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 matrices Matrices
298@ingroup auxdat
299\brief Two dimensional data storages implemented in LEMON.
300
301This group contains two dimensional data storages implemented in LEMON.
302*/
303
304/**
305@defgroup algs Algorithms
306\brief This group contains the several algorithms
307implemented in LEMON.
308
309This group contains the several algorithms
310implemented in LEMON.
311*/
312
313/**
314@defgroup search Graph Search
315@ingroup algs
316\brief Common graph search algorithms.
317
318This group contains the common graph search algorithms, namely
319\e breadth-first \e search (BFS) and \e depth-first \e search (DFS)
320\cite clrs01algorithms.
321*/
322
323/**
324@defgroup shortest_path Shortest Path Algorithms
325@ingroup algs
326\brief Algorithms for finding shortest paths.
327
328This group contains the algorithms for finding shortest paths in digraphs
329\cite clrs01algorithms.
330
331 - \ref Dijkstra algorithm for finding shortest paths from a source node
332   when all arc lengths are non-negative.
333 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
334   from a source node when arc lenghts can be either positive or negative,
335   but the digraph should not contain directed cycles with negative total
336   length.
337 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
338   for solving the \e all-pairs \e shortest \e paths \e problem when arc
339   lenghts can be either positive or negative, but the digraph should
340   not contain directed cycles with negative total length.
341 - \ref Suurballe A successive shortest path algorithm for finding
342   arc-disjoint paths between two nodes having minimum total length.
343*/
344
345/**
346@defgroup spantree Minimum Spanning Tree Algorithms
347@ingroup algs
348\brief Algorithms for finding minimum cost spanning trees and arborescences.
349
350This group contains the algorithms for finding minimum cost spanning
351trees and arborescences \cite clrs01algorithms.
352*/
353
354/**
355@defgroup max_flow Maximum Flow Algorithms
356@ingroup algs
357\brief Algorithms for finding maximum flows.
358
359This group contains the algorithms for finding maximum flows and
360feasible circulations \cite clrs01algorithms, \cite amo93networkflows.
361
362The \e maximum \e flow \e problem is to find a flow of maximum value between
363a single source and a single target. Formally, there is a \f$G=(V,A)\f$
364digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
365\f$s, t \in V\f$ source and target nodes.
366A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
367following optimization problem.
368
369\f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
370\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
371    \quad \forall u\in V\setminus\{s,t\} \f]
372\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
373
374LEMON contains several algorithms for solving maximum flow problems:
375- \ref EdmondsKarp Edmonds-Karp algorithm
376  \cite edmondskarp72theoretical.
377- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
378  \cite goldberg88newapproach.
379- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
380  \cite dinic70algorithm, \cite sleator83dynamic.
381- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
382  \cite goldberg88newapproach, \cite sleator83dynamic.
383
384In most cases the \ref Preflow algorithm provides the
385fastest method for computing a maximum flow. All implementations
386also provide functions to query the minimum cut, which is the dual
387problem of maximum flow.
388
389\ref Circulation is a preflow push-relabel algorithm implemented directly
390for finding feasible circulations, which is a somewhat different problem,
391but it is strongly related to maximum flow.
392For more information, see \ref Circulation.
393*/
394
395/**
396@defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
397@ingroup algs
398
399\brief Algorithms for finding minimum cost flows and circulations.
400
401This group contains the algorithms for finding minimum cost flows and
402circulations \cite amo93networkflows. For more information about this
403problem and its dual solution, see: \ref min_cost_flow
404"Minimum Cost Flow Problem".
405
406LEMON contains several algorithms for this problem.
407 - \ref NetworkSimplex Primal Network Simplex algorithm with various
408   pivot strategies \cite dantzig63linearprog, \cite kellyoneill91netsimplex.
409 - \ref CostScaling Cost Scaling algorithm based on push/augment and
410   relabel operations \cite goldberg90approximation, \cite goldberg97efficient,
411   \cite bunnagel98efficient.
412 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
413   shortest path method \cite edmondskarp72theoretical.
414 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
415   strongly polynomial \cite klein67primal, \cite goldberg89cyclecanceling.
416
417In general, \ref NetworkSimplex and \ref CostScaling are the most efficient
418implementations.
