COIN-OR::LEMON - Graph Library

source: lemon-1.2/doc/groups.dox @ 564:eda12d8ac953

Last change on this file since 564:eda12d8ac953 was 564:eda12d8ac953, checked in by Akos Ladanyi <ladanyi@…>, 11 years ago

Add 'demo' make target for building the demo programs

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[209]1/* -*- mode: C++; indent-tabs-mode: nil; -*-
[40]2 *
[209]3 * This file is a part of LEMON, a generic C++ optimization library.
[40]4 *
[440]5 * Copyright (C) 2003-2009
[40]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 */
[406]19namespace lemon {
22@defgroup datas Data Structures
[559]23This group contains the several data structures implemented in LEMON.
27@defgroup graphs Graph Structures
28@ingroup datas
29\brief Graph structures implemented in LEMON.
[209]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.
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
[83]43some graph features like arc/edge or node deletion.
[209]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
[83]49arcs have to be hidden or the reverse oriented graph have to be used, then
[209]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.
57You are free to use the graph structure that fit your requirements
58the best, most graph algorithms and auxiliary data structures can be used
[314]59with any graph structure.
61<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
[451]65@defgroup graph_adaptors Adaptor Classes for Graphs
[416]66@ingroup graphs
[451]67\brief Adaptor classes for digraphs and graphs
69This group contains several useful adaptor classes for digraphs and graphs.
71The main parts of LEMON are the different graph structures, generic
[451]72graph algorithms, graph concepts, which couple them, and graph
[416]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.
77A short example makes this much clearer.  Suppose that we have an
[451]78instance \c g of a directed graph type, say ListDigraph and an algorithm
80template <typename Digraph>
81int algorithm(const Digraph&);
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
[451]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
[416]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
[451]92obtained by a usual construction like filtering the node or the arc set or
[416]93considering a new orientation, then an adaptor is worthwhile to use.
94To come back to the reverse oriented graph, in this situation
96template<typename Digraph> class ReverseDigraph;
98template class can be used. The code looks as follows
100ListDigraph g;
[451]101ReverseDigraph<ListDigraph> rg(g);
[416]102int result = algorithm(rg);
[451]104During running the algorithm, the original digraph \c g is untouched.
105This techniques give rise to an elegant code, and based on stable
[416]106graph adaptors, complex algorithms can be implemented easily.
[451]108In flow, circulation and matching problems, the residual
[416]109graph is of particular importance. Combining an adaptor implementing
[451]110this with shortest path algorithms or minimum mean cycle algorithms,
[416]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.
115The behavior of graph adaptors can be very different. Some of them keep
116capabilities of the original graph while in other cases this would be
[451]117meaningless. This means that the concepts that they meet depend
118on the graph adaptor, and the wrapped graph.
119For example, if an arc of a reversed digraph is deleted, this is carried
120out by deleting the corresponding arc of the original digraph, thus the
121adaptor modifies the original digraph.
122However in case of a residual digraph, this operation has no sense.
124Let us stand one more example here to simplify your work.
[451]125ReverseDigraph has constructor
127ReverseDigraph(Digraph& digraph);
[451]129This means that in a situation, when a <tt>const %ListDigraph&</tt>
[416]130reference to a graph is given, then it have to be instantiated with
[451]131<tt>Digraph=const %ListDigraph</tt>.
133int algorithm1(const ListDigraph& g) {
[451]134  ReverseDigraph<const ListDigraph> rg(g);
[416]135  return algorithm2(rg);
[50]141@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
[40]142@ingroup graphs
143\brief Graph types between real graphs and graph adaptors.
[559]145This group contains some graph types between real graphs and graph adaptors.
[209]146These classes wrap graphs to give new functionality as the adaptors do it.
[50]147On the other hand they are not light-weight structures as the adaptors.
[209]151@defgroup maps Maps
[40]152@ingroup datas
[50]153\brief Map structures implemented in LEMON.
[559]155This group contains the map structures implemented in LEMON.
