doc/groups.dox
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 09 Jan 2011 16:51:14 +0100
changeset 1023 e0cef67fe565
parent 999 c279b19abc62
child 1164 f63ba40a60f4
permissions -rw-r--r--
Various doc improvements (#406)
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@956
     5
 * Copyright (C) 2003-2010
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@422
    19
namespace lemon {
kpeter@422
    20
alpar@40
    21
/**
alpar@40
    22
@defgroup datas Data Structures
kpeter@606
    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@474
    65
@defgroup graph_adaptors Adaptor Classes for Graphs
deba@432
    66
@ingroup graphs
kpeter@474
    67
\brief Adaptor classes for digraphs and graphs
kpeter@474
    68
kpeter@474
    69
This group contains several useful adaptor classes for digraphs and graphs.
deba@432
    70
deba@432
    71
The main parts of LEMON are the different graph structures, generic
kpeter@474
    72
graph algorithms, graph concepts, which couple them, and graph
deba@432
    73
adaptors. While the previous notions are more or less clear, the
deba@432
    74
latter one needs further explanation. Graph adaptors are graph classes
deba@432
    75
which serve for considering graph structures in different ways.
deba@432
    76
deba@432
    77
A short example makes this much clearer.  Suppose that we have an
kpeter@474
    78
instance \c g of a directed graph type, say ListDigraph and an algorithm
deba@432
    79
\code
deba@432
    80
template <typename Digraph>
deba@432
    81
int algorithm(const Digraph&);
deba@432
    82
\endcode
deba@432
    83
is needed to run on the reverse oriented graph.  It may be expensive
deba@432
    84
(in time or in memory usage) to copy \c g with the reversed
deba@432
    85
arcs.  In this case, an adaptor class is used, which (according
kpeter@474
    86
to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
kpeter@474
    87
The adaptor uses the original digraph structure and digraph operations when
kpeter@474
    88
methods of the reversed oriented graph are called.  This means that the adaptor
kpeter@474
    89
have minor memory usage, and do not perform sophisticated algorithmic
deba@432
    90
actions.  The purpose of it is to give a tool for the cases when a
deba@432
    91
graph have to be used in a specific alteration.  If this alteration is
kpeter@474
    92
obtained by a usual construction like filtering the node or the arc set or
deba@432
    93
considering a new orientation, then an adaptor is worthwhile to use.
deba@432
    94
To come back to the reverse oriented graph, in this situation
deba@432
    95
\code
deba@432
    96
template<typename Digraph> class ReverseDigraph;
deba@432
    97
\endcode
deba@432
    98
template class can be used. The code looks as follows
deba@432
    99
\code
deba@432
   100
ListDigraph g;
kpeter@474
   101
ReverseDigraph<ListDigraph> rg(g);
deba@432
   102
int result = algorithm(rg);
deba@432
   103
\endcode
kpeter@474
   104
During running the algorithm, the original digraph \c g is untouched.
kpeter@474
   105
This techniques give rise to an elegant code, and based on stable
deba@432
   106
graph adaptors, complex algorithms can be implemented easily.
deba@432
   107
kpeter@474
   108
In flow, circulation and matching problems, the residual
deba@432
   109
graph is of particular importance. Combining an adaptor implementing
kpeter@474
   110
this with shortest path algorithms or minimum mean cycle algorithms,
deba@432
   111
a range of weighted and cardinality optimization algorithms can be
deba@432
   112
obtained. For other examples, the interested user is referred to the
deba@432
   113
detailed documentation of particular adaptors.
deba@432
   114
deba@432
   115
The behavior of graph adaptors can be very different. Some of them keep
deba@432
   116
capabilities of the original graph while in other cases this would be
kpeter@474
   117
meaningless. This means that the concepts that they meet depend
kpeter@474
   118
on the graph adaptor, and the wrapped graph.
kpeter@474
   119
For example, if an arc of a reversed digraph is deleted, this is carried
kpeter@474
   120
out by deleting the corresponding arc of the original digraph, thus the
kpeter@474
   121
adaptor modifies the original digraph.
kpeter@474
   122
However in case of a residual digraph, this operation has no sense.
