1 /* -*- mode: C++; indent-tabs-mode: nil; -*-
3 * This file is a part of LEMON, a generic C++ optimization library.
5 * Copyright (C) 2003-2009
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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.
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
22 @defgroup datas Data Structures
23 This group contains the several data structures implemented in LEMON.
27 @defgroup graphs Graph Structures
29 \brief Graph structures implemented in LEMON.
31 The implementation of combinatorial algorithms heavily relies on
32 efficient graph implementations. LEMON offers data structures which are
33 planned to be easily used in an experimental phase of implementation studies,
34 and thereafter the program code can be made efficient by small modifications.
36 The most efficient implementation of diverse applications require the
37 usage of different physical graph implementations. These differences
38 appear in the size of graph we require to handle, memory or time usage
39 limitations or in the set of operations through which the graph can be
40 accessed. LEMON provides several physical graph structures to meet
41 the diverging requirements of the possible users. In order to save on
42 running time or on memory usage, some structures may fail to provide
43 some graph features like arc/edge or node deletion.
45 Alteration of standard containers need a very limited number of
46 operations, these together satisfy the everyday requirements.
47 In the case of graph structures, different operations are needed which do
48 not alter the physical graph, but gives another view. If some nodes or
49 arcs have to be hidden or the reverse oriented graph have to be used, then
50 this is the case. It also may happen that in a flow implementation
51 the residual graph can be accessed by another algorithm, or a node-set
52 is to be shrunk for another algorithm.
53 LEMON also provides a variety of graphs for these requirements called
54 \ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
55 in conjunction with other graph representations.
57 You are free to use the graph structure that fit your requirements
58 the best, most graph algorithms and auxiliary data structures can be used
59 with any graph structure.
61 <b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
65 @defgroup graph_adaptors Adaptor Classes for Graphs
67 \brief Adaptor classes for digraphs and graphs
69 This group contains several useful adaptor classes for digraphs and graphs.
71 The main parts of LEMON are the different graph structures, generic
72 graph algorithms, graph concepts, which couple them, and graph
73 adaptors. While the previous notions are more or less clear, the
74 latter one needs further explanation. Graph adaptors are graph classes
75 which serve for considering graph structures in different ways.
77 A short example makes this much clearer. Suppose that we have an
78 instance \c g of a directed graph type, say ListDigraph and an algorithm
80 template <typename Digraph>
81 int algorithm(const Digraph&);
83 is 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
85 arcs. In this case, an adaptor class is used, which (according
86 to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
87 The adaptor uses the original digraph structure and digraph operations when
88 methods of the reversed oriented graph are called. This means that the adaptor
89 have minor memory usage, and do not perform sophisticated algorithmic
90 actions. The purpose of it is to give a tool for the cases when a
91 graph have to be used in a specific alteration. If this alteration is
92 obtained by a usual construction like filtering the node or the arc set or
93 considering a new orientation, then an adaptor is worthwhile to use.
94 To come back to the reverse oriented graph, in this situation
96 template<typename Digraph> class ReverseDigraph;
98 template class can be used. The code looks as follows
101 ReverseDigraph<ListDigraph> rg(g);
102 int result = algorithm(rg);
104 During running the algorithm, the original digraph \c g is untouched.
105 This techniques give rise to an elegant code, and based on stable
106 graph adaptors, complex algorithms can be implemented easily.
108 In flow, circulation and matching problems, the residual
109 graph is of particular importance. Combining an adaptor implementing
110 this with shortest path algorithms or minimum mean cycle algorithms,
111 a range of weighted and cardinality optimization algorithms can be
112 obtained. For other examples, the interested user is referred to the
113 detailed documentation of particular adaptors.
115 The behavior of graph adaptors can be very different. Some of them keep
116 capabilities of the original graph while in other cases this would be
117 meaningless. This means that the concepts that they meet depend
118 on the graph adaptor, and the wrapped graph.