[314]157LEMON provides several special purpose maps and map adaptors that e.g. combine
[40]158new maps from existing ones.
160<b>See also:</b> \ref map_concepts "Map Concepts".
[209]164@defgroup graph_maps Graph Maps
[40]165@ingroup maps
[83]166\brief Special graph-related maps.
[559]168This group contains maps that are specifically designed to assign
[406]169values to the nodes and arcs/edges of graphs.
171If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
172\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
176\defgroup map_adaptors Map Adaptors
177\ingroup maps
178\brief Tools to create new maps from existing ones
[559]180This group contains map adaptors that are used to create "implicit"
[50]181maps from other maps.
[406]183Most of them are \ref concepts::ReadMap "read-only maps".
[83]184They can make arithmetic and logical operations between one or two maps
185(negation, shifting, addition, multiplication, logical 'and', 'or',
186'not' etc.) or e.g. convert a map to another one of different Value type.
[50]188The typical usage of this classes is passing implicit maps to
[40]189algorithms.  If a function type algorithm is called then the function
190type map adaptors can be used comfortable. For example let's see the
[314]191usage of map adaptors with the \c graphToEps() function.
193  Color nodeColor(int deg) {
194    if (deg >= 2) {
195      return Color(0.5, 0.0, 0.5);
196    } else if (deg == 1) {
197      return Color(1.0, 0.5, 1.0);
198    } else {
199      return Color(0.0, 0.0, 0.0);
200    }
201  }
[83]203  Digraph::NodeMap<int> degree_map(graph);
[314]205  graphToEps(graph, "graph.eps")
[40]206    .coords(coords).scaleToA4().undirected()
[83]207    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
[40]208    .run();
[83]210The \c functorToMap() function makes an \c int to \c Color map from the
[314]211\c nodeColor() function. The \c composeMap() compose the \c degree_map
[83]212and the previously created map. The composed map is a proper function to
213get the color of each node.
215The usage with class type algorithms is little bit harder. In this
216case the function type map adaptors can not be used, because the
[50]217function map adaptors give back temporary objects.
[83]219  Digraph graph;
221  typedef Digraph::ArcMap<double> DoubleArcMap;
222  DoubleArcMap length(graph);
223  DoubleArcMap speed(graph);
225  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
[40]226  TimeMap time(length, speed);
[83]228  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
[40]229, target);
[83]231We have a length map and a maximum speed map on the arcs of a digraph.
232The minimum time to pass the arc can be calculated as the division of
233the two maps which can be done implicitly with the \c DivMap template
[40]234class. We use the implicit minimum time map as the length map of the
235\c Dijkstra algorithm.
[209]239@defgroup matrices Matrices
[40]240@ingroup datas
[50]241\brief Two dimensional data storages implemented in LEMON.
[559]243This group contains two dimensional data storages implemented in LEMON.
247@defgroup paths Path Structures
248@ingroup datas
[318]249\brief %Path structures implemented in LEMON.
[559]251This group contains the path structures implemented in LEMON.
[50]253LEMON provides flexible data structures to work with paths.
254All of them have similar interfaces and they can be copied easily with
255assignment operators and copy constructors. This makes it easy and
[40]256efficient to have e.g. the Dijkstra algorithm to store its result in
257any kind of path structure.
259\sa lemon::concepts::Path
263@defgroup auxdat Auxiliary Data Structures
264@ingroup datas
[50]265\brief Auxiliary data structures implemented in LEMON.
[559]267This group contains some data structures implemented in LEMON in
[40]268order to make it easier to implement combinatorial algorithms.
272@defgroup algs Algorithms
[559]273\brief This group contains the several algorithms
[40]274implemented in LEMON.
[559]276This group contains the several algorithms
[40]277implemented in LEMON.
281@defgroup search Graph Search
282@ingroup algs
[50]283\brief Common graph search algorithms.
[559]285This group contains the common graph search algorithms, namely
[406]286\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
[314]290@defgroup shortest_path Shortest Path Algorithms
[40]291@ingroup algs
[50]292\brief Algorithms for finding shortest paths.
