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) 2003-2013
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
115Since the adaptor classes conform to the \ref graph_concepts "graph concepts",
116an adaptor can even be applied to another one.
117The following image illustrates a situation when a \ref SubDigraph adaptor
118is applied on a digraph and \ref Undirector is applied on the subgraph.
119
120\image html adaptors2.png
121\image latex adaptors2.eps "Using graph adaptors" width=\textwidth
122
123The behavior of graph adaptors can be very different. Some of them keep
124capabilities of the original graph while in other cases this would be
125meaningless. This means that the concepts that they meet depend
126on the graph adaptor, and the wrapped graph.
127For example, if an arc of a reversed digraph is deleted, this is carried
128out by deleting the corresponding arc of the original digraph, thus the
129adaptor modifies the original digraph.
130However in case of a residual digraph, this operation has no sense.
131
132Let us stand one more example here to simplify your work.
133ReverseDigraph has constructor
134\code
135ReverseDigraph(Digraph& digraph);
136\endcode
137This means that in a situation, when a <tt>const %ListDigraph&</tt>
138reference to a graph is given, then it have to be instantiated with
139<tt>Digraph=const %ListDigraph</tt>.
140\code
141int algorithm1(const ListDigraph& g) {
142  ReverseDigraph<const ListDigraph> rg(g);
143  return algorithm2(rg);
144}
145\endcode
146*/
147
148/**
149@defgroup maps Maps
150@ingroup datas
151\brief Map structures implemented in LEMON.
152
153This group contains the map structures implemented in LEMON.
154
155LEMON provides several special purpose maps and map adaptors that e.g. combine
156new maps from existing ones.
157
158<b>See also:</b> \ref map_concepts "Map Concepts".
159*/
160
161/**
162@defgroup graph_maps Graph Maps
163@ingroup maps
164\brief Special graph-related maps.
165
166This group contains maps that are specifically designed to assign
167values to the nodes and arcs/edges of graphs.
168
169If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
170\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
171*/
172
173/**
174\defgroup map_adaptors Map Adaptors
175\ingroup maps
176\brief Tools to create new maps from existing ones
177
178This group contains map adaptors that are used to create "implicit"
179maps from other maps.
180
181Most of them are \ref concepts::ReadMap "read-only maps".
182They can make arithmetic and logical operations between one or two maps
183(negation, shifting, addition, multiplication, logical 'and', 'or',
184'not' etc.) or e.g. convert a map to another one of different Value type.
185
186The typical usage of this classes is passing implicit maps to
187algorithms.  If a function type algorithm is called then the function
188type map adaptors can be used comfortable. For example let's see the
189usage of map adaptors with the \c graphToEps() function.
190\code
191  Color nodeColor(int deg) {
192    if (deg >= 2) {
193      return Color(0.5, 0.0, 0.5);
194    } else if (deg == 1) {
195      return Color(1.0, 0.5, 1.0);
196    } else {
197      return Color(0.0, 0.0, 0.0);
198    }
199  }
200
201  Digraph::NodeMap<int> degree_map(graph);
202
203  graphToEps(graph, "graph.eps")
204    .coords(coords).scaleToA4().undirected()
205    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
206    .run();
207\endcode
208The \c functorToMap() function makes an \c int to \c Color map from the
209\c nodeColor() function. The \c composeMap() compose the \c degree_map
210and the previously created map. The composed map is a proper function to
211get the color of each node.
212
213The usage with class type algorithms is little bit harder. In this
214case the function type map adaptors can not be used, because the
215function map adaptors give back temporary objects.
216\code
217  Digraph graph;
218
219  typedef Digraph::ArcMap<double> DoubleArcMap;
220  DoubleArcMap length(graph);
221  DoubleArcMap speed(graph);
222
223  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
224  TimeMap time(length, speed);
225
226  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
227  dijkstra.run(source, target);
228\endcode
229We have a length map and a maximum speed map on the arcs of a digraph.
230The minimum time to pass the arc can be calculated as the division of
231the two maps which can be done implicitly with the \c DivMap template
232class. We use the implicit minimum time map as the length map of the
233\c Dijkstra algorithm.
234*/
235
236/**
237@defgroup paths Path Structures
238@ingroup datas
239\brief %Path structures implemented in LEMON.