deba@432
   123
deba@432
   124
Let us stand one more example here to simplify your work.
kpeter@474
   125
ReverseDigraph has constructor
deba@432
   126
\code
deba@432
   127
ReverseDigraph(Digraph& digraph);
deba@432
   128
\endcode
kpeter@474
   129
This means that in a situation, when a <tt>const %ListDigraph&</tt>
deba@432
   130
reference to a graph is given, then it have to be instantiated with
kpeter@474
   131
<tt>Digraph=const %ListDigraph</tt>.
deba@432
   132
\code
deba@432
   133
int algorithm1(const ListDigraph& g) {
kpeter@474
   134
  ReverseDigraph<const ListDigraph> rg(g);
deba@432
   135
  return algorithm2(rg);
deba@432
   136
}
deba@432
   137
\endcode
deba@432
   138
*/
deba@432
   139
deba@432
   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@606
   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@606
   158
This group contains maps that are specifically designed to assign
kpeter@422
   159
values to the nodes and arcs/edges of graphs.
kpeter@422
   160
kpeter@422
   161
If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
kpeter@422
   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@606
   170
This group contains map adaptors that are used to create "implicit"
kpeter@50
   171
maps from other maps.
alpar@40
   172
kpeter@422
   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@40
   229
@defgroup paths Path Structures
alpar@40
   230
@ingroup datas
kpeter@318
   231
\brief %Path structures implemented in LEMON.
alpar@40
   232
kpeter@606
   233
This group contains the path structures implemented in LEMON.
alpar@40
   234
kpeter@50
   235
LEMON provides flexible data structures to work with paths.
kpeter@50
   236
All of them have similar interfaces and they can be copied easily with
kpeter@50
   237
assignment operators and copy constructors. This makes it easy and
alpar@40
   238
efficient to have e.g. the Dijkstra algorithm to store its result in
alpar@40
   239
any kind of path structure.
alpar@40
   240
kpeter@757
   241
\sa \ref concepts::Path "Path concept"
kpeter@757
   242
*/
kpeter@757
   243
kpeter@757
   244
/**
kpeter@757
   245
@defgroup heaps Heap Structures
kpeter@757
   246
@ingroup datas
kpeter@757
   247
\brief %Heap structures implemented in LEMON.
kpeter@757
   248
kpeter@757
   249
This group contains the heap structures implemented in LEMON.
kpeter@757
   250
kpeter@757
   251
LEMON provides several heap classes. They are efficient implementations
kpeter@757
   252
of the abstract data type \e priority \e queue. They store items with
kpeter@757
   253
specified values called \e priorities in such a way that finding and
kpeter@757
   254
removing the item with minimum priority are efficient.
kpeter@757
   255
The basic operations are adding and erasing items, changing the priority
kpeter@757
   256
of an item, etc.
kpeter@757
   257
kpeter@757
   258
Heaps are crucial in several algorithms, such as Dijkstra and Prim.
kpeter@757
   259
The heap implementations have the same interface, thus any of them can be
kpeter@757
   260
used easily in such algorithms.
kpeter@757
   261
kpeter@757
   262
\sa \ref concepts::Heap "Heap concept"
kpeter@757
   263
*/
kpeter@757
   264
kpeter@757
   265
/**
alpar@40
   266
@defgroup auxdat Auxiliary Data Structures
alpar@40
   267
@ingroup datas
kpeter@50
   268
\brief Auxiliary data structures implemented in LEMON.
alpar@40
   269
kpeter@606
   270
This group contains some data structures implemented in LEMON in
alpar@40
   271
order to make it easier to implement combinatorial algorithms.
alpar@40
   272
*/
alpar@40
   273
alpar@40
   274
/**
kpeter@761
   275
@defgroup geomdat Geometric Data Structures
kpeter@761
   276
@ingroup auxdat
kpeter@761
   277
\brief Geometric data structures implemented in LEMON.
kpeter@761
   278
kpeter@761
   279
This group contains geometric data structures implemented in LEMON.
kpeter@761
   280
kpeter@761
   281
 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
kpeter@761
   282
   vector with the usual operations.
kpeter@761
   283
 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
kpeter@761
   284
   rectangular bounding box of a set of \ref lemon::dim2::Point
kpeter@761
   285
   "dim2::Point"'s.