[559]294This group contains the algorithms for finding shortest paths in digraphs.
296 - \ref Dijkstra algorithm for finding shortest paths from a source node
297   when all arc lengths are non-negative.
298 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
299   from a source node when arc lenghts can be either positive or negative,
300   but the digraph should not contain directed cycles with negative total
301   length.
302 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
303   for solving the \e all-pairs \e shortest \e paths \e problem when arc
304   lenghts can be either positive or negative, but the digraph should
305   not contain directed cycles with negative total length.
306 - \ref Suurballe A successive shortest path algorithm for finding
307   arc-disjoint paths between two nodes having minimum total length.
[314]311@defgroup max_flow Maximum Flow Algorithms
[209]312@ingroup algs
[50]313\brief Algorithms for finding maximum flows.
[559]315This group contains the algorithms for finding maximum flows and
[40]316feasible circulations.
[406]318The \e maximum \e flow \e problem is to find a flow of maximum value between
319a single source and a single target. Formally, there is a \f$G=(V,A)\f$
320digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
321\f$s, t \in V\f$ source and target nodes.
322A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
323following optimization problem.
[406]325\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
326\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
327    \qquad \forall v\in V\setminus\{s,t\} \f]
328\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
[50]330LEMON contains several algorithms for solving maximum flow problems:
[406]331- \ref EdmondsKarp Edmonds-Karp algorithm.
332- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
333- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
334- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
[406]336In most cases the \ref Preflow "Preflow" algorithm provides the
337fastest method for computing a maximum flow. All implementations
338provides functions to also query the minimum cut, which is the dual
339problem of the maximum flow.
[314]343@defgroup min_cost_flow Minimum Cost Flow Algorithms
[40]344@ingroup algs
[50]346\brief Algorithms for finding minimum cost flows and circulations.
[559]348This group contains the algorithms for finding minimum cost flows and
351The \e minimum \e cost \e flow \e problem is to find a feasible flow of
352minimum total cost from a set of supply nodes to a set of demand nodes
353in a network with capacity constraints and arc costs.
354Formally, let \f$G=(V,A)\f$ be a digraph,
355\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
356upper bounds for the flow values on the arcs,
357\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
358on the arcs, and
359\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
360of the nodes.
361A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
362the following optimization problem.
364\f[ \min\sum_{a\in A} f(a) cost(a) \f]
365\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
366    supply(v) \qquad \forall v\in V \f]
367\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
369LEMON contains several algorithms for solving minimum cost flow problems:
370 - \ref CycleCanceling Cycle-canceling algorithms.
371 - \ref CapacityScaling Successive shortest path algorithm with optional
372   capacity scaling.
373 - \ref CostScaling Push-relabel and augment-relabel algorithms based on
374   cost scaling.
375 - \ref NetworkSimplex Primal network simplex algorithm with various
376   pivot strategies.
[314]380@defgroup min_cut Minimum Cut Algorithms
[209]381@ingroup algs
[50]383\brief Algorithms for finding minimum cut in graphs.
[559]385This group contains the algorithms for finding minimum cut in graphs.
[406]387The \e minimum \e cut \e problem is to find a non-empty and non-complete
388\f$X\f$ subset of the nodes with minimum overall capacity on
389outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
390\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
[50]391cut is the \f$X\f$ solution of the next optimization problem:
[210]393\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
[406]394    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
[50]396LEMON contains several algorithms related to minimum cut problems:
[406]398- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
399  in directed graphs.
400- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
401  calculating minimum cut in undirected graphs.
[559]402- \ref GomoryHu "Gomory-Hu tree computation" for calculating
[406]403  all-pairs minimum cut in undirected graphs.
405If you want to find minimum cut just between two distinict nodes,
[406]406see the \ref max_flow "maximum flow problem".