119 For example, if an arc of a reversed digraph is deleted, this is carried
120 out by deleting the corresponding arc of the original digraph, thus the
121 adaptor modifies the original digraph.
122 However in case of a residual digraph, this operation has no sense.
124 Let us stand one more example here to simplify your work.
125 ReverseDigraph has constructor
127 ReverseDigraph(Digraph& digraph);
129 This means that in a situation, when a <tt>const %ListDigraph&</tt>
130 reference to a graph is given, then it have to be instantiated with
131 <tt>Digraph=const %ListDigraph</tt>.
133 int algorithm1(const ListDigraph& g) {
134 ReverseDigraph<const ListDigraph> rg(g);
135 return algorithm2(rg);
143 \brief Map structures implemented in LEMON.
145 This group contains the map structures implemented in LEMON.
147 LEMON provides several special purpose maps and map adaptors that e.g. combine
148 new maps from existing ones.
150 <b>See also:</b> \ref map_concepts "Map Concepts".
154 @defgroup graph_maps Graph Maps
156 \brief Special graph-related maps.
158 This group contains maps that are specifically designed to assign
159 values to the nodes and arcs/edges of graphs.
161 If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
162 \c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
166 \defgroup map_adaptors Map Adaptors
168 \brief Tools to create new maps from existing ones
170 This group contains map adaptors that are used to create "implicit"
171 maps from other maps.
173 Most of them are \ref concepts::ReadMap "read-only maps".
174 They can make arithmetic and logical operations between one or two maps
175 (negation, shifting, addition, multiplication, logical 'and', 'or',
176 'not' etc.) or e.g. convert a map to another one of different Value type.
178 The typical usage of this classes is passing implicit maps to
179 algorithms. If a function type algorithm is called then the function
180 type map adaptors can be used comfortable. For example let's see the
181 usage of map adaptors with the \c graphToEps() function.
183 Color nodeColor(int deg) {
185 return Color(0.5, 0.0, 0.5);
186 } else if (deg == 1) {
187 return Color(1.0, 0.5, 1.0);
189 return Color(0.0, 0.0, 0.0);
193 Digraph::NodeMap<int> degree_map(graph);
195 graphToEps(graph, "graph.eps")
196 .coords(coords).scaleToA4().undirected()
197 .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
200 The \c functorToMap() function makes an \c int to \c Color map from the
201 \c nodeColor() function. The \c composeMap() compose the \c degree_map
202 and the previously created map. The composed map is a proper function to
203 get the color of each node.
205 The usage with class type algorithms is little bit harder. In this
206 case the function type map adaptors can not be used, because the
207 function map adaptors give back temporary objects.
211 typedef Digraph::ArcMap<double> DoubleArcMap;
212 DoubleArcMap length(graph);
213 DoubleArcMap speed(graph);
215 typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
216 TimeMap time(length, speed);
218 Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
219 dijkstra.run(source, target);
221 We have a length map and a maximum speed map on the arcs of a digraph.
222 The minimum time to pass the arc can be calculated as the division of
223 the two maps which can be done implicitly with the \c DivMap template
224 class. We use the implicit minimum time map as the length map of the
225 \c Dijkstra algorithm.
229 @defgroup paths Path Structures
231 \brief %Path structures implemented in LEMON.
233 This group contains the path structures implemented in LEMON.
235 LEMON provides flexible data structures to work with paths.
236 All of them have similar interfaces and they can be copied easily with
237 assignment operators and copy constructors. This makes it easy and
238 efficient to have e.g. the Dijkstra algorithm to store its result in
239 any kind of path structure.
241 \sa lemon::concepts::Path
245 @defgroup auxdat Auxiliary Data Structures
247 \brief Auxiliary data structures implemented in LEMON.
249 This group contains some data structures implemented in LEMON in
250 order to make it easier to implement combinatorial algorithms.
254 @defgroup geomdat Geometric Data Structures
256 \brief Geometric data structures implemented in LEMON.
