doc/groups.dox
author Alpar Juttner <alpar@cs.elte.hu>
Fri, 25 Feb 2011 21:37:47 +0100
changeset 739 30d5f950aa5f
parent 658 d9cf3b5858ae
child 664 c01a98ce01fd
permissions -rw-r--r--
Fix wrong initialization in Preflow (#414)
alpar@209
     1
/* -*- mode: C++; indent-tabs-mode: nil; -*-
alpar@40
     2
 *
alpar@209
     3
 * This file is a part of LEMON, a generic C++ optimization library.
alpar@40
     4
 *
alpar@440
     5
 * Copyright (C) 2003-2009
alpar@40
     6
 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
alpar@40
     7
 * (Egervary Research Group on Combinatorial Optimization, EGRES).
alpar@40
     8
 *
alpar@40
     9
 * Permission to use, modify and distribute this software is granted
alpar@40
    10
 * provided that this copyright notice appears in all copies. For
alpar@40
    11
 * precise terms see the accompanying LICENSE file.
alpar@40
    12
 *
alpar@40
    13
 * This software is provided "AS IS" with no warranty of any kind,
alpar@40
    14
 * express or implied, and with no claim as to its suitability for any
alpar@40
    15
 * purpose.
alpar@40
    16
 *
alpar@40
    17
 */
alpar@40
    18
kpeter@406
    19
namespace lemon {
kpeter@406
    20
alpar@40
    21
/**
alpar@40
    22
@defgroup datas Data Structures
kpeter@550
    23
This group contains the several data structures implemented in LEMON.
alpar@40
    24
*/
alpar@40
    25
alpar@40
    26
/**
alpar@40
    27
@defgroup graphs Graph Structures
alpar@40
    28
@ingroup datas
alpar@40
    29
\brief Graph structures implemented in LEMON.
alpar@40
    30
alpar@209
    31
The implementation of combinatorial algorithms heavily relies on
alpar@209
    32
efficient graph implementations. LEMON offers data structures which are
alpar@209
    33
planned to be easily used in an experimental phase of implementation studies,
alpar@209
    34
and thereafter the program code can be made efficient by small modifications.
alpar@40
    35
alpar@40
    36
The most efficient implementation of diverse applications require the
alpar@40
    37
usage of different physical graph implementations. These differences
alpar@40
    38
appear in the size of graph we require to handle, memory or time usage
alpar@40
    39
limitations or in the set of operations through which the graph can be
alpar@40
    40
accessed.  LEMON provides several physical graph structures to meet
alpar@40
    41
the diverging requirements of the possible users.  In order to save on
alpar@40
    42
running time or on memory usage, some structures may fail to provide
kpeter@83
    43
some graph features like arc/edge or node deletion.
alpar@40
    44
alpar@209
    45
Alteration of standard containers need a very limited number of
alpar@209
    46
operations, these together satisfy the everyday requirements.
alpar@209
    47
In the case of graph structures, different operations are needed which do
alpar@209
    48
not alter the physical graph, but gives another view. If some nodes or
kpeter@83
    49
arcs have to be hidden or the reverse oriented graph have to be used, then
alpar@209
    50
this is the case. It also may happen that in a flow implementation
alpar@209
    51
the residual graph can be accessed by another algorithm, or a node-set
alpar@209
    52
is to be shrunk for another algorithm.
alpar@209
    53
LEMON also provides a variety of graphs for these requirements called
alpar@209
    54
\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
alpar@209
    55
in conjunction with other graph representations.
alpar@40
    56
alpar@40
    57
You are free to use the graph structure that fit your requirements
alpar@40
    58
the best, most graph algorithms and auxiliary data structures can be used
kpeter@314
    59
with any graph structure.
kpeter@314
    60
kpeter@314
    61
<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
alpar@40
    62
*/
alpar@40
    63
alpar@40
    64
/**
kpeter@451
    65
@defgroup graph_adaptors Adaptor Classes for Graphs
deba@416
    66
@ingroup graphs
kpeter@451
    67
\brief Adaptor classes for digraphs and graphs
kpeter@451
    68
kpeter@451
    69
This group contains several useful adaptor classes for digraphs and graphs.
deba@416
    70
deba@416
    71
The main parts of LEMON are the different graph structures, generic
kpeter@451
    72
graph algorithms, graph concepts, which couple them, and graph
deba@416
    73
adaptors. While the previous notions are more or less clear, the
deba@416
    74
latter one needs further explanation. Graph adaptors are graph classes
deba@416
    75
which serve for considering graph structures in different ways.