[314]410@defgroup graph_prop Connectivity and Other Graph Properties
[40]411@ingroup algs
[50]412\brief Algorithms for discovering the graph properties
[559]414This group contains the algorithms for discovering the graph properties
[50]415like connectivity, bipartiteness, euler property, simplicity etc.
417\image html edge_biconnected_components.png
418\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
[314]422@defgroup planar Planarity Embedding and Drawing
[40]423@ingroup algs
[50]424\brief Algorithms for planarity checking, embedding and drawing
[559]426This group contains the algorithms for planarity checking,
[210]427embedding and drawing.
429\image html planar.png
430\image latex planar.eps "Plane graph" width=\textwidth
[314]434@defgroup matching Matching Algorithms
[40]435@ingroup algs
[50]436\brief Algorithms for finding matchings in graphs and bipartite graphs.
[50]438This group contains algorithm objects and functions to calculate
[40]439matchings in graphs and bipartite graphs. The general matching problem is
[83]440finding a subset of the arcs which does not shares common endpoints.
[40]442There are several different algorithms for calculate matchings in
443graphs.  The matching problems in bipartite graphs are generally
444easier than in general graphs. The goal of the matching optimization
[406]445can be finding maximum cardinality, maximum weight or minimum cost
[40]446matching. The search can be constrained to find perfect or
447maximum cardinality matching.
[406]449The matching algorithms implemented in LEMON:
450- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
451  for calculating maximum cardinality matching in bipartite graphs.
452- \ref PrBipartiteMatching Push-relabel algorithm
453  for calculating maximum cardinality matching in bipartite graphs.
454- \ref MaxWeightedBipartiteMatching
455  Successive shortest path algorithm for calculating maximum weighted
456  matching and maximum weighted bipartite matching in bipartite graphs.
457- \ref MinCostMaxBipartiteMatching
458  Successive shortest path algorithm for calculating minimum cost maximum
459  matching in bipartite graphs.
460- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
461  maximum cardinality matching in general graphs.
462- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
463  maximum weighted matching in general graphs.
464- \ref MaxWeightedPerfectMatching
465  Edmond's blossom shrinking algorithm for calculating maximum weighted
466  perfect matching in general graphs.
468\image html bipartite_matching.png
469\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
[314]473@defgroup spantree Minimum Spanning Tree Algorithms
[40]474@ingroup algs
[50]475\brief Algorithms for finding a minimum cost spanning tree in a graph.
[559]477This group contains the algorithms for finding a minimum cost spanning
[406]478tree in a graph.
[314]482@defgroup auxalg Auxiliary Algorithms
[40]483@ingroup algs
[50]484\brief Auxiliary algorithms implemented in LEMON.
[559]486This group contains some algorithms implemented in LEMON
[50]487in order to make it easier to implement complex algorithms.
[314]491@defgroup approx Approximation Algorithms
492@ingroup algs
[50]493\brief Approximation algorithms.
[559]495This group contains the approximation and heuristic algorithms
[50]496implemented in LEMON.
500@defgroup gen_opt_group General Optimization Tools
[559]501\brief This group contains some general optimization frameworks
[40]502implemented in LEMON.
[559]504This group contains some general optimization frameworks
[40]505implemented in LEMON.
[314]509@defgroup lp_group Lp and Mip Solvers
[40]510@ingroup gen_opt_group
511\brief Lp and Mip solver interfaces for LEMON.
[559]513This group contains Lp and Mip solver interfaces for LEMON. The
[40]514various LP solvers could be used in the same manner with this
[314]519@defgroup lp_utils Tools for Lp and Mip Solvers
[40]520@ingroup lp_group
[50]521\brief Helper tools to the Lp and Mip solvers.
523This group adds some helper tools to general optimization framework
524implemented in LEMON.
528@defgroup metah Metaheuristics
529@ingroup gen_opt_group
530\brief Metaheuristics for LEMON library.
[559]532This group contains some metaheuristic optimization tools.
[209]536@defgroup utils Tools and Utilities
[50]537\brief Tools and utilities for programming in LEMON
[50]539Tools and utilities for programming in LEMON.
