author Peter Kovacs <>
Sat, 16 Mar 2013 14:09:53 +0100
changeset 1219 4f9a45a6d6f0
parent 1218 d9d1cb759951
child 1221 1c978b5bcc65
permissions -rw-r--r--
Add references to papers related to LEMON (#459)
     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  */
    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 Since the adaptor classes conform to the \ref graph_concepts "graph concepts",
   116 an adaptor can even be applied to another one.
   117 The following image illustrates a situation when a \ref SubDigraph adaptor
   118 is applied on a digraph and \ref Undirector is applied on the subgraph.
   120 \image html adaptors2.png
   121 \image latex adaptors2.eps "Using graph adaptors" width=\textwidth
   123 The behavior of graph adaptors can be very different. Some of them keep
   124 capabilities of the original graph while in other cases this would be
   125 meaningless. This means that the concepts that they meet depend
   126 on the graph adaptor, and the wrapped graph.
   127 For example, if an arc of a reversed digraph is deleted, this is carried
   128 out by deleting the corresponding arc of the original digraph, thus the
   129 adaptor modifies the original digraph.
   130 However in case of a residual digraph, this operation has no sense.
   132 Let us stand one more example here to simplify your work.
   133 ReverseDigraph has constructor
   134 \code
   135 ReverseDigraph(Digraph& digraph);
   136 \endcode
   137 This means that in a situation, when a <tt>const %ListDigraph&</tt>
   138 reference to a graph is given, then it have to be instantiated with
   139 <tt>Digraph=const %ListDigraph</tt>.
   140 \code
   141 int algorithm1(const ListDigraph& g) {
   142   ReverseDigraph<const ListDigraph> rg(g);
   143   return algorithm2(rg);
   144 }
   145 \endcode
   146 */
   148 /**
   149 @defgroup maps Maps
   150 @ingroup datas
   151 \brief Map structures implemented in LEMON.
   153 This group contains the map structures implemented in LEMON.
   155 LEMON provides several special purpose maps and map adaptors that e.g. combine
   156 new maps from existing ones.
   158 <b>See also:</b> \ref map_concepts "Map Concepts".
   159 */
   161 /**
   162 @defgroup graph_maps Graph Maps
   163 @ingroup maps
   164 \brief Special graph-related maps.
   166 This group contains maps that are specifically designed to assign
   167 values to the nodes and arcs/edges of graphs.
   169 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
   170 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
   171 */
   173 /**
   174 \defgroup map_adaptors Map Adaptors
   175 \ingroup maps
   176 \brief Tools to create new maps from existing ones
   178 This group contains map adaptors that are used to create "implicit"
   179 maps from other maps.
   181 Most of them are \ref concepts::ReadMap "read-only maps".
   182 They can make arithmetic and logical operations between one or two maps
   183 (negation, shifting, addition, multiplication, logical 'and', 'or',
   184 'not' etc.) or e.g. convert a map to another one of different Value type.
   186 The typical usage of this classes is passing implicit maps to
   187 algorithms.  If a function type algorithm is called then the function
   188 type map adaptors can be used comfortable. For example let's see the
   189 usage of map adaptors with the \c graphToEps() function.
   190 \code
   191   Color nodeColor(int deg) {
   192     if (deg >= 2) {
   193       return Color(0.5, 0.0, 0.5);
   194     } else if (deg == 1) {
   195       return Color(1.0, 0.5, 1.0);
   196     } else {
   197       return Color(0.0, 0.0, 0.0);
   198     }
   199   }
   201   Digraph::NodeMap<int> degree_map(graph);
   203   graphToEps(graph, "graph.eps")
   204     .coords(coords).scaleToA4().undirected()
   205     .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
   206     .run();
   207 \endcode
   208 The \c functorToMap() function makes an \c int to \c Color map from the
   209 \c nodeColor() function. The \c composeMap() compose the \c degree_map
   210 and the previously created map. The composed map is a proper function to
   211 get the color of each node.