240
241This group contains the path structures implemented in LEMON.
242
243LEMON provides flexible data structures to work with paths.
244All of them have similar interfaces and they can be copied easily with
245assignment operators and copy constructors. This makes it easy and
246efficient to have e.g. the Dijkstra algorithm to store its result in
247any kind of path structure.
248
249\sa \ref concepts::Path "Path concept"
250*/
251
252/**
253@defgroup heaps Heap Structures
254@ingroup datas
255\brief %Heap structures implemented in LEMON.
256
257This group contains the heap structures implemented in LEMON.
258
259LEMON provides several heap classes. They are efficient implementations
260of the abstract data type \e priority \e queue. They store items with
261specified values called \e priorities in such a way that finding and
262removing the item with minimum priority are efficient.
263The basic operations are adding and erasing items, changing the priority
264of an item, etc.
265
266Heaps are crucial in several algorithms, such as Dijkstra and Prim.
267The heap implementations have the same interface, thus any of them can be
268used easily in such algorithms.
269
270\sa \ref concepts::Heap "Heap concept"
271*/
272
273/**
274@defgroup auxdat Auxiliary Data Structures
275@ingroup datas
276\brief Auxiliary data structures implemented in LEMON.
277
278This group contains some data structures implemented in LEMON in
279order to make it easier to implement combinatorial algorithms.
280*/
281
282/**
283@defgroup geomdat Geometric Data Structures
284@ingroup auxdat
285\brief Geometric data structures implemented in LEMON.
286
287This group contains geometric data structures implemented in LEMON.
288
289 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
290   vector with the usual operations.
291 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
292   rectangular bounding box of a set of \ref lemon::dim2::Point
293   "dim2::Point"'s.
294*/
295
296/**
297@defgroup algs Algorithms
298\brief This group contains the several algorithms
299implemented in LEMON.
300
301This group contains the several algorithms
302implemented in LEMON.
303*/
304
305/**
306@defgroup search Graph Search
307@ingroup algs
308\brief Common graph search algorithms.
309
310This group contains the common graph search algorithms, namely
311\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
312\cite clrs01algorithms.
313*/
314
315/**
316@defgroup shortest_path Shortest Path Algorithms
317@ingroup algs
318\brief Algorithms for finding shortest paths.
319
320This group contains the algorithms for finding shortest paths in digraphs
321\cite clrs01algorithms.
322
323 - \ref Dijkstra algorithm for finding shortest paths from a source node
324   when all arc lengths are non-negative.
325 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
326   from a source node when arc lenghts can be either positive or negative,
327   but the digraph should not contain directed cycles with negative total
328   length.
329 - \ref Suurballe A successive shortest path algorithm for finding
330   arc-disjoint paths between two nodes having minimum total length.
331*/
332
333/**
334@defgroup spantree Minimum Spanning Tree Algorithms
335@ingroup algs
336\brief Algorithms for finding minimum cost spanning trees and arborescences.
337
338This group contains the algorithms for finding minimum cost spanning
339trees and arborescences \cite clrs01algorithms.
340*/
341
342/**
343@defgroup max_flow Maximum Flow Algorithms
344@ingroup algs
345\brief Algorithms for finding maximum flows.
346
347This group contains the algorithms for finding maximum flows and
348feasible circulations \cite clrs01algorithms, \cite amo93networkflows.
349
350The \e maximum \e flow \e problem is to find a flow of maximum value between
351a single source and a single target. Formally, there is a \f$G=(V,A)\f$
352digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
353\f$s, t \in V\f$ source and target nodes.
354A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
355following optimization problem.
356
357\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
358\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
359    \quad \forall u\in V\setminus\{s,t\} \f]
360\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
361
362\ref Preflow is an efficient implementation of Goldberg-Tarjan's
363preflow push-relabel algorithm \cite goldberg88newapproach for finding
364maximum flows. It also provides functions to query the minimum cut,
365which is the dual problem of maximum flow.
366
367\ref Circulation is a preflow push-relabel algorithm implemented directly
368for finding feasible circulations, which is a somewhat different problem,
369but it is strongly related to maximum flow.
370For more information, see \ref Circulation.
371*/
372
373/**
374@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
375@ingroup algs
376
377\brief Algorithms for finding minimum cost flows and circulations.