543@defgroup gutils Basic Graph Utilities
544@ingroup utils
[50]545\brief Simple basic graph utilities.
[559]547This group contains some simple basic graph utilities.
551@defgroup misc Miscellaneous Tools
552@ingroup utils
[50]553\brief Tools for development, debugging and testing.
[559]555This group contains several useful tools for development,
[40]556debugging and testing.
[314]560@defgroup timecount Time Measuring and Counting
[40]561@ingroup misc
[50]562\brief Simple tools for measuring the performance of algorithms.
[559]564This group contains simple tools for measuring the performance
[40]565of algorithms.
569@defgroup exceptions Exceptions
570@ingroup utils
[50]571\brief Exceptions defined in LEMON.
[559]573This group contains the exceptions defined in LEMON.
577@defgroup io_group Input-Output
[50]578\brief Graph Input-Output methods
[559]580This group contains the tools for importing and exporting graphs
[314]581and graph related data. Now it supports the \ref lgf-format
582"LEMON Graph Format", the \c DIMACS format and the encapsulated
583postscript (EPS) format.
[351]587@defgroup lemon_io LEMON Graph Format
[40]588@ingroup io_group
[314]589\brief Reading and writing LEMON Graph Format.
[559]591This group contains methods for reading and writing
[236]592\ref lgf-format "LEMON Graph Format".
[314]596@defgroup eps_io Postscript Exporting
[40]597@ingroup io_group
598\brief General \c EPS drawer and graph exporter
[559]600This group contains general \c EPS drawing methods and special
[209]601graph exporting tools.
[388]605@defgroup dimacs_group DIMACS format
606@ingroup io_group
607\brief Read and write files in DIMACS format
609Tools to read a digraph from or write it to a file in DIMACS format data.
[351]613@defgroup nauty_group NAUTY Format
614@ingroup io_group
615\brief Read \e Nauty format
[351]617Tool to read graphs from \e Nauty format data.
[40]621@defgroup concept Concepts
622\brief Skeleton classes and concept checking classes
[559]624This group contains the data/algorithm skeletons and concept checking
[40]625classes implemented in LEMON.
627The purpose of the classes in this group is fourfold.
[318]629- These classes contain the documentations of the %concepts. In order
[40]630  to avoid document multiplications, an implementation of a concept
631  simply refers to the corresponding concept class.
633- These classes declare every functions, <tt>typedef</tt>s etc. an
[318]634  implementation of the %concepts should provide, however completely
[40]635  without implementations and real data structures behind the
636  interface. On the other hand they should provide nothing else. All
637  the algorithms working on a data structure meeting a certain concept
638  should compile with these classes. (Though it will not run properly,
639  of course.) In this way it is easily to check if an algorithm
640  doesn't use any extra feature of a certain implementation.
642- The concept descriptor classes also provide a <em>checker class</em>
[50]643  that makes it possible to check whether a certain implementation of a
[40]644  concept indeed provides all the required features.
646- Finally, They can serve as a skeleton of a new implementation of a concept.
650@defgroup graph_concepts Graph Structure Concepts
651@ingroup concept
652\brief Skeleton and concept checking classes for graph structures
[559]654This group contains the skeletons and concept checking classes of LEMON's
[40]655graph structures and helper classes used to implement these.
659@defgroup map_concepts Map Concepts
660@ingroup concept
661\brief Skeleton and concept checking classes for maps
[559]663This group contains the skeletons and concept checking classes of maps.
667\anchor demoprograms
[406]669@defgroup demos Demo Programs
671Some demo programs are listed here. Their full source codes can be found in
672the \c demo subdirectory of the source tree.
[564]674In order to compile them, use the <tt>make demo</tt> or the
675<tt>make check</tt> commands.
[406]679@defgroup tools Standalone Utility Applications
[209]681Some utility applications are listed here.
683The standard compilation procedure (<tt>./configure;make</tt>) will compile
[209]684them, as well.
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