kpeter@761
   286
*/
kpeter@761
   287
kpeter@761
   288
/**
kpeter@761
   289
@defgroup matrices Matrices
kpeter@761
   290
@ingroup auxdat
kpeter@761
   291
\brief Two dimensional data storages implemented in LEMON.
kpeter@761
   292
kpeter@761
   293
This group contains two dimensional data storages implemented in LEMON.
kpeter@761
   294
*/
kpeter@761
   295
kpeter@761
   296
/**
alpar@40
   297
@defgroup algs Algorithms
kpeter@606
   298
\brief This group contains the several algorithms
alpar@40
   299
implemented in LEMON.
alpar@40
   300
kpeter@606
   301
This group contains the several algorithms
alpar@40
   302
implemented in LEMON.
alpar@40
   303
*/
alpar@40
   304
alpar@40
   305
/**
alpar@40
   306
@defgroup search Graph Search
alpar@40
   307
@ingroup algs
kpeter@50
   308
\brief Common graph search algorithms.
alpar@40
   309
kpeter@606
   310
This group contains the common graph search algorithms, namely
kpeter@802
   311
\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
kpeter@802
   312
\ref clrs01algorithms.
alpar@40
   313
*/
alpar@40
   314
alpar@40
   315
/**
kpeter@314
   316
@defgroup shortest_path Shortest Path Algorithms
alpar@40
   317
@ingroup algs
kpeter@50
   318
\brief Algorithms for finding shortest paths.
alpar@40
   319
kpeter@802
   320
This group contains the algorithms for finding shortest paths in digraphs
kpeter@802
   321
\ref clrs01algorithms.
kpeter@422
   322
kpeter@422
   323
 - \ref Dijkstra algorithm for finding shortest paths from a source node
kpeter@422
   324
   when all arc lengths are non-negative.
kpeter@422
   325
 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
kpeter@422
   326
   from a source node when arc lenghts can be either positive or negative,
kpeter@422
   327
   but the digraph should not contain directed cycles with negative total
kpeter@422
   328
   length.
kpeter@422
   329
 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
kpeter@422
   330
   for solving the \e all-pairs \e shortest \e paths \e problem when arc
kpeter@422
   331
   lenghts can be either positive or negative, but the digraph should
kpeter@422
   332
   not contain directed cycles with negative total length.
kpeter@422
   333
 - \ref Suurballe A successive shortest path algorithm for finding
kpeter@422
   334
   arc-disjoint paths between two nodes having minimum total length.
alpar@40
   335
*/
alpar@40
   336
alpar@209
   337
/**
kpeter@761
   338
@defgroup spantree Minimum Spanning Tree Algorithms
kpeter@761
   339
@ingroup algs
kpeter@761
   340
\brief Algorithms for finding minimum cost spanning trees and arborescences.
kpeter@761
   341
kpeter@761
   342
This group contains the algorithms for finding minimum cost spanning
kpeter@802
   343
trees and arborescences \ref clrs01algorithms.
kpeter@761
   344
*/
kpeter@761
   345
kpeter@761
   346
/**
kpeter@314
   347
@defgroup max_flow Maximum Flow Algorithms
alpar@209
   348
@ingroup algs
kpeter@50
   349
\brief Algorithms for finding maximum flows.
alpar@40
   350
kpeter@606
   351
This group contains the algorithms for finding maximum flows and
kpeter@802
   352
feasible circulations \ref clrs01algorithms, \ref amo93networkflows.
alpar@40
   353
kpeter@422
   354
The \e maximum \e flow \e problem is to find a flow of maximum value between
kpeter@422
   355
a single source and a single target. Formally, there is a \f$G=(V,A)\f$
kpeter@656
   356
digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
kpeter@422
   357
\f$s, t \in V\f$ source and target nodes.
kpeter@656
   358
A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
kpeter@422
   359
following optimization problem.
alpar@40
   360
kpeter@656
   361
\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
kpeter@656
   362
\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
kpeter@656
   363
    \quad \forall u\in V\setminus\{s,t\} \f]
kpeter@656
   364
\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
alpar@40
   365
kpeter@50
   366
LEMON contains several algorithms for solving maximum flow problems:
kpeter@802
   367
- \ref EdmondsKarp Edmonds-Karp algorithm
kpeter@802
   368
  \ref edmondskarp72theoretical.