deba@416
    76
deba@416
    77
A short example makes this much clearer.  Suppose that we have an
kpeter@451
    78
instance \c g of a directed graph type, say ListDigraph and an algorithm
deba@416
    79
\code
deba@416
    80
template <typename Digraph>
deba@416
    81
int algorithm(const Digraph&);
deba@416
    82
\endcode
deba@416
    83
is needed to run on the reverse oriented graph.  It may be expensive
deba@416
    84
(in time or in memory usage) to copy \c g with the reversed
deba@416
    85
arcs.  In this case, an adaptor class is used, which (according
kpeter@451
    86
to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
kpeter@451
    87
The adaptor uses the original digraph structure and digraph operations when
kpeter@451
    88
methods of the reversed oriented graph are called.  This means that the adaptor
kpeter@451
    89
have minor memory usage, and do not perform sophisticated algorithmic
deba@416
    90
actions.  The purpose of it is to give a tool for the cases when a
deba@416
    91
graph have to be used in a specific alteration.  If this alteration is
kpeter@451
    92
obtained by a usual construction like filtering the node or the arc set or
deba@416
    93
considering a new orientation, then an adaptor is worthwhile to use.
deba@416
    94
To come back to the reverse oriented graph, in this situation
deba@416
    95
\code
deba@416
    96
template<typename Digraph> class ReverseDigraph;
deba@416
    97
\endcode
deba@416
    98
template class can be used. The code looks as follows
deba@416
    99
\code
deba@416
   100
ListDigraph g;
kpeter@451
   101
ReverseDigraph<ListDigraph> rg(g);
deba@416
   102
int result = algorithm(rg);
deba@416
   103
\endcode
kpeter@451
   104
During running the algorithm, the original digraph \c g is untouched.
kpeter@451
   105
This techniques give rise to an elegant code, and based on stable
deba@416
   106
graph adaptors, complex algorithms can be implemented easily.
deba@416
   107
kpeter@451
   108
In flow, circulation and matching problems, the residual
deba@416
   109
graph is of particular importance. Combining an adaptor implementing
kpeter@451
   110
this with shortest path algorithms or minimum mean cycle algorithms,
deba@416
   111
a range of weighted and cardinality optimization algorithms can be
deba@416
   112
obtained. For other examples, the interested user is referred to the
deba@416
   113
detailed documentation of particular adaptors.
deba@416
   114
deba@416
   115
The behavior of graph adaptors can be very different. Some of them keep
deba@416
   116
capabilities of the original graph while in other cases this would be
kpeter@451
   117
meaningless. This means that the concepts that they meet depend
kpeter@451
   118
on the graph adaptor, and the wrapped graph.
kpeter@451
   119
For example, if an arc of a reversed digraph is deleted, this is carried
kpeter@451
   120
out by deleting the corresponding arc of the original digraph, thus the
kpeter@451
   121
adaptor modifies the original digraph.
kpeter@451
   122
However in case of a residual digraph, this operation has no sense.
deba@416
   123
deba@416
   124
Let us stand one more example here to simplify your work.
kpeter@451
   125
ReverseDigraph has constructor
deba@416
   126
\code
deba@416
   127
ReverseDigraph(Digraph& digraph);
deba@416
   128
\endcode
kpeter@451
   129
This means that in a situation, when a <tt>const %ListDigraph&</tt>
deba@416
   130
reference to a graph is given, then it have to be instantiated with
kpeter@451
   131
<tt>Digraph=const %ListDigraph</tt>.
deba@416
   132
\code
deba@416
   133
int algorithm1(const ListDigraph& g) {
kpeter@451
   134
  ReverseDigraph<const ListDigraph> rg(g);
deba@416
   135
  return algorithm2(rg);
deba@416
   136
}
deba@416
   137
\endcode
deba@416
   138
*/
deba@416
   139
deba@416
   140
/**
alpar@209
   141
@defgroup maps Maps
alpar@40
   142
@ingroup datas
kpeter@50
   143
\brief Map structures implemented in LEMON.
alpar@40
   144
kpeter@550
   145
This group contains the map structures implemented in LEMON.
kpeter@50
   146
kpeter@314
   147
LEMON provides several special purpose maps and map adaptors that e.g. combine
alpar@40
   148
new maps from existing ones.