   213 The usage with class type algorithms is little bit harder. In this
   214 case the function type map adaptors can not be used, because the
   215 function map adaptors give back temporary objects.
   216 \code
   217   Digraph graph;
   219   typedef Digraph::ArcMap<double> DoubleArcMap;
   220   DoubleArcMap length(graph);
   221   DoubleArcMap speed(graph);
   223   typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
   224   TimeMap time(length, speed);
   226   Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
   227, target);
   228 \endcode
   229 We have a length map and a maximum speed map on the arcs of a digraph.
   230 The minimum time to pass the arc can be calculated as the division of
   231 the two maps which can be done implicitly with the \c DivMap template
   232 class. We use the implicit minimum time map as the length map of the
   233 \c Dijkstra algorithm.
   234 */
   236 /**
   237 @defgroup paths Path Structures
   238 @ingroup datas
   239 \brief %Path structures implemented in LEMON.
   241 This group contains the path structures implemented in LEMON.
   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.
   249 \sa \ref concepts::Path "Path concept"
   250 */
   252 /**
   253 @defgroup heaps Heap Structures
   254 @ingroup datas
   255 \brief %Heap structures implemented in LEMON.
   257 This group contains the heap structures implemented in LEMON.
   259 LEMON provides several heap classes. They are efficient implementations
   260 of the abstract data type \e priority \e queue. They store items with
   261 specified values called \e priorities in such a way that finding and
   262 removing the item with minimum priority are efficient.
   263 The basic operations are adding and erasing items, changing the priority
   264 of an item, etc.
   266 Heaps are crucial in several algorithms, such as Dijkstra and Prim.
   267 The heap implementations have the same interface, thus any of them can be
   268 used easily in such algorithms.
   270 \sa \ref concepts::Heap "Heap concept"
   271 */
   273 /**
   274 @defgroup auxdat Auxiliary Data Structures
   275 @ingroup datas
   276 \brief Auxiliary data structures implemented in LEMON.
   278 This group contains some data structures implemented in LEMON in
   279 order to make it easier to implement combinatorial algorithms.
   280 */
   282 /**
   283 @defgroup geomdat Geometric Data Structures
   284 @ingroup auxdat
   285 \brief Geometric data structures implemented in LEMON.
   287 This group contains geometric data structures implemented in LEMON.
   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 */
   296 /**
   297 @defgroup matrices Matrices
   298 @ingroup auxdat
   299 \brief Two dimensional data storages implemented in LEMON.
   301 This group contains two dimensional data storages implemented in LEMON.
   302 */
   304 /**
   305 @defgroup algs Algorithms
   306 \brief This group contains the several algorithms
   307 implemented in LEMON.
   309 This group contains the several algorithms
   310 implemented in LEMON.
   311 */
   313 /**
   314 @defgroup search Graph Search
   315 @ingroup algs
   316 \brief Common graph search algorithms.
   318 This group contains the common graph search algorithms, namely
   319 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
   320 \ref clrs01algorithms.
   321 */
   323 /**
   324 @defgroup shortest_path Shortest Path Algorithms
   325 @ingroup algs
   326 \brief Algorithms for finding shortest paths.
   328 This group contains the algorithms for finding shortest paths in digraphs
   329 \ref clrs01algorithms.
   331  - \ref Dijkstra algorithm for finding shortest paths from a source node
   332    when all arc lengths are non-negative.
   333  - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
   334    from a source node when arc lenghts can be either positive or negative,
   335    but the digraph should not contain directed cycles with negative total
   336    length.
   337  - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
   338    for solving the \e all-pairs \e shortest \e paths \e problem when arc
   339    lenghts can be either positive or negative, but the digraph should
   340    not contain directed cycles with negative total length.
   341  - \ref Suurballe A successive shortest path algorithm for finding
   342    arc-disjoint paths between two nodes having minimum total length.
   343 */
   345 /**
   346 @defgroup spantree Minimum Spanning Tree Algorithms
   347 @ingroup algs
   348 \brief Algorithms for finding minimum cost spanning trees and arborescences.