kpeter@802
   369
- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
kpeter@802
   370
  \ref goldberg88newapproach.
kpeter@802
   371
- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
kpeter@802
   372
  \ref dinic70algorithm, \ref sleator83dynamic.
kpeter@802
   373
- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
kpeter@802
   374
  \ref goldberg88newapproach, \ref sleator83dynamic.
alpar@40
   375
kpeter@802
   376
In most cases the \ref Preflow algorithm provides the
kpeter@422
   377
fastest method for computing a maximum flow. All implementations
kpeter@698
   378
also provide functions to query the minimum cut, which is the dual
kpeter@698
   379
problem of maximum flow.
kpeter@698
   380
deba@948
   381
\ref Circulation is a preflow push-relabel algorithm implemented directly
kpeter@698
   382
for finding feasible circulations, which is a somewhat different problem,
kpeter@698
   383
but it is strongly related to maximum flow.
kpeter@698
   384
For more information, see \ref Circulation.
alpar@40
   385
*/
alpar@40
   386
alpar@40
   387
/**
kpeter@710
   388
@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
alpar@40
   389
@ingroup algs
alpar@40
   390
kpeter@50
   391
\brief Algorithms for finding minimum cost flows and circulations.
alpar@40
   392
kpeter@656
   393
This group contains the algorithms for finding minimum cost flows and
kpeter@802
   394
circulations \ref amo93networkflows. For more information about this
kpeter@802
   395
problem and its dual solution, see \ref min_cost_flow
kpeter@802
   396
"Minimum Cost Flow Problem".
kpeter@422
   397
kpeter@710
   398
LEMON contains several algorithms for this problem.
kpeter@656
   399
 - \ref NetworkSimplex Primal Network Simplex algorithm with various
kpeter@802
   400
   pivot strategies \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
kpeter@879
   401
 - \ref CostScaling Cost Scaling algorithm based on push/augment and
kpeter@879
   402
   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
kpeter@802
   403
   \ref bunnagel98efficient.
kpeter@879
   404
 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
kpeter@879
   405
   shortest path method \ref edmondskarp72theoretical.
kpeter@879
   406
 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
kpeter@879
   407
   strongly polynomial \ref klein67primal, \ref goldberg89cyclecanceling.
kpeter@656
   408
kpeter@1023
   409
In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
kpeter@1023
   410
implementations, but the other two algorithms could be faster in special cases.
kpeter@656
   411
For example, if the total supply and/or capacities are rather small,
kpeter@1023
   412
\ref CapacityScaling is usually the fastest algorithm (without effective scaling).
alpar@40
   413
*/
alpar@40
   414
alpar@40
   415
/**
kpeter@314
   416
@defgroup min_cut Minimum Cut Algorithms
alpar@209
   417
@ingroup algs
alpar@40
   418
kpeter@50
   419
\brief Algorithms for finding minimum cut in graphs.
alpar@40
   420
kpeter@606
   421
This group contains the algorithms for finding minimum cut in graphs.
alpar@40
   422
kpeter@422
   423
The \e minimum \e cut \e problem is to find a non-empty and non-complete
kpeter@422
   424
\f$X\f$ subset of the nodes with minimum overall capacity on
kpeter@422
   425
outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
kpeter@422
   426
\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
kpeter@50
   427
cut is the \f$X\f$ solution of the next optimization problem:
alpar@40
   428
alpar@210
   429
\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
kpeter@760
   430
    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
alpar@40
   431
kpeter@50
   432
LEMON contains several algorithms related to minimum cut problems:
alpar@40
   433
kpeter@422
   434
- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
kpeter@422
   435
  in directed graphs.
kpeter@422
   436
- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
kpeter@422
   437
  calculating minimum cut in undirected graphs.
kpeter@606
   438
- \ref GomoryHu "Gomory-Hu tree computation" for calculating
kpeter@422
   439
  all-pairs minimum cut in undirected graphs.