258 This group contains geometric data structures implemented in LEMON.
260 - \ref lemon::dim2::Point "dim2::Point" implements a two dimensional
261 vector with the usual operations.
262 - \ref lemon::dim2::Box "dim2::Box" can be used to determine the
263 rectangular bounding box of a set of \ref lemon::dim2::Point
268 @defgroup matrices Matrices
270 \brief Two dimensional data storages implemented in LEMON.
272 This group contains two dimensional data storages implemented in LEMON.
276 @defgroup algs Algorithms
277 \brief This group contains the several algorithms
278 implemented in LEMON.
280 This group contains the several algorithms
281 implemented in LEMON.
285 @defgroup search Graph Search
287 \brief Common graph search algorithms.
289 This group contains the common graph search algorithms, namely
290 \e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
294 @defgroup shortest_path Shortest Path Algorithms
296 \brief Algorithms for finding shortest paths.
298 This group contains the algorithms for finding shortest paths in digraphs.
300 - \ref Dijkstra algorithm for finding shortest paths from a source node
301 when all arc lengths are non-negative.
302 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
303 from a source node when arc lenghts can be either positive or negative,
304 but the digraph should not contain directed cycles with negative total
306 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
307 for solving the \e all-pairs \e shortest \e paths \e problem when arc
308 lenghts can be either positive or negative, but the digraph should
309 not contain directed cycles with negative total length.
310 - \ref Suurballe A successive shortest path algorithm for finding
311 arc-disjoint paths between two nodes having minimum total length.
315 @defgroup spantree Minimum Spanning Tree Algorithms
317 \brief Algorithms for finding minimum cost spanning trees and arborescences.
319 This group contains the algorithms for finding minimum cost spanning
320 trees and arborescences.
324 @defgroup max_flow Maximum Flow Algorithms
326 \brief Algorithms for finding maximum flows.
328 This group contains the algorithms for finding maximum flows and
329 feasible circulations.
331 The \e maximum \e flow \e problem is to find a flow of maximum value between
332 a single source and a single target. Formally, there is a \f$G=(V,A)\f$
333 digraph, a \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function and
334 \f$s, t \in V\f$ source and target nodes.
335 A maximum flow is an \f$f: A\rightarrow\mathbf{R}^+_0\f$ solution of the
336 following optimization problem.
338 \f[ \max\sum_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]
339 \f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)
340 \quad \forall u\in V\setminus\{s,t\} \f]
341 \f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\in A \f]
343 LEMON contains several algorithms for solving maximum flow problems:
344 - \ref EdmondsKarp Edmonds-Karp algorithm.
345 - \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
346 - \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
347 - \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
349 In most cases the \ref Preflow "Preflow" algorithm provides the
350 fastest method for computing a maximum flow. All implementations
351 also provide functions to query the minimum cut, which is the dual
352 problem of maximum flow.
354 \ref Circulation is a preflow push-relabel algorithm implemented directly
355 for finding feasible circulations, which is a somewhat different problem,
356 but it is strongly related to maximum flow.
357 For more information, see \ref Circulation.
361 @defgroup min_cost_flow_algs Minimum Cost Flow Algorithms
364 \brief Algorithms for finding minimum cost flows and circulations.
366 This group contains the algorithms for finding minimum cost flows and
367 circulations. For more information about this problem and its dual
368 solution see \ref min_cost_flow "Minimum Cost Flow Problem".
370 LEMON contains several algorithms for this problem.
371 - \ref NetworkSimplex Primal Network Simplex algorithm with various
373 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on
375 - \ref CapacityScaling Successive Shortest %Path algorithm with optional
377 - \ref CancelAndTighten The Cancel and Tighten algorithm.
378 - \ref CycleCanceling Cycle-Canceling algorithms.
380 In general NetworkSimplex is the most efficient implementation,
381 but in special cases other algorithms could be faster.
382 For example, if the total supply and/or capacities are rather small,
383 CapacityScaling is usually the fastest algorithm (without effective scaling).
387 @defgroup min_cut Minimum Cut Algorithms
390 \brief Algorithms for finding minimum cut in graphs.