419\ref NetworkSimplex is usually the fastest on relatively small graphs (up to
420several thousands of nodes) and on dense graphs, while \ref CostScaling is
421typically more efficient on large graphs (e.g. hundreds of thousands of
422nodes or above), especially if they are sparse.
423However, other algorithms could be faster in special cases.
424For example, if the total supply and/or capacities are rather small,
425\ref CapacityScaling is usually the fastest algorithm (without effective scaling).
426
427These classes are intended to be used with integer-valued input data
428(capacities, supply values, and costs), except for \ref CapacityScaling,
429which is capable of handling real-valued arc costs (other numerical
430data are required to be integer).
431
432For more details about these implementations and for a comprehensive
433experimental study, see the paper \cite KiralyKovacs12MCF.
434It also compares these codes to other publicly available
435minimum cost flow solvers.
436*/
437
438/**
439@defgroup min_cut Minimum Cut Algorithms
440@ingroup algs
441
442\brief Algorithms for finding minimum cut in graphs.
443
444This group contains the algorithms for finding minimum cut in graphs.
445
446The \e minimum \e cut \e problem is to find a non-empty and non-complete
447\f$X\f$ subset of the nodes with minimum overall capacity on
448outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
449\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
450cut is the \f$X\f$ solution of the next optimization problem:
451
452\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
453    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
454
455LEMON contains several algorithms related to minimum cut problems:
456
457- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
458  in directed graphs.
459- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
460  calculating minimum cut in undirected graphs.
461- \ref GomoryHu "Gomory-Hu tree computation" for calculating
462  all-pairs minimum cut in undirected graphs.
463
464If you want to find minimum cut just between two distinict nodes,
465see the \ref max_flow "maximum flow problem".
466*/
467
468/**
469@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
470@ingroup algs
471\brief Algorithms for finding minimum mean cycles.
472
473This group contains the algorithms for finding minimum mean cycles
474\cite amo93networkflows, \cite karp78characterization.
475
476The \e minimum \e mean \e cycle \e problem is to find a directed cycle
477of minimum mean length (cost) in a digraph.
478The mean length of a cycle is the average length of its arcs, i.e. the
479ratio between the total length of the cycle and the number of arcs on it.
480
481This problem has an important connection to \e conservative \e length
482\e functions, too. A length function on the arcs of a digraph is called
483conservative if and only if there is no directed cycle of negative total
484length. For an arbitrary length function, the negative of the minimum
485cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
486arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
487function.
488
489LEMON contains three algorithms for solving the minimum mean cycle problem:
490- \ref KarpMmc Karp's original algorithm \cite karp78characterization.
491- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
492  version of Karp's algorithm \cite hartmann93finding.
493- \ref HowardMmc Howard's policy iteration algorithm
494  \cite dasdan98minmeancycle, \cite dasdan04experimental.
495
496In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
497most efficient one, though the best known theoretical bound on its running
498time is exponential.
499Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
500run in time O(nm) and use space O(n<sup>2</sup>+m).
501*/
502
503/**
504@defgroup matching Matching Algorithms
505@ingroup algs
506\brief Algorithms for finding matchings in graphs and bipartite graphs.
507
508This group contains the algorithms for calculating
509matchings in graphs and bipartite graphs. The general matching problem is
510finding a subset of the edges for which each node has at most one incident
511edge.
512
513There are several different algorithms for calculate matchings in
514graphs.  The matching problems in bipartite graphs are generally
515easier than in general graphs. The goal of the matching optimization
516can be finding maximum cardinality, maximum weight or minimum cost
517matching. The search can be constrained to find perfect or
518maximum cardinality matching.
519
520The matching algorithms implemented in LEMON:
521- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
522  for calculating maximum cardinality matching in bipartite graphs.
523- \ref PrBipartiteMatching Push-relabel algorithm
524  for calculating maximum cardinality matching in bipartite graphs.
525- \ref MaxWeightedBipartiteMatching
526  Successive shortest path algorithm for calculating maximum weighted
527  matching and maximum weighted bipartite matching in bipartite graphs.
528- \ref MinCostMaxBipartiteMatching
529  Successive shortest path algorithm for calculating minimum cost maximum
530  matching in bipartite graphs.
531- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
532  maximum cardinality matching in general graphs.
533- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
534  maximum weighted matching in general graphs.