alpar@40
   440
alpar@40
   441
If you want to find minimum cut just between two distinict nodes,
kpeter@422
   442
see the \ref max_flow "maximum flow problem".
alpar@40
   443
*/
alpar@40
   444
alpar@40
   445
/**
kpeter@815
   446
@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
alpar@40
   447
@ingroup algs
kpeter@815
   448
\brief Algorithms for finding minimum mean cycles.
alpar@40
   449
kpeter@818
   450
This group contains the algorithms for finding minimum mean cycles
kpeter@818
   451
\ref clrs01algorithms, \ref amo93networkflows.
alpar@40
   452
kpeter@815
   453
The \e minimum \e mean \e cycle \e problem is to find a directed cycle
kpeter@815
   454
of minimum mean length (cost) in a digraph.
kpeter@815
   455
The mean length of a cycle is the average length of its arcs, i.e. the
kpeter@815
   456
ratio between the total length of the cycle and the number of arcs on it.
alpar@40
   457
kpeter@815
   458
This problem has an important connection to \e conservative \e length
kpeter@815
   459
\e functions, too. A length function on the arcs of a digraph is called
kpeter@815
   460
conservative if and only if there is no directed cycle of negative total
kpeter@815
   461
length. For an arbitrary length function, the negative of the minimum
kpeter@815
   462
cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
kpeter@815
   463
arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
kpeter@815
   464
function.
alpar@40
   465
kpeter@815
   466
LEMON contains three algorithms for solving the minimum mean cycle problem:
kpeter@959
   467
- \ref KarpMmc Karp's original algorithm \ref amo93networkflows,
kpeter@818
   468
  \ref dasdan98minmeancycle.
kpeter@959
   469
- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
kpeter@818
   470
  version of Karp's algorithm \ref dasdan98minmeancycle.
kpeter@959
   471
- \ref HowardMmc Howard's policy iteration algorithm
kpeter@818
   472
  \ref dasdan98minmeancycle.
alpar@40
   473
kpeter@1023
   474
In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
kpeter@959
   475
most efficient one, though the best known theoretical bound on its running
kpeter@959
   476
time is exponential.
kpeter@959
   477
Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
kpeter@959
   478
run in time O(ne) and use space O(n<sup>2</sup>+e), but the latter one is
kpeter@959
   479
typically faster due to the applied early termination scheme.
alpar@40
   480
*/
alpar@40
   481
alpar@40
   482
/**
kpeter@314
   483
@defgroup matching Matching Algorithms
alpar@40
   484
@ingroup algs
kpeter@50
   485
\brief Algorithms for finding matchings in graphs and bipartite graphs.
alpar@40
   486
kpeter@637
   487
This group contains the algorithms for calculating
alpar@40
   488
matchings in graphs and bipartite graphs. The general matching problem is
kpeter@637
   489
finding a subset of the edges for which each node has at most one incident
kpeter@637
   490
edge.
alpar@209
   491
alpar@40
   492
There are several different algorithms for calculate matchings in
alpar@40
   493
graphs.  The matching problems in bipartite graphs are generally
alpar@40
   494
easier than in general graphs. The goal of the matching optimization
kpeter@422
   495
can be finding maximum cardinality, maximum weight or minimum cost
alpar@40
   496
matching. The search can be constrained to find perfect or
alpar@40
   497
maximum cardinality matching.
alpar@40
   498
kpeter@422
   499
The matching algorithms implemented in LEMON:
kpeter@422
   500
- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
kpeter@422
   501
  for calculating maximum cardinality matching in bipartite graphs.
kpeter@422
   502
- \ref PrBipartiteMatching Push-relabel algorithm
kpeter@422
   503
  for calculating maximum cardinality matching in bipartite graphs.
kpeter@422
   504
- \ref MaxWeightedBipartiteMatching
kpeter@422
   505
  Successive shortest path algorithm for calculating maximum weighted
kpeter@422
   506
  matching and maximum weighted bipartite matching in bipartite graphs.
kpeter@422
   507
- \ref MinCostMaxBipartiteMatching
kpeter@422
   508
  Successive shortest path algorithm for calculating minimum cost maximum
kpeter@422
   509
  matching in bipartite graphs.