392 This group contains the algorithms for finding minimum cut in graphs.
394 The \e minimum \e cut \e problem is to find a non-empty and non-complete
395 \f$X\f$ subset of the nodes with minimum overall capacity on
396 outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
397 \f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
398 cut is the \f$X\f$ solution of the next optimization problem:
400 \f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
401 \sum_{uv\in A: u\in X, v\not\in X}cap(uv) \f]
403 LEMON contains several algorithms related to minimum cut problems:
405 - \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
407 - \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
408 calculating minimum cut in undirected graphs.
409 - \ref GomoryHu "Gomory-Hu tree computation" for calculating
410 all-pairs minimum cut in undirected graphs.
412 If you want to find minimum cut just between two distinict nodes,
413 see the \ref max_flow "maximum flow problem".
417 @defgroup matching Matching Algorithms
419 \brief Algorithms for finding matchings in graphs and bipartite graphs.
421 This group contains the algorithms for calculating
422 matchings in graphs and bipartite graphs. The general matching problem is
423 finding a subset of the edges for which each node has at most one incident
426 There are several different algorithms for calculate matchings in
427 graphs. The matching problems in bipartite graphs are generally
428 easier than in general graphs. The goal of the matching optimization
429 can be finding maximum cardinality, maximum weight or minimum cost
430 matching. The search can be constrained to find perfect or
431 maximum cardinality matching.
433 The matching algorithms implemented in LEMON:
434 - \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
435 for calculating maximum cardinality matching in bipartite graphs.
436 - \ref PrBipartiteMatching Push-relabel algorithm
437 for calculating maximum cardinality matching in bipartite graphs.
438 - \ref MaxWeightedBipartiteMatching
439 Successive shortest path algorithm for calculating maximum weighted
440 matching and maximum weighted bipartite matching in bipartite graphs.
441 - \ref MinCostMaxBipartiteMatching
442 Successive shortest path algorithm for calculating minimum cost maximum
443 matching in bipartite graphs.
444 - \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
445 maximum cardinality matching in general graphs.
446 - \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
447 maximum weighted matching in general graphs.
448 - \ref MaxWeightedPerfectMatching
449 Edmond's blossom shrinking algorithm for calculating maximum weighted
450 perfect matching in general graphs.
452 \image html bipartite_matching.png
453 \image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
457 @defgroup graph_properties Connectivity and Other Graph Properties
459 \brief Algorithms for discovering the graph properties
461 This group contains the algorithms for discovering the graph properties
462 like connectivity, bipartiteness, euler property, simplicity etc.
464 \image html connected_components.png
465 \image latex connected_components.eps "Connected components" width=\textwidth
469 @defgroup planar Planarity Embedding and Drawing
471 \brief Algorithms for planarity checking, embedding and drawing
473 This group contains the algorithms for planarity checking,
474 embedding and drawing.
476 \image html planar.png
477 \image latex planar.eps "Plane graph" width=\textwidth
481 @defgroup approx Approximation Algorithms
483 \brief Approximation algorithms.
485 This group contains the approximation and heuristic algorithms
486 implemented in LEMON.
490 @defgroup auxalg Auxiliary Algorithms
492 \brief Auxiliary algorithms implemented in LEMON.
494 This group contains some algorithms implemented in LEMON
495 in order to make it easier to implement complex algorithms.
499 @defgroup gen_opt_group General Optimization Tools
500 \brief This group contains some general optimization frameworks
501 implemented in LEMON.
503 This group contains some general optimization frameworks
504 implemented in LEMON.
508 @defgroup lp_group Lp and Mip Solvers
509 @ingroup gen_opt_group
510 \brief Lp and Mip solver interfaces for LEMON.
512 This group contains Lp and Mip solver interfaces for LEMON. The
513 various LP solvers could be used in the same manner with this
518 @defgroup lp_utils Tools for Lp and Mip Solvers
520 \brief Helper tools to the Lp and Mip solvers.
