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) 2003-2010
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\ref 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\ref 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 \ref 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 \ref clrs01algorithms, \ref 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  \ref edmondskarp72theoretical.
377- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm
378  \ref goldberg88newapproach.
379- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees
380  \ref dinic70algorithm, \ref sleator83dynamic.
381- \ref GoldbergTarjan !Preflow push-relabel algorithm with dynamic trees
382  \ref goldberg88newapproach, \ref 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 \ref 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 \ref dantzig63linearprog, \ref kellyoneill91netsimplex.
409 - \ref CostScaling Cost Scaling algorithm based on push/augment and
410   relabel operations \ref goldberg90approximation, \ref goldberg97efficient,
411   \ref bunnagel98efficient.
412 - \ref CapacityScaling Capacity Scaling algorithm based on the successive
413   shortest path method \ref edmondskarp72theoretical.
414 - \ref CycleCanceling Cycle-Canceling algorithms, two of which are
415   strongly polynomial \ref klein67primal, \ref 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*/
432
433/**
434@defgroup min_cut Minimum Cut Algorithms
435@ingroup algs
436
437\brief Algorithms for finding minimum cut in graphs.
438
439This group contains the algorithms for finding minimum cut in graphs.
440
441The \e minimum \e cut \e problem is to find a non-empty and non-complete
442\f$X\f$ subset of the nodes with minimum overall capacity on
443outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
444\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
445cut is the \f$X\f$ solution of the next optimization problem:
446
447\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
448    \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
449
450LEMON contains several algorithms related to minimum cut problems:
451
452- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
453  in directed graphs.
454- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
455  calculating minimum cut in undirected graphs.
456- \ref GomoryHu "Gomory-Hu tree computation" for calculating
457  all-pairs minimum cut in undirected graphs.
458
459If you want to find minimum cut just between two distinict nodes,
460see the \ref max_flow "maximum flow problem".
461*/
462
463/**
464@defgroup min_mean_cycle Minimum Mean Cycle Algorithms
465@ingroup algs
466\brief Algorithms for finding minimum mean cycles.
467
468This group contains the algorithms for finding minimum mean cycles
469\ref amo93networkflows, \ref karp78characterization.
470
471The \e minimum \e mean \e cycle \e problem is to find a directed cycle
472of minimum mean length (cost) in a digraph.
473The mean length of a cycle is the average length of its arcs, i.e. the
474ratio between the total length of the cycle and the number of arcs on it.
475
476This problem has an important connection to \e conservative \e length
477\e functions, too. A length function on the arcs of a digraph is called
478conservative if and only if there is no directed cycle of negative total
479length. For an arbitrary length function, the negative of the minimum
480cycle mean is the smallest \f$\epsilon\f$ value so that increasing the
481arc lengths uniformly by \f$\epsilon\f$ results in a conservative length
482function.
483
484LEMON contains three algorithms for solving the minimum mean cycle problem:
485- \ref KarpMmc Karp's original algorithm \ref karp78characterization.
486- \ref HartmannOrlinMmc Hartmann-Orlin's algorithm, which is an improved
487  version of Karp's algorithm \ref hartmann93finding.
488- \ref HowardMmc Howard's policy iteration algorithm
489  \ref dasdan98minmeancycle, \ref dasdan04experimental.
490
491In practice, the \ref HowardMmc "Howard" algorithm turned out to be by far the
492most efficient one, though the best known theoretical bound on its running
493time is exponential.
494Both \ref KarpMmc "Karp" and \ref HartmannOrlinMmc "Hartmann-Orlin" algorithms
495run in time O(ne) and use space O(n<sup>2</sup>+e).
496*/
497
498/**
499@defgroup matching Matching Algorithms
500@ingroup algs
501\brief Algorithms for finding matchings in graphs and bipartite graphs.
502
503This group contains the algorithms for calculating
504matchings in graphs and bipartite graphs. The general matching problem is
505finding a subset of the edges for which each node has at most one incident
506edge.
507
508There are several different algorithms for calculate matchings in
509graphs.  The matching problems in bipartite graphs are generally
510easier than in general graphs. The goal of the matching optimization
511can be finding maximum cardinality, maximum weight or minimum cost
512matching. The search can be constrained to find perfect or
513maximum cardinality matching.
514
515The matching algorithms implemented in LEMON:
516- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
517  for calculating maximum cardinality matching in bipartite graphs.
518- \ref PrBipartiteMatching Push-relabel algorithm
519  for calculating maximum cardinality matching in bipartite graphs.
520- \ref MaxWeightedBipartiteMatching
521  Successive shortest path algorithm for calculating maximum weighted
522  matching and maximum weighted bipartite matching in bipartite graphs.