kpeter@314
   149
kpeter@314
   150
<b>See also:</b> \ref map_concepts "Map Concepts".
alpar@40
   151
*/
alpar@40
   152
alpar@40
   153
/**
alpar@209
   154
@defgroup graph_maps Graph Maps
alpar@40
   155
@ingroup maps
kpeter@83
   156
\brief Special graph-related maps.
alpar@40
   157
kpeter@550
   158
This group contains maps that are specifically designed to assign
kpeter@406
   159
values to the nodes and arcs/edges of graphs.
kpeter@406
   160
kpeter@406
   161
If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
kpeter@406
   162
\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
alpar@40
   163
*/
alpar@40
   164
alpar@40
   165
/**
alpar@40
   166
\defgroup map_adaptors Map Adaptors
alpar@40
   167
\ingroup maps
alpar@40
   168
\brief Tools to create new maps from existing ones
alpar@40
   169
kpeter@550
   170
This group contains map adaptors that are used to create "implicit"
kpeter@50
   171
maps from other maps.
alpar@40
   172
kpeter@406
   173
Most of them are \ref concepts::ReadMap "read-only maps".
kpeter@83
   174
They can make arithmetic and logical operations between one or two maps
kpeter@83
   175
(negation, shifting, addition, multiplication, logical 'and', 'or',
kpeter@83
   176
'not' etc.) or e.g. convert a map to another one of different Value type.
alpar@40
   177
kpeter@50
   178
The typical usage of this classes is passing implicit maps to
alpar@40
   179
algorithms.  If a function type algorithm is called then the function
alpar@40
   180
type map adaptors can be used comfortable. For example let's see the
kpeter@314
   181
usage of map adaptors with the \c graphToEps() function.
alpar@40
   182
\code
alpar@40
   183
  Color nodeColor(int deg) {
alpar@40
   184
    if (deg >= 2) {
alpar@40
   185
      return Color(0.5, 0.0, 0.5);
alpar@40
   186
    } else if (deg == 1) {
alpar@40
   187
      return Color(1.0, 0.5, 1.0);
alpar@40
   188
    } else {
alpar@40
   189
      return Color(0.0, 0.0, 0.0);
alpar@40
   190
    }
alpar@40
   191
  }
alpar@209
   192
kpeter@83
   193
  Digraph::NodeMap<int> degree_map(graph);
alpar@209
   194
kpeter@314
   195
  graphToEps(graph, "graph.eps")
alpar@40
   196
    .coords(coords).scaleToA4().undirected()
kpeter@83
   197
    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
alpar@40
   198
    .run();
alpar@209
   199
\endcode
kpeter@83
   200
The \c functorToMap() function makes an \c int to \c Color map from the
kpeter@314
   201
\c nodeColor() function. The \c composeMap() compose the \c degree_map
kpeter@83
   202
and the previously created map. The composed map is a proper function to
kpeter@83
   203
get the color of each node.
alpar@40
   204
alpar@40
   205
The usage with class type algorithms is little bit harder. In this
alpar@40
   206
case the function type map adaptors can not be used, because the
kpeter@50
   207
function map adaptors give back temporary objects.
alpar@40
   208
\code
kpeter@83
   209
  Digraph graph;
kpeter@83
   210
kpeter@83
   211
  typedef Digraph::ArcMap<double> DoubleArcMap;
kpeter@83
   212
  DoubleArcMap length(graph);
kpeter@83
   213
  DoubleArcMap speed(graph);
kpeter@83
   214
kpeter@83
   215
  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
alpar@40
   216
  TimeMap time(length, speed);
alpar@209
   217
kpeter@83
   218
  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
alpar@40
   219
  dijkstra.run(source, target);
alpar@40
   220
\endcode
kpeter@83
   221
We have a length map and a maximum speed map on the arcs of a digraph.
kpeter@83
   222
The minimum time to pass the arc can be calculated as the division of
kpeter@83
   223
the two maps which can be done implicitly with the \c DivMap template
alpar@40
   224
class. We use the implicit minimum time map as the length map of the
alpar@40
   225
\c Dijkstra algorithm.
alpar@40
   226
*/
alpar@40
   227
alpar@40
   228
/**
alpar@209
   229
@defgroup matrices Matrices
alpar@40
   230
@ingroup datas
kpeter@50
   231
\brief Two dimensional data storages implemented in LEMON.
alpar@40
   232
kpeter@550
   233
This group contains two dimensional data storages implemented in LEMON.
