COIN-OR::LEMON - Graph Library

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