   350 This group contains the algorithms for finding minimum cost spanning
   351 trees and arborescences \ref clrs01algorithms.
   352 */
   354 /**
   355 @defgroup max_flow Maximum Flow Algorithms
   356 @ingroup algs
   357 \brief Algorithms for finding maximum flows.
   359 This group contains the algorithms for finding maximum flows and
   360 feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
   362 The \e maximum \e flow \e problem is to find a flow of maximum value between
   363 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
   364 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
   365 \f$s, t \in V\f$ source and target nodes.
   366 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
   367 following optimization problem.
   369 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
   370 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
   371     \quad \forall u\in V\setminus\{s,t\} \f]
   372 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
   374 LEMON contains several algorithms for solving maximum flow problems:
   375 - \ref EdmondsKarp Edmonds-Karp algorithm
   376   \ref edmondskarp72theoretical.
   377 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
   378   \ref goldberg88newapproach.
   379 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
   380   \ref dinic70algorithm, \ref sleator83dynamic.
   381 - \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
   382   \ref goldberg88newapproach, \ref sleator83dynamic.
   384 In most cases the \ref Preflow algorithm provides the
   385 fastest method for computing a maximum flow. All implementations
   386 also provide functions to query the minimum cut, which is the dual
   387 problem of maximum flow.
   389 \ref Circulation is a preflow push-relabel algorithm implemented directly
   390 for finding feasible circulations, which is a somewhat different problem,
   391 but it is strongly related to maximum flow.
   392 For more information, see \ref Circulation.
   393 */
   395 /**
   396 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
   397 @ingroup algs
   399 \brief Algorithms for finding minimum cost flows and circulations.
   401 This group contains the algorithms for finding minimum cost flows and
   402 circulations \ref amo93networkflows. For more information about this
   403 problem and its dual solution, see: \ref min_cost_flow
   404 "Minimum Cost Flow Problem".
   406 LEMON contains several algorithms for this problem.
   407  - \ref NetworkSimplex Primal Network Simplex algorithm with various
   408    pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
   409  - \ref CostScaling Cost Scaling algorithm based on push/augment and
   410    relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
   411    \ref bunnagel98efficient.
   412  - \ref CapacityScaling Capacity Scaling algorithm based on the successive
   413    shortest path method \ref edmondskarp72theoretical.
   414  - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
   415    strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
   417 In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
   418 implementations.
   419 \ref NetworkSimplex is usually the fastest on relatively small graphs (up to
   420 several thousands of nodes) and on dense graphs, while \ref CostScaling is
   421 typically more efficient on large graphs (e.g. hundreds of thousands of
   422 nodes or above), especially if they are sparse.
   423 However, other algorithms could be faster in special cases.
   424 For example, if the total supply and/or capacities are rather small,
   425 \ref CapacityScaling is usually the fastest algorithm (without effective scaling).
   427 These classes are intended to be used with integer-valued input data
   428 (capacities, supply values, and costs), except for \ref CapacityScaling,
   429 which is capable of handling real-valued arc costs (other numerical
   430 data are required to be integer).
   432 For more details about these implementations and for a comprehensive 
   433 experimental study, see the paper \ref KiralyKovacs12MCF.
   434 It also compares these codes to other publicly available
   435 minimum cost flow solvers.
   436 */
   438 /**
   439 @defgroup min_cut Minimum Cut Algorithms
   440 @ingroup algs
   442 \brief Algorithms for finding minimum cut in graphs.
   444 This group contains the algorithms for finding minimum cut in graphs.
   446 The \e minimum \e cut \e problem is to find a non-empty and non-complete
   447 \f$X\f$ subset of the nodes with minimum overall capacity on
   448 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
   449 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
   450 cut is the \f$X\f$ solution of the next optimization problem:
   452 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
   453     \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
   455 LEMON contains several algorithms related to minimum cut problems:
   457 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
   458   in directed graphs.
   459 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
   460   calculating minimum cut in undirected graphs.
   461 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
   462   all-pairs minimum cut in undirected graphs.