alpar@40
   234
*/
alpar@40
   235
alpar@40
   236
/**
alpar@40
   237
@defgroup paths Path Structures
alpar@40
   238
@ingroup datas
kpeter@318
   239
\brief %Path structures implemented in LEMON.
alpar@40
   240
kpeter@550
   241
This group contains the path structures implemented in LEMON.
alpar@40
   242
kpeter@50
   243
LEMON provides flexible data structures to work with paths.
kpeter@50
   244
All of them have similar interfaces and they can be copied easily with
kpeter@50
   245
assignment operators and copy constructors. This makes it easy and
alpar@40
   246
efficient to have e.g. the Dijkstra algorithm to store its result in
alpar@40
   247
any kind of path structure.
alpar@40
   248
alpar@40
   249
\sa lemon::concepts::Path
alpar@40
   250
*/
alpar@40
   251
alpar@40
   252
/**
alpar@40
   253
@defgroup auxdat Auxiliary Data Structures
alpar@40
   254
@ingroup datas
kpeter@50
   255
\brief Auxiliary data structures implemented in LEMON.
alpar@40
   256
kpeter@550
   257
This group contains some data structures implemented in LEMON in
alpar@40
   258
order to make it easier to implement combinatorial algorithms.
alpar@40
   259
*/
alpar@40
   260
alpar@40
   261
/**
alpar@40
   262
@defgroup algs Algorithms
kpeter@550
   263
\brief This group contains the several algorithms
alpar@40
   264
implemented in LEMON.
alpar@40
   265
kpeter@550
   266
This group contains the several algorithms
alpar@40
   267
implemented in LEMON.
alpar@40
   268
*/
alpar@40
   269
alpar@40
   270
/**
alpar@40
   271
@defgroup search Graph Search
alpar@40
   272
@ingroup algs
kpeter@50
   273
\brief Common graph search algorithms.
alpar@40
   274
kpeter@550
   275
This group contains the common graph search algorithms, namely
kpeter@406
   276
\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
alpar@40
   277
*/
alpar@40
   278
alpar@40
   279
/**
kpeter@314
   280
@defgroup shortest_path Shortest Path Algorithms
alpar@40
   281
@ingroup algs
kpeter@50
   282
\brief Algorithms for finding shortest paths.
alpar@40
   283
kpeter@550
   284
This group contains the algorithms for finding shortest paths in digraphs.
kpeter@406
   285
kpeter@406
   286
 - \ref Dijkstra algorithm for finding shortest paths from a source node
kpeter@406
   287
   when all arc lengths are non-negative.
kpeter@406
   288
 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
kpeter@406
   289
   from a source node when arc lenghts can be either positive or negative,
kpeter@406
   290
   but the digraph should not contain directed cycles with negative total
kpeter@406
   291
   length.
kpeter@406
   292
 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
kpeter@406
   293
   for solving the \e all-pairs \e shortest \e paths \e problem when arc
kpeter@406
   294
   lenghts can be either positive or negative, but the digraph should
kpeter@406
   295
   not contain directed cycles with negative total length.
kpeter@406
   296
 - \ref Suurballe A successive shortest path algorithm for finding
kpeter@406
   297
   arc-disjoint paths between two nodes having minimum total length.
alpar@40
   298
*/
alpar@40
   299
alpar@209
   300
/**
kpeter@314
   301
@defgroup max_flow Maximum Flow Algorithms
alpar@209
   302
@ingroup algs
kpeter@50
   303
\brief Algorithms for finding maximum flows.
alpar@40
   304
kpeter@550
   305
This group contains the algorithms for finding maximum flows and
alpar@40
   306
feasible circulations.
alpar@40
   307
kpeter@406
   308
The \e maximum \e flow \e problem is to find a flow of maximum value between
kpeter@406
   309
a single source and a single target. Formally, there is a \f$G=(V,A)\f$
kpeter@601
   310
digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
kpeter@406
   311
\f$s, t \in V\f$ source and target nodes.
kpeter@601
   312
A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
kpeter@406
   313
following optimization problem.
alpar@40
   314
kpeter@601
   315
\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
kpeter@601
   316
\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
kpeter@601
   317
    \quad \forall u\in V\setminus\{s,t\} \f]
kpeter@601
   318
\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
alpar@40
   319
kpeter@50
   320
LEMON contains several algorithms for solving maximum flow problems:
kpeter@406
   321
- \ref EdmondsKarp Edmonds-Karp algorithm.