kpeter@422
   510
- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
kpeter@422
   511
  maximum cardinality matching in general graphs.
kpeter@422
   512
- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
kpeter@422
   513
  maximum weighted matching in general graphs.
kpeter@422
   514
- \ref MaxWeightedPerfectMatching
kpeter@422
   515
  Edmond's blossom shrinking algorithm for calculating maximum weighted
kpeter@422
   516
  perfect matching in general graphs.
deba@948
   517
- \ref MaxFractionalMatching Push-relabel algorithm for calculating
deba@948
   518
  maximum cardinality fractional matching in general graphs.
deba@948
   519
- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
deba@948
   520
  maximum weighted fractional matching in general graphs.
deba@948
   521
- \ref MaxWeightedPerfectFractionalMatching
deba@948
   522
  Augmenting path algorithm for calculating maximum weighted
deba@948
   523
  perfect fractional matching in general graphs.
alpar@40
   524
alpar@943
   525
\image html matching.png
alpar@952
   526
\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
alpar@40
   527
*/
alpar@40
   528
alpar@40
   529
/**
kpeter@761
   530
@defgroup graph_properties Connectivity and Other Graph Properties
alpar@40
   531
@ingroup algs
kpeter@761
   532
\brief Algorithms for discovering the graph properties
alpar@40
   533
kpeter@761
   534
This group contains the algorithms for discovering the graph properties
kpeter@761
   535
like connectivity, bipartiteness, euler property, simplicity etc.
kpeter@761
   536
kpeter@761
   537
\image html connected_components.png
kpeter@761
   538
\image latex connected_components.eps "Connected components" width=\textwidth
kpeter@761
   539
*/
kpeter@761
   540
kpeter@761
   541
/**
kpeter@1023
   542
@defgroup planar Planar Embedding and Drawing
kpeter@761
   543
@ingroup algs
kpeter@761
   544
\brief Algorithms for planarity checking, embedding and drawing
kpeter@761
   545
kpeter@761
   546
This group contains the algorithms for planarity checking,
kpeter@761
   547
embedding and drawing.
kpeter@761
   548
kpeter@761
   549
\image html planar.png
kpeter@761
   550
\image latex planar.eps "Plane graph" width=\textwidth
kpeter@761
   551
*/
kpeter@761
   552
kpeter@761
   553
/**
kpeter@999
   554
@defgroup approx_algs Approximation Algorithms
kpeter@761
   555
@ingroup algs
kpeter@761
   556
\brief Approximation algorithms.
kpeter@761
   557
kpeter@761
   558
This group contains the approximation and heuristic algorithms
kpeter@761
   559
implemented in LEMON.
kpeter@999
   560
kpeter@999
   561
<b>Maximum Clique Problem</b>
kpeter@999
   562
  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
kpeter@999
   563
    Grosso, Locatelli, and Pullan.
alpar@40
   564
*/
alpar@40
   565
alpar@40
   566
/**
kpeter@314
   567
@defgroup auxalg Auxiliary Algorithms
alpar@40
   568
@ingroup algs
kpeter@50
   569
\brief Auxiliary algorithms implemented in LEMON.
alpar@40
   570
kpeter@606
   571
This group contains some algorithms implemented in LEMON
kpeter@50
   572
in order to make it easier to implement complex algorithms.
alpar@40
   573
*/
alpar@40
   574
alpar@40
   575
/**
alpar@40
   576
@defgroup gen_opt_group General Optimization Tools
kpeter@606
   577
\brief This group contains some general optimization frameworks
alpar@40
   578
implemented in LEMON.
alpar@40
   579
kpeter@606
   580
This group contains some general optimization frameworks
alpar@40
   581
implemented in LEMON.
alpar@40
   582
*/
alpar@40
   583
alpar@40
   584
/**
kpeter@802
   585
@defgroup lp_group LP and MIP Solvers
alpar@40
   586
@ingroup gen_opt_group
kpeter@802
   587
\brief LP and MIP solver interfaces for LEMON.
alpar@40
   588
kpeter@802
   589
This group contains LP and MIP solver interfaces for LEMON.
kpeter@802
   590
Various LP solvers could be used in the same manner with this
kpeter@802
   591
high-level interface.