523- \ref MinCostMaxBipartiteMatching
524  Successive shortest path algorithm for calculating minimum cost maximum
525  matching in bipartite graphs.
526- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
527  maximum cardinality matching in general graphs.
528- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
529  maximum weighted matching in general graphs.
530- \ref MaxWeightedPerfectMatching
531  Edmond's blossom shrinking algorithm for calculating maximum weighted
532  perfect matching in general graphs.
533- \ref MaxFractionalMatching Push-relabel algorithm for calculating
534  maximum cardinality fractional matching in general graphs.
535- \ref MaxWeightedFractionalMatching Augmenting path algorithm for calculating
536  maximum weighted fractional matching in general graphs.
537- \ref MaxWeightedPerfectFractionalMatching
538  Augmenting path algorithm for calculating maximum weighted
539  perfect fractional matching in general graphs.
540
541\image html matching.png
542\image latex matching.eps "Min Cost Perfect Matching" width=\textwidth
543*/
544
545/**
546@defgroup graph_properties Connectivity and Other Graph Properties
547@ingroup algs
548\brief Algorithms for discovering the graph properties
549
550This group contains the algorithms for discovering the graph properties
551like connectivity, bipartiteness, euler property, simplicity etc.
552
553\image html connected_components.png
554\image latex connected_components.eps "Connected components" width=\textwidth
555*/
556
557/**
558@defgroup planar Planar Embedding and Drawing
559@ingroup algs
560\brief Algorithms for planarity checking, embedding and drawing
561
562This group contains the algorithms for planarity checking,
563embedding and drawing.
564
565\image html planar.png
566\image latex planar.eps "Plane graph" width=\textwidth
567*/
568 
569/**
570@defgroup tsp Traveling Salesman Problem
571@ingroup algs
572\brief Algorithms for the symmetric traveling salesman problem
573
574This group contains basic heuristic algorithms for the the symmetric
575\e traveling \e salesman \e problem (TSP).
576Given an \ref FullGraph "undirected full graph" with a cost map on its edges,
577the problem is to find a shortest possible tour that visits each node exactly
578once (i.e. the minimum cost Hamiltonian cycle).
579
580These TSP algorithms are intended to be used with a \e metric \e cost
581\e function, i.e. the edge costs should satisfy the triangle inequality.
582Otherwise the algorithms could yield worse results.
583
584LEMON provides five well-known heuristics for solving symmetric TSP:
585 - \ref NearestNeighborTsp Neareast neighbor algorithm
586 - \ref GreedyTsp Greedy algorithm
587 - \ref InsertionTsp Insertion heuristic (with four selection methods)
588 - \ref ChristofidesTsp Christofides algorithm
589 - \ref Opt2Tsp 2-opt algorithm
590
591\ref NearestNeighborTsp, \ref GreedyTsp, and \ref InsertionTsp are the fastest
592solution methods. Furthermore, \ref InsertionTsp is usually quite effective.
593
594\ref ChristofidesTsp is somewhat slower, but it has the best guaranteed
595approximation factor: 3/2.
596
597\ref Opt2Tsp usually provides the best results in practice, but
598it is the slowest method. It can also be used to improve given tours,
599for example, the results of other algorithms.
600
601\image html tsp.png
602\image latex tsp.eps "Traveling salesman problem" width=\textwidth
603*/
604
605/**
606@defgroup approx_algs Approximation Algorithms
607@ingroup algs
608\brief Approximation algorithms.
609
610This group contains the approximation and heuristic algorithms
611implemented in LEMON.
612
613<b>Maximum Clique Problem</b>
614  - \ref GrossoLocatelliPullanMc An efficient heuristic algorithm of
615    Grosso, Locatelli, and Pullan.
616*/
617
618/**
619@defgroup auxalg Auxiliary Algorithms
620@ingroup algs
621\brief Auxiliary algorithms implemented in LEMON.
622
623This group contains some algorithms implemented in LEMON
624in order to make it easier to implement complex algorithms.
625*/
626
627/**
628@defgroup gen_opt_group General Optimization Tools
629\brief This group contains some general optimization frameworks
630implemented in LEMON.
631
632This group contains some general optimization frameworks
633implemented in LEMON.
634*/
635
636/**
637@defgroup lp_group LP and MIP Solvers
638@ingroup gen_opt_group
639\brief LP and MIP solver interfaces for LEMON.
640
641This group contains LP and MIP solver interfaces for LEMON.
642Various LP solvers could be used in the same manner with this
643high-level interface.
644
645The currently supported solvers are \ref glpk, \ref clp, \ref cbc,
646\ref cplex, \ref soplex.