   464 If you want to find minimum cut just between two distinict nodes,
   465 see the \ref max_flow "maximum flow problem".
   466 */
   468 /**
   469 @defgroup min_mean_cycle Minimum Mean Cycle Algorithms
   470 @ingroup algs
   471 \brief Algorithms for finding minimum mean cycles.
   473 This group contains the algorithms for finding minimum mean cycles
   474 \ref amo93networkflows, \ref karp78characterization.
   476 The \e minimum \e mean \e cycle \e problem is to find a directed cycle
   477 of minimum mean length (cost) in a digraph.
   478 The mean length of a cycle is the average length of its arcs, i.e. the
   479 ratio between the total length of the cycle and the number of arcs on it.
   481 This problem has an important connection to \e conservative \e length
   482 \e functions, too. A length function on the arcs of a digraph is called
   483 conservative if and only if there is no directed cycle of negative total
   484 length. For an arbitrary length function, the negative of the minimum
   485 cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
   486 arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
   487 function.
   489 LEMON contains three algorithms for solving the minimum mean cycle problem:
   490 - \ref KarpMmc Karp's original algorithm \ref karp78characterization.
   491 - \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
   492   version of Karp's algorithm \ref hartmann93finding.
   493 - \ref HowardMmc Howard's policy iteration algorithm
   494   \ref dasdan98minmeancycle, \ref dasdan04experimental.
   496 In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
   497 most efficient one, though the best known theoretical bound on its running
   498 time is exponential.
   499 Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
   500 run in time O(ne) and use space O(n<sup>2</sup>+e).
   501 */
   503 /**
   504 @defgroup matching Matching Algorithms
   505 @ingroup algs
   506 \brief Algorithms for finding matchings in graphs and bipartite graphs.
   508 This group contains the algorithms for calculating
   509 matchings in graphs and bipartite graphs. The general matching problem is
   510 finding a subset of the edges for which each node has at most one incident
   511 edge.
   513 There are several different algorithms for calculate matchings in
   514 graphs.  The matching problems in bipartite graphs are generally
   515 easier than in general graphs. The goal of the matching optimization
   516 can be finding maximum cardinality, maximum weight or minimum cost
   517 matching. The search can be constrained to find perfect or
   518 maximum cardinality matching.
   520 The matching algorithms implemented in LEMON:
   521 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
   522   for calculating maximum cardinality matching in bipartite graphs.
   523 - \ref PrBipartiteMatching Push-relabel algorithm
   524   for calculating maximum cardinality matching in bipartite graphs.
   525 - \ref MaxWeightedBipartiteMatching
   526   Successive shortest path algorithm for calculating maximum weighted
   527   matching and maximum weighted bipartite matching in bipartite graphs.
   528 - \ref MinCostMaxBipartiteMatching
   529   Successive shortest path algorithm for calculating minimum cost maximum
   530   matching in bipartite graphs.
   531 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
   532   maximum cardinality matching in general graphs.
   533 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
   534   maximum weighted matching in general graphs.
   535 - \ref MaxWeightedPerfectMatching
   536   Edmond's blossom shrinking algorithm for calculating maximum weighted
   537   perfect matching in general graphs.
   538 - \ref MaxFractionalMatching Push-relabel algorithm for calculating
   539   maximum cardinality fractional matching in general graphs.
   540 - \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
   541   maximum weighted fractional matching in general graphs.
   542 - \ref MaxWeightedPerfectFractionalMatching
   543   Augmenting path algorithm for calculating maximum weighted
   544   perfect fractional matching in general graphs.
   546 \image html matching.png
   547 \image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
   548 */
   550 /**
   551 @defgroup graph_properties Connectivity and Other Graph Properties
   552 @ingroup algs
   553 \brief Algorithms for discovering the graph properties
   555 This group contains the algorithms for discovering the graph properties
   556 like connectivity, bipartiteness, euler property, simplicity etc.