535- \ref MaxWeightedPerfectMatching
536  Edmond's blossom shrinking algorithm for calculating maximum weighted
537  perfect matching in general graphs.
538- \ref MaxFractionalMatching Push-relabel algorithm for calculating
539  maximum cardinality fractional matching in general graphs.
540- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
541  maximum weighted fractional matching in general graphs.
542- \ref MaxWeightedPerfectFractionalMatching
543  Augmenting path algorithm for calculating maximum weighted
544  perfect fractional matching in general graphs.
545
546\image html matching.png
547\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
548*/
549
550/**
551@defgroup graph_properties Connectivity and Other Graph Properties
552@ingroup algs
553\brief Algorithms for discovering the graph properties
554
555This group contains the algorithms for discovering the graph properties
556like connectivity, bipartiteness, euler property, simplicity etc.
557
558\image html connected_components.png
559\image latex connected_components.eps "Connected components" width=\textwidth
560*/
561
562/**
563@defgroup planar Planar Embedding and Drawing
564@ingroup algs
565\brief Algorithms for planarity checking, embedding and drawing
566
567This group contains the algorithms for planarity checking,
568embedding and drawing.
569
570\image html planar.png
571\image latex planar.eps "Plane graph" width=\textwidth
572*/
573
574/**
575@defgroup tsp Traveling Salesman Problem
576@ingroup algs
577\brief Algorithms for the symmetric traveling salesman problem
578
579This group contains basic heuristic algorithms for the the symmetric
580\e traveling \e salesman \e problem (TSP).
581Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
582the problem is to find a shortest possible tour that visits each node exactly
583once (i.e. the minimum cost Hamiltonian cycle).
584
585These TSP algorithms are intended to be used with a \e metric \e cost
586\e function, i.e. the edge costs should satisfy the triangle inequality.
587Otherwise the algorithms could yield worse results.
588
589LEMON provides five well-known heuristics for solving symmetric TSP:
590 - \ref NearestNeighborTsp Neareast neighbor algorithm
591 - \ref GreedyTsp Greedy algorithm
592 - \ref InsertionTsp Insertion heuristic (with four selection methods)
593 - \ref ChristofidesTsp Christofides algorithm
594 - \ref Opt2Tsp 2-opt algorithm
595
596\ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
597solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
598
599\ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
600approximation factor: 3/2.
601
602\ref Opt2Tsp usually provides the best results in practice, but
603it is the slowest method. It can also be used to improve given tours,
604for example, the results of other algorithms.
605
606\image html tsp.png
607\image latex tsp.eps "Traveling salesman problem" width=\textwidth
608*/
609
610/**
611@defgroup approx_algs Approximation Algorithms
612@ingroup algs
613\brief Approximation algorithms.
614
615This group contains the approximation and heuristic algorithms
616implemented in LEMON.
617
618<b>Maximum Clique Problem</b>
619  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
620    Grosso, Locatelli, and Pullan.
621*/
622
623/**
624@defgroup auxalg Auxiliary Algorithms
625@ingroup algs
626\brief Auxiliary algorithms implemented in LEMON.
627
628This group contains some algorithms implemented in LEMON
629in order to make it easier to implement complex algorithms.
630*/
631
632/**
633@defgroup gen_opt_group General Optimization Tools
634\brief This group contains some general optimization frameworks
635implemented in LEMON.
636
637This group contains some general optimization frameworks
638implemented in LEMON.
639*/
640
641/**
642@defgroup lp_group LP and MIP Solvers
643@ingroup gen_opt_group
644\brief LP and MIP solver interfaces for LEMON.
645
646This group contains LP and MIP solver interfaces for LEMON.
647Various LP solvers could be used in the same manner with this
648high-level interface.
649
650The currently supported solvers are \cite glpk, \cite clp, \cite cbc,
651\cite cplex, \cite soplex.
652*/
653
654/**
655@defgroup lp_utils Tools for Lp and Mip Solvers
656@ingroup lp_group
657\brief Helper tools to the Lp and Mip solvers.
658
659This group adds some helper tools to general optimization framework
660implemented in LEMON.
661*/
662
663/**
664@defgroup metah Metaheuristics
665@ingroup gen_opt_group
666\brief Metaheuristics for LEMON library.
667
668This group contains some metaheuristic optimization tools.