kpeter@406
   322
- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
kpeter@406
   323
- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
kpeter@406
   324
- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
alpar@40
   325
kpeter@406
   326
In most cases the \ref Preflow "Preflow" algorithm provides the
kpeter@406
   327
fastest method for computing a maximum flow. All implementations
kpeter@649
   328
also provide functions to query the minimum cut, which is the dual
kpeter@649
   329
problem of maximum flow.
kpeter@649
   330
kpeter@649
   331
\ref Circulation is a preflow push-relabel algorithm implemented directly 
kpeter@649
   332
for finding feasible circulations, which is a somewhat different problem,
kpeter@649
   333
but it is strongly related to maximum flow.
kpeter@649
   334
For more information, see \ref Circulation.
alpar@40
   335
*/
alpar@40
   336
alpar@40
   337
/**
kpeter@661
   338
@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
alpar@40
   339
@ingroup algs
alpar@40
   340
kpeter@50
   341
\brief Algorithms for finding minimum cost flows and circulations.
alpar@40
   342
kpeter@601
   343
This group contains the algorithms for finding minimum cost flows and
kpeter@661
   344
circulations. For more information about this problem and its dual
kpeter@661
   345
solution see \ref min_cost_flow "Minimum Cost Flow Problem".
kpeter@406
   346
kpeter@661
   347
LEMON contains several algorithms for this problem.
kpeter@601
   348
 - \ref NetworkSimplex Primal Network Simplex algorithm with various
kpeter@601
   349
   pivot strategies.
kpeter@601
   350
 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
kpeter@601
   351
   cost scaling.
kpeter@601
   352
 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
kpeter@406
   353
   capacity scaling.
kpeter@601
   354
 - \ref CancelAndTighten The Cancel and Tighten algorithm.
kpeter@601
   355
 - \ref CycleCanceling Cycle-Canceling algorithms.
kpeter@601
   356
kpeter@601
   357
In general NetworkSimplex is the most efficient implementation,
kpeter@601
   358
but in special cases other algorithms could be faster.
kpeter@601
   359
For example, if the total supply and/or capacities are rather small,
kpeter@601
   360
CapacityScaling is usually the fastest algorithm (without effective scaling).
alpar@40
   361
*/
alpar@40
   362
alpar@40
   363
/**
kpeter@314
   364
@defgroup min_cut Minimum Cut Algorithms
alpar@209
   365
@ingroup algs
alpar@40
   366
kpeter@50
   367
\brief Algorithms for finding minimum cut in graphs.
alpar@40
   368
kpeter@550
   369
This group contains the algorithms for finding minimum cut in graphs.
alpar@40
   370
kpeter@406
   371
The \e minimum \e cut \e problem is to find a non-empty and non-complete
kpeter@406
   372
\f$X\f$ subset of the nodes with minimum overall capacity on
kpeter@406
   373
outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
kpeter@406
   374
\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
kpeter@50
   375
cut is the \f$X\f$ solution of the next optimization problem:
alpar@40
   376
alpar@210
   377
\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
kpeter@406
   378
    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
alpar@40
   379
kpeter@50
   380
LEMON contains several algorithms related to minimum cut problems:
alpar@40
   381
kpeter@406
   382
- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
kpeter@406
   383
  in directed graphs.
kpeter@406
   384
- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
kpeter@406
   385
  calculating minimum cut in undirected graphs.
kpeter@550
   386
- \ref GomoryHu "Gomory-Hu tree computation" for calculating
kpeter@406
   387
  all-pairs minimum cut in undirected graphs.
alpar@40
   388
alpar@40
   389
If you want to find minimum cut just between two distinict nodes,
kpeter@406
   390
see the \ref max_flow "maximum flow problem".
alpar@40
   391
*/
alpar@40
   392
alpar@40
   393
/**
kpeter@578
   394
@defgroup graph_properties Connectivity and Other Graph Properties
alpar@40
   395
@ingroup algs
kpeter@50
   396
\brief Algorithms for discovering the graph properties
alpar@40
   397
kpeter@550
   398
This group contains the algorithms for discovering the graph properties
kpeter@50
   399
like connectivity, bipartiteness, euler property, simplicity etc.