522 This group adds some helper tools to general optimization framework
523 implemented in LEMON.
527 @defgroup metah Metaheuristics
528 @ingroup gen_opt_group
529 \brief Metaheuristics for LEMON library.
531 This group contains some metaheuristic optimization tools.
535 @defgroup utils Tools and Utilities
536 \brief Tools and utilities for programming in LEMON
538 Tools and utilities for programming in LEMON.
542 @defgroup gutils Basic Graph Utilities
544 \brief Simple basic graph utilities.
546 This group contains some simple basic graph utilities.
550 @defgroup misc Miscellaneous Tools
552 \brief Tools for development, debugging and testing.
554 This group contains several useful tools for development,
555 debugging and testing.
559 @defgroup timecount Time Measuring and Counting
561 \brief Simple tools for measuring the performance of algorithms.
563 This group contains simple tools for measuring the performance
568 @defgroup exceptions Exceptions
570 \brief Exceptions defined in LEMON.
572 This group contains the exceptions defined in LEMON.
576 @defgroup io_group Input-Output
577 \brief Graph Input-Output methods
579 This group contains the tools for importing and exporting graphs
580 and graph related data. Now it supports the \ref lgf-format
581 "LEMON Graph Format", the \c DIMACS format and the encapsulated
582 postscript (EPS) format.
586 @defgroup lemon_io LEMON Graph Format
588 \brief Reading and writing LEMON Graph Format.
590 This group contains methods for reading and writing
591 \ref lgf-format "LEMON Graph Format".
595 @defgroup eps_io Postscript Exporting
597 \brief General \c EPS drawer and graph exporter
599 This group contains general \c EPS drawing methods and special
600 graph exporting tools.
604 @defgroup dimacs_group DIMACS Format
606 \brief Read and write files in DIMACS format
608 Tools to read a digraph from or write it to a file in DIMACS format data.
612 @defgroup nauty_group NAUTY Format
614 \brief Read \e Nauty format
616 Tool to read graphs from \e Nauty format data.
620 @defgroup concept Concepts
621 \brief Skeleton classes and concept checking classes
623 This group contains the data/algorithm skeletons and concept checking
624 classes implemented in LEMON.
626 The purpose of the classes in this group is fourfold.
628 - These classes contain the documentations of the %concepts. In order
629 to avoid document multiplications, an implementation of a concept
630 simply refers to the corresponding concept class.
632 - These classes declare every functions, <tt>typedef</tt>s etc. an
633 implementation of the %concepts should provide, however completely
634 without implementations and real data structures behind the
635 interface. On the other hand they should provide nothing else. All
636 the algorithms working on a data structure meeting a certain concept
637 should compile with these classes. (Though it will not run properly,
638 of course.) In this way it is easily to check if an algorithm
639 doesn't use any extra feature of a certain implementation.
641 - The concept descriptor classes also provide a <em>checker class</em>
642 that makes it possible to check whether a certain implementation of a
643 concept indeed provides all the required features.
645 - Finally, They can serve as a skeleton of a new implementation of a concept.
649 @defgroup graph_concepts Graph Structure Concepts
651 \brief Skeleton and concept checking classes for graph structures
653 This group contains the skeletons and concept checking classes of LEMON's
654 graph structures and helper classes used to implement these.
658 @defgroup map_concepts Map Concepts
660 \brief Skeleton and concept checking classes for maps
662 This group contains the skeletons and concept checking classes of maps.
666 @defgroup tools Standalone Utility Applications
668 Some utility applications are listed here.
670 The standard compilation procedure (<tt>./configure;make</tt>) will compile
677 @defgroup demos Demo Programs
679 Some demo programs are listed here. Their full source codes can be found in
680 the \c demo subdirectory of the source tree.
682 In order to compile them, use the <tt>make demo</tt> or the
683 <tt>make check</tt> commands.