378
379This group contains the algorithms for finding minimum cost flows and
380circulations \cite amo93networkflows. For more information about this
381problem and its dual solution, see: \ref min_cost_flow
382"Minimum Cost Flow Problem".
383
384LEMON contains several algorithms for this problem.
385 - \ref NetworkSimplex Primal Network Simplex algorithm with various
386   pivot strategies \cite dantzig63linearprog, \cite kellyoneill91netsimplex.
387 - \ref CostScaling Cost Scaling algorithm based on push/augment and
388   relabel operations \cite goldberg90approximation, \cite goldberg97efficient,
389   \cite bunnagel98efficient.
390 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
391   shortest path method \cite edmondskarp72theoretical.
392 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
393   strongly polynomial \cite klein67primal, \cite goldberg89cyclecanceling.
394
395In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
396implementations.
397\ref NetworkSimplex is usually the fastest on relatively small graphs (up to
398several thousands of nodes) and on dense graphs, while \ref CostScaling is
399typically more efficient on large graphs (e.g. hundreds of thousands of
400nodes or above), especially if they are sparse.
401However, other algorithms could be faster in special cases.
402For example, if the total supply and/or capacities are rather small,
403\ref CapacityScaling is usually the fastest algorithm
404(without effective scaling).
405
406These classes are intended to be used with integer-valued input data
407(capacities, supply values, and costs), except for \ref CapacityScaling,
408which is capable of handling real-valued arc costs (other numerical
409data are required to be integer).
410
411For more details about these implementations and for a comprehensive
412experimental study, see the paper \cite KiralyKovacs12MCF.
413It also compares these codes to other publicly available
414minimum cost flow solvers.
415*/
416
417/**
418@defgroup min_cut Minimum Cut Algorithms
419@ingroup algs
420
421\brief Algorithms for finding minimum cut in graphs.
422
423This group contains the algorithms for finding minimum cut in graphs.
424
425The \e minimum \e cut \e problem is to find a non-empty and non-complete
426\f$X\f$ subset of the nodes with minimum overall capacity on
427outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
428\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
429cut is the \f$X\f$ solution of the next optimization problem:
430
431\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
432    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
433
434LEMON contains several algorithms related to minimum cut problems:
435
436- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
437  in directed graphs.
438- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
439  calculating minimum cut in undirected graphs.
440- \ref GomoryHu "Gomory-Hu tree computation" for calculating
441  all-pairs minimum cut in undirected graphs.
442
443If you want to find minimum cut just between two distinict nodes,
444see the \ref max_flow "maximum flow problem".
445*/
446
447/**
448@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
449@ingroup algs
450\brief Algorithms for finding minimum mean cycles.
451
452This group contains the algorithms for finding minimum mean cycles
453\cite amo93networkflows, \cite karp78characterization.
454
455The \e minimum \e mean \e cycle \e problem is to find a directed cycle
456of minimum mean length (cost) in a digraph.
457The mean length of a cycle is the average length of its arcs, i.e. the
458ratio between the total length of the cycle and the number of arcs on it.
459
460This problem has an important connection to \e conservative \e length
461\e functions, too. A length function on the arcs of a digraph is called
462conservative if and only if there is no directed cycle of negative total
463length. For an arbitrary length function, the negative of the minimum
464cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
465arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
466function.
467
468LEMON contains three algorithms for solving the minimum mean cycle problem:
469- \ref KarpMmc Karp's original algorithm \cite karp78characterization.
470- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
471  version of Karp's algorithm \cite hartmann93finding.
472- \ref HowardMmc Howard's policy iteration algorithm
473  \cite dasdan98minmeancycle, \cite dasdan04experimental.
474
475In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
476most efficient one, though the best known theoretical bound on its running
477time is exponential.
478Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
479run in time O(nm) and use space O(n<sup>2</sup>+m).
480*/
481
482/**
483@defgroup matching Matching Algorithms
484@ingroup algs
485\brief Algorithms for finding matchings in graphs and bipartite graphs.
486
487This group contains the algorithms for calculating
488matchings in graphs and bipartite graphs. The general matching problem is
489finding a subset of the edges for which each node has at most one incident
490edge.