647*/
648
649/**
650@defgroup lp_utils Tools for Lp and Mip Solvers
651@ingroup lp_group
652\brief Helper tools to the Lp and Mip solvers.
653
654This group adds some helper tools to general optimization framework
655implemented in LEMON.
656*/
657
658/**
659@defgroup metah Metaheuristics
660@ingroup gen_opt_group
661\brief Metaheuristics for LEMON library.
662
663This group contains some metaheuristic optimization tools.
664*/
665
666/**
667@defgroup utils Tools and Utilities
668\brief Tools and utilities for programming in LEMON
669
670Tools and utilities for programming in LEMON.
671*/
672
673/**
674@defgroup gutils Basic Graph Utilities
675@ingroup utils
676\brief Simple basic graph utilities.
677
678This group contains some simple basic graph utilities.
679*/
680
681/**
682@defgroup misc Miscellaneous Tools
683@ingroup utils
684\brief Tools for development, debugging and testing.
685
686This group contains several useful tools for development,
687debugging and testing.
688*/
689
690/**
691@defgroup timecount Time Measuring and Counting
692@ingroup misc
693\brief Simple tools for measuring the performance of algorithms.
694
695This group contains simple tools for measuring the performance
696of algorithms.
697*/
698
699/**
700@defgroup exceptions Exceptions
701@ingroup utils
702\brief Exceptions defined in LEMON.
703
704This group contains the exceptions defined in LEMON.
705*/
706
707/**
708@defgroup io_group Input-Output
709\brief Graph Input-Output methods
710
711This group contains the tools for importing and exporting graphs
712and graph related data. Now it supports the \ref lgf-format
713"LEMON Graph Format", the \c DIMACS format and the encapsulated
714postscript (EPS) format.
715*/
716
717/**
718@defgroup lemon_io LEMON Graph Format
719@ingroup io_group
720\brief Reading and writing LEMON Graph Format.
721
722This group contains methods for reading and writing
723\ref lgf-format "LEMON Graph Format".
724*/
725
726/**
727@defgroup eps_io Postscript Exporting
728@ingroup io_group
729\brief General \c EPS drawer and graph exporter
730
731This group contains general \c EPS drawing methods and special
732graph exporting tools.
733
734\image html graph_to_eps.png
735*/
736
737/**
738@defgroup dimacs_group DIMACS Format
739@ingroup io_group
740\brief Read and write files in DIMACS format
741
742Tools to read a digraph from or write it to a file in DIMACS format data.
743*/
744
745/**
746@defgroup nauty_group NAUTY Format
747@ingroup io_group
748\brief Read \e Nauty format
749
750Tool to read graphs from \e Nauty format data.
751*/
752
753/**
754@defgroup concept Concepts
755\brief Skeleton classes and concept checking classes
756
757This group contains the data/algorithm skeletons and concept checking
758classes implemented in LEMON.
759
760The purpose of the classes in this group is fourfold.
761
762- These classes contain the documentations of the %concepts. In order
763  to avoid document multiplications, an implementation of a concept
764  simply refers to the corresponding concept class.
765
766- These classes declare every functions, <tt>typedef</tt>s etc. an
767  implementation of the %concepts should provide, however completely
768  without implementations and real data structures behind the
769  interface. On the other hand they should provide nothing else. All
770  the algorithms working on a data structure meeting a certain concept
771  should compile with these classes. (Though it will not run properly,
772  of course.) In this way it is easily to check if an algorithm
773  doesn't use any extra feature of a certain implementation.
774
775- The concept descriptor classes also provide a <em>checker class</em>
776  that makes it possible to check whether a certain implementation of a
777  concept indeed provides all the required features.
778
779- Finally, They can serve as a skeleton of a new implementation of a concept.
780*/
781
782/**
783@defgroup graph_concepts Graph Structure Concepts
784@ingroup concept
785\brief Skeleton and concept checking classes for graph structures
786
787This group contains the skeletons and concept checking classes of
788graph structures.
789*/
790
791/**
792@defgroup map_concepts Map Concepts
793@ingroup concept
794\brief Skeleton and concept checking classes for maps
795
796This group contains the skeletons and concept checking classes of maps.
797*/
798
799/**
800@defgroup tools Standalone Utility Applications
801
802Some utility applications are listed here.
803
804The standard compilation procedure (<tt>./configure;make</tt>) will compile
805them, as well.
806*/
807
808/**
809\anchor demoprograms
810
811@defgroup demos Demo Programs
812
813Some demo programs are listed here. Their full source codes can be found in
814the \c demo subdirectory of the source tree.
815
816In order to compile them, use the <tt>make demo</tt> or the
817<tt>make check</tt> commands.
818*/
819
820}
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