kpeter@802
   592
kpeter@802
   593
The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
kpeter@802
   594
\ref cplex, \ref soplex.
alpar@40
   595
*/
alpar@40
   596
alpar@209
   597
/**
kpeter@314
   598
@defgroup lp_utils Tools for Lp and Mip Solvers
alpar@40
   599
@ingroup lp_group
kpeter@50
   600
\brief Helper tools to the Lp and Mip solvers.
alpar@40
   601
alpar@40
   602
This group adds some helper tools to general optimization framework
alpar@40
   603
implemented in LEMON.
alpar@40
   604
*/
alpar@40
   605
alpar@40
   606
/**
alpar@40
   607
@defgroup metah Metaheuristics
alpar@40
   608
@ingroup gen_opt_group
alpar@40
   609
\brief Metaheuristics for LEMON library.
alpar@40
   610
kpeter@606
   611
This group contains some metaheuristic optimization tools.
alpar@40
   612
*/
alpar@40
   613
alpar@40
   614
/**
alpar@209
   615
@defgroup utils Tools and Utilities
kpeter@50
   616
\brief Tools and utilities for programming in LEMON
alpar@40
   617
kpeter@50
   618
Tools and utilities for programming in LEMON.
alpar@40
   619
*/
alpar@40
   620
alpar@40
   621
/**
alpar@40
   622
@defgroup gutils Basic Graph Utilities
alpar@40
   623
@ingroup utils
kpeter@50
   624
\brief Simple basic graph utilities.
alpar@40
   625
kpeter@606
   626
This group contains some simple basic graph utilities.
alpar@40
   627
*/
alpar@40
   628
alpar@40
   629
/**
alpar@40
   630
@defgroup misc Miscellaneous Tools
alpar@40
   631
@ingroup utils
kpeter@50
   632
\brief Tools for development, debugging and testing.
kpeter@50
   633
kpeter@606
   634
This group contains several useful tools for development,
alpar@40
   635
debugging and testing.
alpar@40
   636
*/
alpar@40
   637
alpar@40
   638
/**
kpeter@314
   639
@defgroup timecount Time Measuring and Counting
alpar@40
   640
@ingroup misc
kpeter@50
   641
\brief Simple tools for measuring the performance of algorithms.
kpeter@50
   642
kpeter@606
   643
This group contains simple tools for measuring the performance
alpar@40
   644
of algorithms.
alpar@40
   645
*/
alpar@40
   646
alpar@40
   647
/**
alpar@40
   648
@defgroup exceptions Exceptions
alpar@40
   649
@ingroup utils
kpeter@50
   650
\brief Exceptions defined in LEMON.
kpeter@50
   651
kpeter@606
   652
This group contains the exceptions defined in LEMON.
alpar@40
   653
*/
alpar@40
   654
alpar@40
   655
/**
alpar@40
   656
@defgroup io_group Input-Output
kpeter@50
   657
\brief Graph Input-Output methods
alpar@40
   658
kpeter@606
   659
This group contains the tools for importing and exporting graphs
kpeter@314
   660
and graph related data. Now it supports the \ref lgf-format
kpeter@314
   661
"LEMON Graph Format", the \c DIMACS format and the encapsulated
kpeter@314
   662
postscript (EPS) format.
alpar@40
   663
*/
alpar@40
   664
alpar@40
   665
/**
kpeter@363
   666
@defgroup lemon_io LEMON Graph Format
alpar@40
   667
@ingroup io_group
kpeter@314
   668
\brief Reading and writing LEMON Graph Format.
alpar@40
   669
kpeter@606
   670
This group contains methods for reading and writing
ladanyi@236
   671
\ref lgf-format "LEMON Graph Format".
alpar@40
   672
*/
alpar@40
   673
alpar@40
   674
/**
kpeter@314
   675
@defgroup eps_io Postscript Exporting
alpar@40
   676
@ingroup io_group
alpar@40
   677
\brief General \c EPS drawer and graph exporter
alpar@40
   678
kpeter@606
   679
This group contains general \c EPS drawing methods and special
alpar@209
   680
graph exporting tools.