491
492There are several different algorithms for calculate matchings in
493graphs.  The matching problems in bipartite graphs are generally
494easier than in general graphs. The goal of the matching optimization
495can be finding maximum cardinality, maximum weight or minimum cost
496matching. The search can be constrained to find perfect or
497maximum cardinality matching.
498
499The matching algorithms implemented in LEMON:
500- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
501  maximum cardinality matching in general graphs.
502- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
503  maximum weighted matching in general graphs.
504- \ref MaxWeightedPerfectMatching
505  Edmond's blossom shrinking algorithm for calculating maximum weighted
506  perfect matching in general graphs.
507- \ref MaxFractionalMatching Push-relabel algorithm for calculating
508  maximum cardinality fractional matching in general graphs.
509- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
510  maximum weighted fractional matching in general graphs.
511- \ref MaxWeightedPerfectFractionalMatching
512  Augmenting path algorithm for calculating maximum weighted
513  perfect fractional matching in general graphs.
514
515\image html matching.png
516\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
517*/
518
519/**
520@defgroup graph_properties Connectivity and Other Graph Properties
521@ingroup algs
522\brief Algorithms for discovering the graph properties
523
524This group contains the algorithms for discovering the graph properties
525like connectivity, bipartiteness, euler property, simplicity etc.
526
527\image html connected_components.png
528\image latex connected_components.eps "Connected components" width=\textwidth
529*/
530
531/**
532@defgroup planar Planar Embedding and Drawing
533@ingroup algs
534\brief Algorithms for planarity checking, embedding and drawing
535
536This group contains the algorithms for planarity checking,
537embedding and drawing.
538
539\image html planar.png
540\image latex planar.eps "Plane graph" width=\textwidth
541*/
542
543/**
544@defgroup tsp Traveling Salesman Problem
545@ingroup algs
546\brief Algorithms for the symmetric traveling salesman problem
547
548This group contains basic heuristic algorithms for the the symmetric
549\e traveling \e salesman \e problem (TSP).
550Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
551the problem is to find a shortest possible tour that visits each node exactly
552once (i.e. the minimum cost Hamiltonian cycle).
553
554These TSP algorithms are intended to be used with a \e metric \e cost
555\e function, i.e. the edge costs should satisfy the triangle inequality.
556Otherwise the algorithms could yield worse results.
557
558LEMON provides five well-known heuristics for solving symmetric TSP:
559 - \ref NearestNeighborTsp Neareast neighbor algorithm
560 - \ref GreedyTsp Greedy algorithm
561 - \ref InsertionTsp Insertion heuristic (with four selection methods)
562 - \ref ChristofidesTsp Christofides algorithm
563 - \ref Opt2Tsp 2-opt algorithm
564
565\ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
566solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
567
568\ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
569approximation factor: 3/2.
570
571\ref Opt2Tsp usually provides the best results in practice, but
572it is the slowest method. It can also be used to improve given tours,
573for example, the results of other algorithms.
574
575\image html tsp.png
576\image latex tsp.eps "Traveling salesman problem" width=\textwidth
577*/
578
579/**
580@defgroup approx_algs Approximation Algorithms
581@ingroup algs
582\brief Approximation algorithms.
583
584This group contains the approximation and heuristic algorithms
585implemented in LEMON.
586
587<b>Maximum Clique Problem</b>
588  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
589    Grosso, Locatelli, and Pullan.
590*/
591
592/**
593@defgroup auxalg Auxiliary Algorithms
594@ingroup algs
595\brief Auxiliary algorithms implemented in LEMON.
596
597This group contains some algorithms implemented in LEMON
598in order to make it easier to implement complex algorithms.
599*/
600
601/**
602@defgroup gen_opt_group General Optimization Tools
603\brief This group contains some general optimization frameworks
604implemented in LEMON.
605
606This group contains some general optimization frameworks
607implemented in LEMON.
608*/
609
610/**
611@defgroup lp_group LP and MIP Solvers
612@ingroup gen_opt_group
613\brief LP and MIP solver interfaces for LEMON.
614
615This group contains LP and MIP solver interfaces for LEMON.
616Various LP solvers could be used in the same manner with this
617high-level interface.
618
619The currently supported solvers are \cite glpk, \cite clp, \cite cbc,
620\cite cplex, \cite soplex.
