponential.
   477 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
   478 run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
   479 typically faster due to the applied early termination scheme.
   480 */
   481 
   482 /**
   483 @defgroup matching Matching Algorithms
   484 @ingroup algs
   485 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   486 
   487 This group contains the algorithms for calculating
   488 matchings in graphs and bipartite graphs. The general matching problem is
   489 finding a subset of the edges for which each node has at most one incident
   490 edge.
   491 
   492 There are several different algorithms for calculate matchings in
   493 graphs.  The matching problems in bipartite graphs are generally
   494 easier than in general graphs. The goal of the matching optimization
   495 can be finding maximum cardinality, maximum weight or minimum cost
   496 matching. The search can be constrained to find perfect or
   497 maximum cardinality matching.
   498 
   499 The matching algorithms implemented in LEMON:
   500 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   501   for calculating maximum cardinality matching in bipartite graphs.
   502 - \ref PrBipartiteMatching Push-relabel algorithm
   503   for calculating maximum cardinality matching in bipartite graphs.
   504 - \ref MaxWeightedBipartiteMatching
   505   Successive shortest path algorithm for calculating maximum weighted
   506   matching and maximum weighted bipartite matching in bipartite graphs.
   507 - \ref MinCostMaxBipartiteMatching
   508   Successive shortest path algorithm for calculating minimum cost maximum
   509   matching in bipartite graphs.
   510 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   511   maximum cardinality matching in general graphs.
   512 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   513   maximum weighted matching in general graphs.
   514 - \ref MaxWeightedPerfectMatching
   515   Edmond's blossom shrinking algorithm for calculating maximum weighted
   516   perfect matching in general graphs.
   517 - \ref MaxFractionalMatching Push-relabel algorithm for calculating
   518   maximum cardinality fractional matching in general graphs.
   519 - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
   520   maximum weighted fractional matching in general graphs.
   521 - \ref MaxWeightedPerfectFractionalMatching
   522   Augmenting path algorithm for calculating maximum weighted
   523   perfect fractional matching in general graphs.
   524 
   525 \image html matching.png
   526 \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
   527 */
   528 
   529 /**
   530 @defgroup graph_properties Connectivity and Other Graph Properties
   531 @ingroup algs
   532 \brief Algorithms for discovering the graph properties
   533 
   534 This group contains the algorithms for discovering the graph properties
   535 like connectivity, bipartiteness, euler property, simplicity etc.
   536 
   537 \image html connected_components.png
   538 \image latex connected_components.eps "Connected components" width=\textwidth
   539 */
   540 
   541 /**
   542 @defgroup planar Planarity Embedding and Drawing
   543 @ingroup algs
   544 \brief Algorithms for planarity checking, embedding and drawing
   545 
   546 This group contains the algorithms for planarity checking,
   547 embedding and drawing.
   548 
   549 \image html planar.png
   550 \image latex planar.eps "Plane graph" width=\textwidth
   551 */
   552  
   553 /**
   554 @defgroup tsp Traveling Salesman Problem
   555 @ingroup algs
   556 \brief Algorithms for the symmetric traveling salesman problem
   557 
   558 This group contains basic heuristic algorithms for the the symmetric
   559 \e traveling \e salesman \e problem (TSP).
   560 Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
   561 the problem is to find a shortest possible tour that visits each node exactly
   562 once (i.e. the minimum cost Hamiltonian cycle).
   563 
   564 These TSP algorithms are intended to be used with a \e metric \e cost
   565 \e function, i.e. the edge costs should satisfy the triangle inequality.
   566 Otherwise the algorithms could yield worse results.
   567 
   568 LEMON provides five well-known heuristics for solving symmetric TSP:
   569  - \ref NearestNeighborTsp Neareast neighbor algorithm
   570  - \ref GreedyTsp Greedy algorithm
   571  - \ref InsertionTsp Insertion heuristic (with four selection methods)
   572  - \ref ChristofidesTsp Christofides algorithm
   573  - \ref Opt2Tsp 2-opt algorithm
   574 
   575 \ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
   576 solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
   577 
   578 \ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
   579 approximation factor: 3/2.
   580 
   581 \ref Opt2Tsp usually provides the best results in practice, but
   582 it is the slowest method. It can also be used to improve given tours,
   583 for example, the results of other algorithms.
   584 
   585 \image html tsp.png
   586 \image latex tsp.eps "Traveling salesman problem" width=\textwidth
   587 */
   588 
   589 /**
   590 @defgroup approx_algs Approximation Algorithms
   591 @ingroup algs
   592 \brief Approximation algorithms.
   593 
   594 This group contains the approximation and heuristic algorithms
   595 implemented in LEMON.
   596 
   597 <b>Maximum Clique Problem</b>
   598   - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
   599     Grosso, Locatelli, and Pullan.
   600 */
   601 
   602 /**
   603 @defgroup auxalg Auxiliary Algorithms
   604 @ingroup algs
   605 \brief Auxiliary algorithms implemented in LEMON.
   606 
   607 This group contains some algorithms implemented in LEMON
   608 in order to make it easier to implement complex algorithms.
   609 */
   610 
   611 /**
   612 @defgroup gen_opt_group General Optimization Tools
   613 \brief This group contains some general optimization frameworks
   614 implemented in LEMON.
   615 
   616 This group contains some general optimization frameworks
   617 implemented in LEMON.
   618 */
   619 
   620 /**
   621 @defgroup lp_group LP and MIP Solvers
   622 @ingroup gen_opt_group
   623 \brief LP and MIP solver interfaces for LEMON.