alpar@40
   681
*/
alpar@40
   682
alpar@40
   683
/**
kpeter@761
   684
@defgroup dimacs_group DIMACS Format
kpeter@403
   685
@ingroup io_group
kpeter@403
   686
\brief Read and write files in DIMACS format
kpeter@403
   687
kpeter@403
   688
Tools to read a digraph from or write it to a file in DIMACS format data.
kpeter@403
   689
*/
kpeter@403
   690
kpeter@403
   691
/**
kpeter@363
   692
@defgroup nauty_group NAUTY Format
kpeter@363
   693
@ingroup io_group
kpeter@363
   694
\brief Read \e Nauty format
kpeter@403
   695
kpeter@363
   696
Tool to read graphs from \e Nauty format data.
kpeter@363
   697
*/
kpeter@363
   698
kpeter@363
   699
/**
alpar@40
   700
@defgroup concept Concepts
alpar@40
   701
\brief Skeleton classes and concept checking classes
alpar@40
   702
kpeter@606
   703
This group contains the data/algorithm skeletons and concept checking
alpar@40
   704
classes implemented in LEMON.
alpar@40
   705
alpar@40
   706
The purpose of the classes in this group is fourfold.
alpar@209
   707
kpeter@318
   708
- These classes contain the documentations of the %concepts. In order
alpar@40
   709
  to avoid document multiplications, an implementation of a concept
alpar@40
   710
  simply refers to the corresponding concept class.
alpar@40
   711
alpar@40
   712
- These classes declare every functions, <tt>typedef</tt>s etc. an
kpeter@318
   713
  implementation of the %concepts should provide, however completely
alpar@40
   714
  without implementations and real data structures behind the
alpar@40
   715
  interface. On the other hand they should provide nothing else. All
alpar@40
   716
  the algorithms working on a data structure meeting a certain concept
alpar@40
   717
  should compile with these classes. (Though it will not run properly,
alpar@40
   718
  of course.) In this way it is easily to check if an algorithm
alpar@40
   719
  doesn't use any extra feature of a certain implementation.
alpar@40
   720
alpar@40
   721
- The concept descriptor classes also provide a <em>checker class</em>
kpeter@50
   722
  that makes it possible to check whether a certain implementation of a
alpar@40
   723
  concept indeed provides all the required features.
alpar@40
   724
alpar@40
   725
- Finally, They can serve as a skeleton of a new implementation of a concept.
alpar@40
   726
*/
alpar@40
   727
alpar@40
   728
/**
alpar@40
   729
@defgroup graph_concepts Graph Structure Concepts
alpar@40
   730
@ingroup concept
alpar@40
   731
\brief Skeleton and concept checking classes for graph structures
alpar@40
   732
kpeter@782
   733
This group contains the skeletons and concept checking classes of
kpeter@782
   734
graph structures.
alpar@40
   735
*/
alpar@40
   736
kpeter@314
   737
/**
kpeter@314
   738
@defgroup map_concepts Map Concepts
kpeter@314
   739
@ingroup concept
kpeter@314
   740
\brief Skeleton and concept checking classes for maps
kpeter@314
   741
kpeter@606
   742
This group contains the skeletons and concept checking classes of maps.
alpar@40
   743
*/
alpar@40
   744
alpar@40
   745
/**
kpeter@761
   746
@defgroup tools Standalone Utility Applications
kpeter@761
   747
kpeter@761
   748
Some utility applications are listed here.
kpeter@761
   749
kpeter@761
   750
The standard compilation procedure (<tt>./configure;make</tt>) will compile
kpeter@761
   751
them, as well.
kpeter@761
   752
*/
kpeter@761
   753
kpeter@761
   754
/**
alpar@40
   755
\anchor demoprograms
alpar@40
   756
kpeter@422
   757
@defgroup demos Demo Programs
alpar@40
   758
alpar@40
   759
Some demo programs are listed here. Their full source codes can be found in
alpar@40
   760
the \c demo subdirectory of the source tree.
alpar@40
   761
ladanyi@611
   762
In order to compile them, use the <tt>make demo</tt> or the
ladanyi@611
   763
<tt>make check</tt> commands.
alpar@40
   764
*/
alpar@40
   765
kpeter@422
   766
}