669*/
670
671/**
672@defgroup utils Tools and Utilities
673\brief Tools and utilities for programming in LEMON
674
675Tools and utilities for programming in LEMON.
676*/
677
678/**
679@defgroup gutils Basic Graph Utilities
680@ingroup utils
681\brief Simple basic graph utilities.
682
683This group contains some simple basic graph utilities.
684*/
685
686/**
687@defgroup misc Miscellaneous Tools
688@ingroup utils
689\brief Tools for development, debugging and testing.
690
691This group contains several useful tools for development,
692debugging and testing.
693*/
694
695/**
696@defgroup timecount Time Measuring and Counting
697@ingroup misc
698\brief Simple tools for measuring the performance of algorithms.
699
700This group contains simple tools for measuring the performance
701of algorithms.
702*/
703
704/**
705@defgroup exceptions Exceptions
706@ingroup utils
707\brief Exceptions defined in LEMON.
708
709This group contains the exceptions defined in LEMON.
710*/
711
712/**
713@defgroup io_group Input-Output
714\brief Graph Input-Output methods
715
716This group contains the tools for importing and exporting graphs
717and graph related data. Now it supports the \ref lgf-format
718"LEMON Graph Format", the \c DIMACS format and the encapsulated
719postscript (EPS) format.
720*/
721
722/**
723@defgroup lemon_io LEMON Graph Format
724@ingroup io_group
725\brief Reading and writing LEMON Graph Format.
726
727This group contains methods for reading and writing
728\ref lgf-format "LEMON Graph Format".
729*/
730
731/**
732@defgroup eps_io Postscript Exporting
733@ingroup io_group
734\brief General \c EPS drawer and graph exporter
735
736This group contains general \c EPS drawing methods and special
737graph exporting tools.
738
739\image html graph_to_eps.png
740*/
741
742/**
743@defgroup dimacs_group DIMACS Format
744@ingroup io_group
745\brief Read and write files in DIMACS format
746
747Tools to read a digraph from or write it to a file in DIMACS format data.
748*/
749
750/**
751@defgroup nauty_group NAUTY Format
752@ingroup io_group
753\brief Read \e Nauty format
754
755Tool to read graphs from \e Nauty format data.
756*/
757
758/**
759@defgroup concept Concepts
760\brief Skeleton classes and concept checking classes
761
762This group contains the data/algorithm skeletons and concept checking
763classes implemented in LEMON.
764
765The purpose of the classes in this group is fourfold.
766
767- These classes contain the documentations of the %concepts. In order
768  to avoid document multiplications, an implementation of a concept
769  simply refers to the corresponding concept class.
770
771- These classes declare every functions, <tt>typedef</tt>s etc. an
772  implementation of the %concepts should provide, however completely
773  without implementations and real data structures behind the
774  interface. On the other hand they should provide nothing else. All
775  the algorithms working on a data structure meeting a certain concept
776  should compile with these classes. (Though it will not run properly,
777  of course.) In this way it is easily to check if an algorithm
778  doesn't use any extra feature of a certain implementation.
779
780- The concept descriptor classes also provide a <em>checker class</em>
781  that makes it possible to check whether a certain implementation of a
782  concept indeed provides all the required features.
783
784- Finally, They can serve as a skeleton of a new implementation of a concept.
785*/
786
787/**
788@defgroup graph_concepts Graph Structure Concepts
789@ingroup concept
790\brief Skeleton and concept checking classes for graph structures
791
792This group contains the skeletons and concept checking classes of
793graph structures.
794*/
795
796/**
797@defgroup map_concepts Map Concepts
798@ingroup concept
799\brief Skeleton and concept checking classes for maps
800
801This group contains the skeletons and concept checking classes of maps.
802*/
803
804/**
805@defgroup tools Standalone Utility Applications
806
807Some utility applications are listed here.
808
809The standard compilation procedure (<tt>./configure;make</tt>) will compile
810them, as well.
811*/
812
813/**
814\anchor demoprograms
815
816@defgroup demos Demo Programs
817
818Some demo programs are listed here. Their full source codes can be found in
819the \c demo subdirectory of the source tree.
820
821In order to compile them, use the <tt>make demo</tt> or the
822<tt>make check</tt> commands.
823*/
824
825}
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