   624 
   625 This group contains LP and MIP solver interfaces for LEMON.
   626 Various LP solvers could be used in the same manner with this
   627 high-level interface.
   628 
   629 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
   630 \ref cplex, \ref soplex.
   631 */
   632 
   633 /**
   634 @defgroup lp_utils Tools for Lp and Mip Solvers
   635 @ingroup lp_group
   636 \brief Helper tools to the Lp and Mip solvers.
   637 
   638 This group adds some helper tools to general optimization framework
   639 implemented in LEMON.
   640 */
   641 
   642 /**
   643 @defgroup metah Metaheuristics
   644 @ingroup gen_opt_group
   645 \brief Metaheuristics for LEMON library.
   646 
   647 This group contains some metaheuristic optimization tools.
   648 */
   649 
   650 /**
   651 @defgroup utils Tools and Utilities
   652 \brief Tools and utilities for programming in LEMON
   653 
   654 Tools and utilities for programming in LEMON.
   655 */
   656 
   657 /**
   658 @defgroup gutils Basic Graph Utilities
   659 @ingroup utils
   660 \brief Simple basic graph utilities.
   661 
   662 This group contains some simple basic graph utilities.
   663 */
   664 
   665 /**
   666 @defgroup misc Miscellaneous Tools
   667 @ingroup utils
   668 \brief Tools for development, debugging and testing.
   669 
   670 This group contains several useful tools for development,
   671 debugging and testing.
   672 */
   673 
   674 /**
   675 @defgroup timecount Time Measuring and Counting
   676 @ingroup misc
   677 \brief Simple tools for measuring the performance of algorithms.
   678 
   679 This group contains simple tools for measuring the performance
   680 of algorithms.
   681 */
   682 
   683 /**
   684 @defgroup exceptions Exceptions
   685 @ingroup utils
   686 \brief Exceptions defined in LEMON.
   687 
   688 This group contains the exceptions defined in LEMON.
   689 */
   690 
   691 /**
   692 @defgroup io_group Input-Output
   693 \brief Graph Input-Output methods
   694 
   695 This group contains the tools for importing and exporting graphs
   696 and graph related data. Now it supports the \ref lgf-format
   697 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   698 postscript (EPS) format.
   699 */
   700 
   701 /**
   702 @defgroup lemon_io LEMON Graph Format
   703 @ingroup io_group
   704 \brief Reading and writing LEMON Graph Format.
   705 
   706 This group contains methods for reading and writing
   707 \ref lgf-format "LEMON Graph Format".
   708 */
   709 
   710 /**
   711 @defgroup eps_io Postscript Exporting
   712 @ingroup io_group
   713 \brief General \c EPS drawer and graph exporter
   714 
   715 This group contains general \c EPS drawing methods and special
   716 graph exporting tools.
   717 */
   718 
   719 /**
   720 @defgroup dimacs_group DIMACS Format
   721 @ingroup io_group
   722 \brief Read and write files in DIMACS format
   723 
   724 Tools to read a digraph from or write it to a file in DIMACS format data.
   725 */
   726 
   727 /**
   728 @defgroup nauty_group NAUTY Format
   729 @ingroup io_group
   730 \brief Read \e Nauty format
   731 
   732 Tool to read graphs from \e Nauty format data.
   733 */
   734 
   735 /**
   736 @defgroup concept Concepts
   737 \brief Skeleton classes and concept checking classes
   738 
   739 This group contains the data/algorithm skeletons and concept checking
   740 classes implemented in LEMON.
   741 
   742 The purpose of the classes in this group is fourfold.
   743 
   744 - These classes contain the documentations of the %concepts. In order
   745   to avoid document multiplications, an implementation of a concept
   746   simply refers to the corresponding concept class.
   747 
   748 - These classes declare every functions, <tt>typedef</tt>s etc. an
   749   implementation of the %concepts should provide, however completely
   750   without implementations and real data structures behind the
   751   interface. On the other hand they should provide nothing else. All
   752   the algorithms working on a data structure meeting a certain concept
   753   should compile with these classes. (Though it will not run properly,
   754   of course.) In this way it is easily to check if an algorithm
   755   doesn't use any extra feature of a certain implementation.
   756 
   757 - The concept descriptor classes also provide a <em>checker class</em>
   758   that makes it possible to check whether a certain implementation of a
   759   concept indeed provides all the required features.
   760 
   761 - Finally, They can serve as a skeleton of a new implementation of a concept.
   762 */
   763 
   764 /**
   765 @defgroup graph_concepts Graph Structure Concepts
   766 @ingroup concept
   767 \brief Skeleton and concept checking classes for graph structures
   768 
   769 This group contains the skeletons and concept checking classes of
   770 graph structures.
   771 */
   772 
   773 /**
   774 @defgroup map_concepts Map Concepts
   775 @ingroup concept
   776 \brief Skeleton and concept checking classes for maps
   777 
   778 This group contains the skeletons and concept checking classes of maps.
   779 */
   780 
   781 /**
   782 @defgroup tools Standalone Utility Applications
   783 
   784 Some utility applications are listed here.
   785 
   786 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   787 them, as well.
   788 */
   789 
   790 /**
   791 \anchor demoprograms
   792 
   793 @defgroup demos Demo Programs
   794 
   795 Some demo programs are listed here. Their full source codes can be found in
   796 the \c demo subdirectory of the source tree.
   797 
   798 In order to compile them, use the <tt>make demo</tt> or the
   799 <tt>make check</tt> commands.
   800 */
   801 
   802 }