   558 \image html connected_components.png
   559 \image latex connected_components.eps "Connected components" width=\textwidth
   560 */
   562 /**
   563 @defgroup planar Planar Embedding and Drawing
   564 @ingroup algs
   565 \brief Algorithms for planarity checking, embedding and drawing
   567 This group contains the algorithms for planarity checking,
   568 embedding and drawing.
   570 \image html planar.png
   571 \image latex planar.eps "Plane graph" width=\textwidth
   572 */
   574 /**
   575 @defgroup tsp Traveling Salesman Problem
   576 @ingroup algs
   577 \brief Algorithms for the symmetric traveling salesman problem
   579 This group contains basic heuristic algorithms for the the symmetric
   580 \e traveling \e salesman \e problem (TSP).
   581 Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
   582 the problem is to find a shortest possible tour that visits each node exactly
   583 once (i.e. the minimum cost Hamiltonian cycle).
   585 These TSP algorithms are intended to be used with a \e metric \e cost
   586 \e function, i.e. the edge costs should satisfy the triangle inequality.
   587 Otherwise the algorithms could yield worse results.
   589 LEMON provides five well-known heuristics for solving symmetric TSP:
   590  - \ref NearestNeighborTsp Neareast neighbor algorithm
   591  - \ref GreedyTsp Greedy algorithm
   592  - \ref InsertionTsp Insertion heuristic (with four selection methods)
   593  - \ref ChristofidesTsp Christofides algorithm
   594  - \ref Opt2Tsp 2-opt algorithm
   596 \ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
   597 solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
   599 \ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
   600 approximation factor: 3/2.
   602 \ref Opt2Tsp usually provides the best results in practice, but
   603 it is the slowest method. It can also be used to improve given tours,
   604 for example, the results of other algorithms.
   606 \image html tsp.png
   607 \image latex tsp.eps "Traveling salesman problem" width=\textwidth
   608 */
   610 /**
   611 @defgroup approx_algs Approximation Algorithms
   612 @ingroup algs
   613 \brief Approximation algorithms.
   615 This group contains the approximation and heuristic algorithms
   616 implemented in LEMON.
   618 <b>Maximum Clique Problem</b>
   619   - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
   620     Grosso, Locatelli, and Pullan.
   621 */
   623 /**
   624 @defgroup auxalg Auxiliary Algorithms
   625 @ingroup algs
   626 \brief Auxiliary algorithms implemented in LEMON.
   628 This group contains some algorithms implemented in LEMON
   629 in order to make it easier to implement complex algorithms.
   630 */
   632 /**
   633 @defgroup gen_opt_group General Optimization Tools
   634 \brief This group contains some general optimization frameworks
   635 implemented in LEMON.
   637 This group contains some general optimization frameworks
   638 implemented in LEMON.
   639 */
   641 /**
   642 @defgroup lp_group LP and MIP Solvers
   643 @ingroup gen_opt_group
   644 \brief LP and MIP solver interfaces for LEMON.
   646 This group contains LP and MIP solver interfaces for LEMON.
   647 Various LP solvers could be used in the same manner with this
   648 high-level interface.
   650 The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
   651 \ref cplex, \ref soplex.
   652 */
   654 /**
   655 @defgroup lp_utils Tools for Lp and Mip Solvers
   656 @ingroup lp_group
   657 \brief Helper tools to the Lp and Mip solvers.
   659 This group adds some helper tools to general optimization framework
   660 implemented in LEMON.
   661 */
   663 /**
   664 @defgroup metah Metaheuristics
   665 @ingroup gen_opt_group
   666 \brief Metaheuristics for LEMON library.
   668 This group contains some metaheuristic optimization tools.
   669 */
   671 /**
   672 @defgroup utils Tools and Utilities
   673 \brief Tools and utilities for programming in LEMON
   675 Tools and utilities for programming in LEMON.
   676 */
   678 /**
   679 @defgroup gutils Basic Graph Utilities
   680 @ingroup utils
   681 \brief Simple basic graph utilities.
   683 This group contains some simple basic graph utilities.
   684 */
   686 /**
   687 @defgroup misc Miscellaneous Tools
   688 @ingroup utils
   689 \brief Tools for development, debugging and testing.