alpar@40
   400
alpar@40
   401
\image html edge_biconnected_components.png
alpar@40
   402
\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
alpar@40
   403
*/
alpar@40
   404
alpar@40
   405
/**
kpeter@314
   406
@defgroup planar Planarity Embedding and Drawing
alpar@40
   407
@ingroup algs
kpeter@50
   408
\brief Algorithms for planarity checking, embedding and drawing
alpar@40
   409
kpeter@550
   410
This group contains the algorithms for planarity checking,
alpar@210
   411
embedding and drawing.
alpar@40
   412
alpar@40
   413
\image html planar.png
alpar@40
   414
\image latex planar.eps "Plane graph" width=\textwidth
alpar@40
   415
*/
alpar@40
   416
alpar@40
   417
/**
kpeter@314
   418
@defgroup matching Matching Algorithms
alpar@40
   419
@ingroup algs
kpeter@50
   420
\brief Algorithms for finding matchings in graphs and bipartite graphs.
alpar@40
   421
kpeter@582
   422
This group contains the algorithms for calculating
alpar@40
   423
matchings in graphs and bipartite graphs. The general matching problem is
kpeter@582
   424
finding a subset of the edges for which each node has at most one incident
kpeter@582
   425
edge.
alpar@209
   426
alpar@40
   427
There are several different algorithms for calculate matchings in
alpar@40
   428
graphs.  The matching problems in bipartite graphs are generally
alpar@40
   429
easier than in general graphs. The goal of the matching optimization
kpeter@406
   430
can be finding maximum cardinality, maximum weight or minimum cost
alpar@40
   431
matching. The search can be constrained to find perfect or
alpar@40
   432
maximum cardinality matching.
alpar@40
   433
kpeter@406
   434
The matching algorithms implemented in LEMON:
kpeter@406
   435
- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
kpeter@406
   436
  for calculating maximum cardinality matching in bipartite graphs.
kpeter@406
   437
- \ref PrBipartiteMatching Push-relabel algorithm
kpeter@406
   438
  for calculating maximum cardinality matching in bipartite graphs.
kpeter@406
   439
- \ref MaxWeightedBipartiteMatching
kpeter@406
   440
  Successive shortest path algorithm for calculating maximum weighted
kpeter@406
   441
  matching and maximum weighted bipartite matching in bipartite graphs.
kpeter@406
   442
- \ref MinCostMaxBipartiteMatching
kpeter@406
   443
  Successive shortest path algorithm for calculating minimum cost maximum
kpeter@406
   444
  matching in bipartite graphs.
kpeter@406
   445
- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
kpeter@406
   446
  maximum cardinality matching in general graphs.
kpeter@406
   447
- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
kpeter@406
   448
  maximum weighted matching in general graphs.
kpeter@406
   449
- \ref MaxWeightedPerfectMatching
kpeter@406
   450
  Edmond's blossom shrinking algorithm for calculating maximum weighted
kpeter@406
   451
  perfect matching in general graphs.
alpar@40
   452
alpar@40
   453
\image html bipartite_matching.png
alpar@40
   454
\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
alpar@40
   455
*/
alpar@40
   456
alpar@40
   457
/**
kpeter@314
   458
@defgroup spantree Minimum Spanning Tree Algorithms
alpar@40
   459
@ingroup algs
kpeter@649
   460
\brief Algorithms for finding minimum cost spanning trees and arborescences.
alpar@40
   461
kpeter@649
   462
This group contains the algorithms for finding minimum cost spanning
kpeter@649
   463
trees and arborescences.
alpar@40
   464
*/
alpar@40
   465
alpar@40
   466
/**
kpeter@314
   467
@defgroup auxalg Auxiliary Algorithms
alpar@40
   468
@ingroup algs
kpeter@50
   469
\brief Auxiliary algorithms implemented in LEMON.
alpar@40
   470
kpeter@550
   471
This group contains some algorithms implemented in LEMON
kpeter@50
   472
in order to make it easier to implement complex algorithms.
alpar@40
   473
*/
alpar@40
   474
alpar@40
   475
/**
kpeter@314
   476
@defgroup approx Approximation Algorithms
kpeter@314
   477
@ingroup algs
kpeter@50
   478
\brief Approximation algorithms.
alpar@40
   479
kpeter@550
   480
This group contains the approximation and heuristic algorithms
kpeter@50
   481
implemented in LEMON.
alpar@40
   482
*/
alpar@40
   483
alpar@40
   484
/**
alpar@40
   485
@defgroup gen_opt_group General Optimization Tools
kpeter@550
   486
\brief This group contains some general optimization frameworks
alpar@40
   487
implemented in LEMON.