621*/
622
623/**
624@defgroup utils Tools and Utilities
625\brief Tools and utilities for programming in LEMON
626
627Tools and utilities for programming in LEMON.
628*/
629
630/**
631@defgroup gutils Basic Graph Utilities
632@ingroup utils
633\brief Simple basic graph utilities.
634
635This group contains some simple basic graph utilities.
636*/
637
638/**
639@defgroup misc Miscellaneous Tools
640@ingroup utils
641\brief Tools for development, debugging and testing.
642
643This group contains several useful tools for development,
644debugging and testing.
645*/
646
647/**
648@defgroup timecount Time Measuring and Counting
649@ingroup misc
650\brief Simple tools for measuring the performance of algorithms.
651
652This group contains simple tools for measuring the performance
653of algorithms.
654*/
655
656/**
657@defgroup exceptions Exceptions
658@ingroup utils
659\brief Exceptions defined in LEMON.
660
661This group contains the exceptions defined in LEMON.
662*/
663
664/**
665@defgroup io_group Input-Output
666\brief Graph Input-Output methods
667
668This group contains the tools for importing and exporting graphs
669and graph related data. Now it supports the \ref lgf-format
670"LEMON Graph Format", the \c DIMACS format and the encapsulated
671postscript (EPS) format.
672*/
673
674/**
675@defgroup lemon_io LEMON Graph Format
676@ingroup io_group
677\brief Reading and writing LEMON Graph Format.
678
679This group contains methods for reading and writing
680\ref lgf-format "LEMON Graph Format".
681*/
682
683/**
684@defgroup eps_io Postscript Exporting
685@ingroup io_group
686\brief General \c EPS drawer and graph exporter
687
688This group contains general \c EPS drawing methods and special
689graph exporting tools.
690
691\image html graph_to_eps.png
692*/
693
694/**
695@defgroup dimacs_group DIMACS Format
696@ingroup io_group
697\brief Read and write files in DIMACS format
698
699Tools to read a digraph from or write it to a file in DIMACS format data.
700*/
701
702/**
703@defgroup nauty_group NAUTY Format
704@ingroup io_group
705\brief Read \e Nauty format
706
707Tool to read graphs from \e Nauty format data.
708*/
709
710/**
711@defgroup concept Concepts
712\brief Skeleton classes and concept checking classes
713
714This group contains the data/algorithm skeletons and concept checking
715classes implemented in LEMON.
716
717The purpose of the classes in this group is fourfold.
718
719- These classes contain the documentations of the %concepts. In order
720  to avoid document multiplications, an implementation of a concept
721  simply refers to the corresponding concept class.
722
723- These classes declare every functions, <tt>typedef</tt>s etc. an
724  implementation of the %concepts should provide, however completely
725  without implementations and real data structures behind the
726  interface. On the other hand they should provide nothing else. All
727  the algorithms working on a data structure meeting a certain concept
728  should compile with these classes. (Though it will not run properly,
729  of course.) In this way it is easily to check if an algorithm
730  doesn't use any extra feature of a certain implementation.
731
732- The concept descriptor classes also provide a <em>checker class</em>
733  that makes it possible to check whether a certain implementation of a
734  concept indeed provides all the required features.
735
736- Finally, They can serve as a skeleton of a new implementation of a concept.
737*/
738
739/**
740@defgroup graph_concepts Graph Structure Concepts
741@ingroup concept
742\brief Skeleton and concept checking classes for graph structures
743
744This group contains the skeletons and concept checking classes of
745graph structures.
746*/
747
748/**
749@defgroup map_concepts Map Concepts
750@ingroup concept
751\brief Skeleton and concept checking classes for maps
752
753This group contains the skeletons and concept checking classes of maps.
754*/
755
756/**
757@defgroup tools Standalone Utility Applications
758
759Some utility applications are listed here.
760
761The standard compilation procedure (<tt>./configure;make</tt>) will compile
762them, as well.
763*/
764
765/**
766\anchor demoprograms
767
768@defgroup demos Demo Programs
769
770Some demo programs are listed here. Their full source codes can be found in
771the \c demo subdirectory of the source tree.
772
773In order to compile them, use the <tt>make demo</tt> or the
774<tt>make check</tt> commands.
775*/
776
777}
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