doc/groups.dox
author Peter Kovacs <kpeter@inf.elte.hu>
Sun, 30 Nov 2008 21:53:24 +0100
changeset 422 a578265aa8a6
parent 403 0a3ec097a76c
child 434 ad483acf1654
permissions -rw-r--r--
Improvements in groups.dox (#188)

- Unify the notations used for formulas.
- Add 'namespace lemon {...}' to simplify the references.
- Improved doc for algorithm groups.
- Extend the doc of the "shortest path" and "minimum cost flow" modules.
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/* -*- mode: C++; indent-tabs-mode: nil; -*-
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 *
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 * This file is a part of LEMON, a generic C++ optimization library.
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 *
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 * Copyright (C) 2003-2008
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 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
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 * (Egervary Research Group on Combinatorial Optimization, EGRES).
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 *
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 * Permission to use, modify and distribute this software is granted
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 * provided that this copyright notice appears in all copies. For
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 * precise terms see the accompanying LICENSE file.
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 *
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 * This software is provided "AS IS" with no warranty of any kind,
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 * express or implied, and with no claim as to its suitability for any
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 * purpose.
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 *
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 */
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namespace lemon {
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/**
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@defgroup datas Data Structures
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This group describes the several data structures implemented in LEMON.
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*/
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/**
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@defgroup graphs Graph Structures
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@ingroup datas
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\brief Graph structures implemented in LEMON.
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The implementation of combinatorial algorithms heavily relies on
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efficient graph implementations. LEMON offers data structures which are
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planned to be easily used in an experimental phase of implementation studies,
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and thereafter the program code can be made efficient by small modifications.
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The most efficient implementation of diverse applications require the
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usage of different physical graph implementations. These differences
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appear in the size of graph we require to handle, memory or time usage
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limitations or in the set of operations through which the graph can be
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accessed.  LEMON provides several physical graph structures to meet
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the diverging requirements of the possible users.  In order to save on
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running time or on memory usage, some structures may fail to provide
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some graph features like arc/edge or node deletion.
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Alteration of standard containers need a very limited number of
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operations, these together satisfy the everyday requirements.
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In the case of graph structures, different operations are needed which do
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not alter the physical graph, but gives another view. If some nodes or
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arcs have to be hidden or the reverse oriented graph have to be used, then
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this is the case. It also may happen that in a flow implementation
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the residual graph can be accessed by another algorithm, or a node-set
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is to be shrunk for another algorithm.
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LEMON also provides a variety of graphs for these requirements called
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\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
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in conjunction with other graph representations.
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You are free to use the graph structure that fit your requirements
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the best, most graph algorithms and auxiliary data structures can be used
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with any graph structure.
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<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
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*/
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/**
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@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
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@ingroup graphs
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\brief Graph types between real graphs and graph adaptors.
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This group describes some graph types between real graphs and graph adaptors.
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These classes wrap graphs to give new functionality as the adaptors do it.
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On the other hand they are not light-weight structures as the adaptors.
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*/
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/**
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@defgroup maps Maps
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@ingroup datas
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\brief Map structures implemented in LEMON.
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This group describes the map structures implemented in LEMON.
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LEMON provides several special purpose maps and map adaptors that e.g. combine
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new maps from existing ones.
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<b>See also:</b> \ref map_concepts "Map Concepts".
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*/
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/**
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@defgroup graph_maps Graph Maps
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@ingroup maps
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\brief Special graph-related maps.
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This group describes maps that are specifically designed to assign
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values to the nodes and arcs/edges of graphs.
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If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
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\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
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*/
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/**
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\defgroup map_adaptors Map Adaptors
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\ingroup maps
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\brief Tools to create new maps from existing ones
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This group describes map adaptors that are used to create "implicit"
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maps from other maps.
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Most of them are \ref concepts::ReadMap "read-only maps".
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They can make arithmetic and logical operations between one or two maps
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(negation, shifting, addition, multiplication, logical 'and', 'or',
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'not' etc.) or e.g. convert a map to another one of different Value type.
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The typical usage of this classes is passing implicit maps to
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algorithms.  If a function type algorithm is called then the function
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type map adaptors can be used comfortable. For example let's see the
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usage of map adaptors with the \c graphToEps() function.
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\code
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  Color nodeColor(int deg) {
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    if (deg >= 2) {
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      return Color(0.5, 0.0, 0.5);
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    } else if (deg == 1) {
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      return Color(1.0, 0.5, 1.0);
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    } else {
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      return Color(0.0, 0.0, 0.0);
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    }
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  }
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  Digraph::NodeMap<int> degree_map(graph);
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  graphToEps(graph, "graph.eps")
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    .coords(coords).scaleToA4().undirected()
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    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
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    .run();
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\endcode
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The \c functorToMap() function makes an \c int to \c Color map from the
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\c nodeColor() function. The \c composeMap() compose the \c degree_map
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and the previously created map. The composed map is a proper function to
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get the color of each node.
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The usage with class type algorithms is little bit harder. In this
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case the function type map adaptors can not be used, because the
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function map adaptors give back temporary objects.
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\code
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  Digraph graph;
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  typedef Digraph::ArcMap<double> DoubleArcMap;
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  DoubleArcMap length(graph);
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  DoubleArcMap speed(graph);
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  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
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  TimeMap time(length, speed);
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  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
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  dijkstra.run(source, target);
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\endcode
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We have a length map and a maximum speed map on the arcs of a digraph.
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The minimum time to pass the arc can be calculated as the division of
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the two maps which can be done implicitly with the \c DivMap template
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class. We use the implicit minimum time map as the length map of the
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\c Dijkstra algorithm.