alpar@40
   488
kpeter@550
   489
This group contains some general optimization frameworks
alpar@40
   490
implemented in LEMON.
alpar@40
   491
*/
alpar@40
   492
alpar@40
   493
/**
kpeter@314
   494
@defgroup lp_group Lp and Mip Solvers
alpar@40
   495
@ingroup gen_opt_group
alpar@40
   496
\brief Lp and Mip solver interfaces for LEMON.
alpar@40
   497
kpeter@550
   498
This group contains Lp and Mip solver interfaces for LEMON. The
alpar@40
   499
various LP solvers could be used in the same manner with this
alpar@40
   500
interface.
alpar@40
   501
*/
alpar@40
   502
alpar@209
   503
/**
kpeter@314
   504
@defgroup lp_utils Tools for Lp and Mip Solvers
alpar@40
   505
@ingroup lp_group
kpeter@50
   506
\brief Helper tools to the Lp and Mip solvers.
alpar@40
   507
alpar@40
   508
This group adds some helper tools to general optimization framework
alpar@40
   509
implemented in LEMON.
alpar@40
   510
*/
alpar@40
   511
alpar@40
   512
/**
alpar@40
   513
@defgroup metah Metaheuristics
alpar@40
   514
@ingroup gen_opt_group
alpar@40
   515
\brief Metaheuristics for LEMON library.
alpar@40
   516
kpeter@550
   517
This group contains some metaheuristic optimization tools.
alpar@40
   518
*/
alpar@40
   519
alpar@40
   520
/**
alpar@209
   521
@defgroup utils Tools and Utilities
kpeter@50
   522
\brief Tools and utilities for programming in LEMON
alpar@40
   523
kpeter@50
   524
Tools and utilities for programming in LEMON.
alpar@40
   525
*/
alpar@40
   526
alpar@40
   527
/**
alpar@40
   528
@defgroup gutils Basic Graph Utilities
alpar@40
   529
@ingroup utils
kpeter@50
   530
\brief Simple basic graph utilities.
alpar@40
   531
kpeter@550
   532
This group contains some simple basic graph utilities.
alpar@40
   533
*/
alpar@40
   534
alpar@40
   535
/**
alpar@40
   536
@defgroup misc Miscellaneous Tools
alpar@40
   537
@ingroup utils
kpeter@50
   538
\brief Tools for development, debugging and testing.
kpeter@50
   539
kpeter@550
   540
This group contains several useful tools for development,
alpar@40
   541
debugging and testing.
alpar@40
   542
*/
alpar@40
   543
alpar@40
   544
/**
kpeter@314
   545
@defgroup timecount Time Measuring and Counting
alpar@40
   546
@ingroup misc
kpeter@50
   547
\brief Simple tools for measuring the performance of algorithms.
kpeter@50
   548
kpeter@550
   549
This group contains simple tools for measuring the performance
alpar@40
   550
of algorithms.
alpar@40
   551
*/
alpar@40
   552
alpar@40
   553
/**
alpar@40
   554
@defgroup exceptions Exceptions
alpar@40
   555
@ingroup utils
kpeter@50
   556
\brief Exceptions defined in LEMON.
kpeter@50
   557
kpeter@550
   558
This group contains the exceptions defined in LEMON.
alpar@40
   559
*/
alpar@40
   560
alpar@40
   561
/**
alpar@40
   562
@defgroup io_group Input-Output
kpeter@50
   563
\brief Graph Input-Output methods
alpar@40
   564
kpeter@550
   565
This group contains the tools for importing and exporting graphs
kpeter@314
   566
and graph related data. Now it supports the \ref lgf-format
kpeter@314
   567
"LEMON Graph Format", the \c DIMACS format and the encapsulated
kpeter@314
   568
postscript (EPS) format.
alpar@40
   569
*/
alpar@40
   570
alpar@40
   571
/**
kpeter@351
   572
@defgroup lemon_io LEMON Graph Format
alpar@40
   573
@ingroup io_group
kpeter@314
   574
\brief Reading and writing LEMON Graph Format.
alpar@40
   575
kpeter@550
   576
This group contains methods for reading and writing
ladanyi@236
   577
\ref lgf-format "LEMON Graph Format".
alpar@40
   578
*/
alpar@40
   579
alpar@40
   580
/**
kpeter@314
   581
@defgroup eps_io Postscript Exporting
alpar@40
   582
@ingroup io_group
alpar@40
   583
\brief General \c EPS drawer and graph exporter
alpar@40
   584
kpeter@550
   585
This group contains general \c EPS drawing methods and special
alpar@209
   586
graph exporting tools.