   691 This group contains several useful tools for development,
   692 debugging and testing.
   693 */
   695 /**
   696 @defgroup timecount Time Measuring and Counting
   697 @ingroup misc
   698 \brief Simple tools for measuring the performance of algorithms.
   700 This group contains simple tools for measuring the performance
   701 of algorithms.
   702 */
   704 /**
   705 @defgroup exceptions Exceptions
   706 @ingroup utils
   707 \brief Exceptions defined in LEMON.
   709 This group contains the exceptions defined in LEMON.
   710 */
   712 /**
   713 @defgroup io_group Input-Output
   714 \brief Graph Input-Output methods
   716 This group contains the tools for importing and exporting graphs
   717 and graph related data. Now it supports the \ref lgf-format
   718 "LEMON Graph Format", the \c DIMACS format and the encapsulated
   719 postscript (EPS) format.
   720 */
   722 /**
   723 @defgroup lemon_io LEMON Graph Format
   724 @ingroup io_group
   725 \brief Reading and writing LEMON Graph Format.
   727 This group contains methods for reading and writing
   728 \ref lgf-format "LEMON Graph Format".
   729 */
   731 /**
   732 @defgroup eps_io Postscript Exporting
   733 @ingroup io_group
   734 \brief General \c EPS drawer and graph exporter
   736 This group contains general \c EPS drawing methods and special
   737 graph exporting tools.
   739 \image html graph_to_eps.png
   740 */
   742 /**
   743 @defgroup dimacs_group DIMACS Format
   744 @ingroup io_group
   745 \brief Read and write files in DIMACS format
   747 Tools to read a digraph from or write it to a file in DIMACS format data.
   748 */
   750 /**
   751 @defgroup nauty_group NAUTY Format
   752 @ingroup io_group
   753 \brief Read \e Nauty format
   755 Tool to read graphs from \e Nauty format data.
   756 */
   758 /**
   759 @defgroup concept Concepts
   760 \brief Skeleton classes and concept checking classes
   762 This group contains the data/algorithm skeletons and concept checking
   763 classes implemented in LEMON.
   765 The purpose of the classes in this group is fourfold.
   767 - These classes contain the documentations of the %concepts. In order
   768   to avoid document multiplications, an implementation of a concept
   769   simply refers to the corresponding concept class.
   771 - These classes declare every functions, <tt>typedef</tt>s etc. an
   772   implementation of the %concepts should provide, however completely
   773   without implementations and real data structures behind the
   774   interface. On the other hand they should provide nothing else. All
   775   the algorithms working on a data structure meeting a certain concept
   776   should compile with these classes. (Though it will not run properly,
   777   of course.) In this way it is easily to check if an algorithm
   778   doesn't use any extra feature of a certain implementation.
   780 - The concept descriptor classes also provide a <em>checker class</em>
   781   that makes it possible to check whether a certain implementation of a
   782   concept indeed provides all the required features.
   784 - Finally, They can serve as a skeleton of a new implementation of a concept.
   785 */
   787 /**
   788 @defgroup graph_concepts Graph Structure Concepts
   789 @ingroup concept
   790 \brief Skeleton and concept checking classes for graph structures
   792 This group contains the skeletons and concept checking classes of
   793 graph structures.
   794 */
   796 /**
   797 @defgroup map_concepts Map Concepts
   798 @ingroup concept
   799 \brief Skeleton and concept checking classes for maps
   801 This group contains the skeletons and concept checking classes of maps.
   802 */
   804 /**
   805 @defgroup tools Standalone Utility Applications
   807 Some utility applications are listed here.
   809 The standard compilation procedure (<tt>./configure;make</tt>) will compile
   810 them, as well.
   811 */
   813 /**
   814 \anchor demoprograms
   816 @defgroup demos Demo Programs
   818 Some demo programs are listed here. Their full source codes can be found in
   819 the \c demo subdirectory of the source tree.
   821 In order to compile them, use the <tt>make demo</tt> or the
   822 <tt>make check</tt> commands.
   823 */
   825 }