alpar@40
   587
*/
alpar@40
   588
alpar@40
   589
/**
kpeter@388
   590
@defgroup dimacs_group DIMACS format
kpeter@388
   591
@ingroup io_group
kpeter@388
   592
\brief Read and write files in DIMACS format
kpeter@388
   593
kpeter@388
   594
Tools to read a digraph from or write it to a file in DIMACS format data.
kpeter@388
   595
*/
kpeter@388
   596
kpeter@388
   597
/**
kpeter@351
   598
@defgroup nauty_group NAUTY Format
kpeter@351
   599
@ingroup io_group
kpeter@351
   600
\brief Read \e Nauty format
kpeter@388
   601
kpeter@351
   602
Tool to read graphs from \e Nauty format data.
kpeter@351
   603
*/
kpeter@351
   604
kpeter@351
   605
/**
alpar@40
   606
@defgroup concept Concepts
alpar@40
   607
\brief Skeleton classes and concept checking classes
alpar@40
   608
kpeter@550
   609
This group contains the data/algorithm skeletons and concept checking
alpar@40
   610
classes implemented in LEMON.
alpar@40
   611
alpar@40
   612
The purpose of the classes in this group is fourfold.
alpar@209
   613
kpeter@318
   614
- These classes contain the documentations of the %concepts. In order
alpar@40
   615
  to avoid document multiplications, an implementation of a concept
alpar@40
   616
  simply refers to the corresponding concept class.
alpar@40
   617
alpar@40
   618
- These classes declare every functions, <tt>typedef</tt>s etc. an
kpeter@318
   619
  implementation of the %concepts should provide, however completely
alpar@40
   620
  without implementations and real data structures behind the
alpar@40
   621
  interface. On the other hand they should provide nothing else. All
alpar@40
   622
  the algorithms working on a data structure meeting a certain concept
alpar@40
   623
  should compile with these classes. (Though it will not run properly,
alpar@40
   624
  of course.) In this way it is easily to check if an algorithm
alpar@40
   625
  doesn't use any extra feature of a certain implementation.
alpar@40
   626
alpar@40
   627
- The concept descriptor classes also provide a <em>checker class</em>
kpeter@50
   628
  that makes it possible to check whether a certain implementation of a
alpar@40
   629
  concept indeed provides all the required features.
alpar@40
   630
alpar@40
   631
- Finally, They can serve as a skeleton of a new implementation of a concept.
alpar@40
   632
*/
alpar@40
   633
alpar@40
   634
/**
alpar@40
   635
@defgroup graph_concepts Graph Structure Concepts
alpar@40
   636
@ingroup concept
alpar@40
   637
\brief Skeleton and concept checking classes for graph structures
alpar@40
   638
kpeter@550
   639
This group contains the skeletons and concept checking classes of LEMON's
alpar@40
   640
graph structures and helper classes used to implement these.
alpar@40
   641
*/
alpar@40
   642
kpeter@314
   643
/**
kpeter@314
   644
@defgroup map_concepts Map Concepts
kpeter@314
   645
@ingroup concept
kpeter@314
   646
\brief Skeleton and concept checking classes for maps
kpeter@314
   647
kpeter@550
   648
This group contains the skeletons and concept checking classes of maps.
alpar@40
   649
*/
alpar@40
   650
alpar@40
   651
/**
alpar@40
   652
\anchor demoprograms
alpar@40
   653
kpeter@406
   654
@defgroup demos Demo Programs
alpar@40
   655
alpar@40
   656
Some demo programs are listed here. Their full source codes can be found in
alpar@40
   657
the \c demo subdirectory of the source tree.
alpar@40
   658
ladanyi@556
   659
In order to compile them, use the <tt>make demo</tt> or the
ladanyi@556
   660
<tt>make check</tt> commands.
alpar@40
   661
*/
alpar@40
   662
alpar@40
   663
/**
kpeter@406
   664
@defgroup tools Standalone Utility Applications
alpar@40
   665
alpar@209
   666
Some utility applications are listed here.
alpar@40
   667
alpar@40
   668
The standard compilation procedure (<tt>./configure;make</tt>) will compile
alpar@209
   669
them, as well.
alpar@40
   670
*/
alpar@40
   671
kpeter@406
   672
}