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*/
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/**
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@defgroup matrices Matrices
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@ingroup datas
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\brief Two dimensional data storages implemented in LEMON.
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This group describes two dimensional data storages implemented in LEMON.
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*/
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/**
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@defgroup paths Path Structures
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@ingroup datas
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\brief %Path structures implemented in LEMON.
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This group describes the path structures implemented in LEMON.
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LEMON provides flexible data structures to work with paths.
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All of them have similar interfaces and they can be copied easily with
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assignment operators and copy constructors. This makes it easy and
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efficient to have e.g. the Dijkstra algorithm to store its result in
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any kind of path structure.
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\sa lemon::concepts::Path
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*/
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/**
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@defgroup auxdat Auxiliary Data Structures
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@ingroup datas
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\brief Auxiliary data structures implemented in LEMON.
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This group describes some data structures implemented in LEMON in
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order to make it easier to implement combinatorial algorithms.
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*/
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/**
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@defgroup algs Algorithms
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\brief This group describes the several algorithms
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implemented in LEMON.
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This group describes the several algorithms
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implemented in LEMON.
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*/
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/**
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@defgroup search Graph Search
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@ingroup algs
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\brief Common graph search algorithms.
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This group describes the common graph search algorithms, namely
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\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
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*/
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/**
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@defgroup shortest_path Shortest Path Algorithms
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@ingroup algs
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\brief Algorithms for finding shortest paths.
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This group describes the algorithms for finding shortest paths in digraphs.
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 - \ref Dijkstra algorithm for finding shortest paths from a source node
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   when all arc lengths are non-negative.
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 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
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   from a source node when arc lenghts can be either positive or negative,
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   but the digraph should not contain directed cycles with negative total
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   length.
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 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
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   for solving the \e all-pairs \e shortest \e paths \e problem when arc
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   lenghts can be either positive or negative, but the digraph should
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   not contain directed cycles with negative total length.
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 - \ref Suurballe A successive shortest path algorithm for finding
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   arc-disjoint paths between two nodes having minimum total length.
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*/
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/**
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@defgroup max_flow Maximum Flow Algorithms
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@ingroup algs
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\brief Algorithms for finding maximum flows.
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This group describes the algorithms for finding maximum flows and
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feasible circulations.
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The \e maximum \e flow \e problem is to find a flow of maximum value between
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a single source and a single target. Formally, there is a \f$G=(V,A)\f$
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digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
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\f$s, t \in V\f$ source and target nodes.
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A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
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following optimization problem.
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\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
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\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
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    \qquad \forall v\in V\setminus\{s,t\} \f]
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\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
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LEMON contains several algorithms for solving maximum flow problems:
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- \ref EdmondsKarp Edmonds-Karp algorithm.
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- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
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- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
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- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
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In most cases the \ref Preflow "Preflow" algorithm provides the
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fastest method for computing a maximum flow. All implementations
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provides functions to also query the minimum cut, which is the dual
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problem of the maximum flow.
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*/
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/**
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@defgroup min_cost_flow Minimum Cost Flow Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cost flows and circulations.
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This group describes the algorithms for finding minimum cost flows and
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circulations.
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The \e minimum \e cost \e flow \e problem is to find a feasible flow of
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minimum total cost from a set of supply nodes to a set of demand nodes
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in a network with capacity constraints and arc costs.
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Formally, let \f$G=(V,A)\f$ be a digraph,
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\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
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upper bounds for the flow values on the arcs,
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\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
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on the arcs, and
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\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
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of the nodes.
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A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
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the following optimization problem.
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\f[ \min\sum_{a\in A} f(a) cost(a) \f]
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\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
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    supply(v) \qquad \forall v\in V \f]
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\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
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LEMON contains several algorithms for solving minimum cost flow problems:
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 - \ref CycleCanceling Cycle-canceling algorithms.
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 - \ref CapacityScaling Successive shortest path algorithm with optional
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   capacity scaling.
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 - \ref CostScaling Push-relabel and augment-relabel algorithms based on
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   cost scaling.
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 - \ref NetworkSimplex Primal network simplex algorithm with various
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   pivot strategies.
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*/
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/**
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@defgroup min_cut Minimum Cut Algorithms
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@ingroup algs
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\brief Algorithms for finding minimum cut in graphs.
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This group describes the algorithms for finding minimum cut in graphs.
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The \e minimum \e cut \e problem is to find a non-empty and non-complete
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\f$X\f$ subset of the nodes with minimum overall capacity on
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outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
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\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
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cut is the \f$X\f$ solution of the next optimization problem:
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\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
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    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
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LEMON contains several algorithms related to minimum cut problems:
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- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
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  in directed graphs.
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- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
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  calculating minimum cut in undirected graphs.
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- \ref GomoryHuTree "Gomory-Hu tree computation" for calculating
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  all-pairs minimum cut in undirected graphs.
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If you want to find minimum cut just between two distinict nodes,
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see the \ref max_flow "maximum flow problem".
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*/
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/**
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@defgroup graph_prop Connectivity and Other Graph Properties
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@ingroup algs
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\brief Algorithms for discovering the graph properties
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This group describes the algorithms for discovering the graph properties
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like connectivity, bipartiteness, euler property, simplicity etc.
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\image html edge_biconnected_components.png
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\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
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*/
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/**
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@defgroup planar Planarity Embedding and Drawing
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@ingroup algs
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\brief Algorithms for planarity checking, embedding and drawing
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This group describes the algorithms for planarity checking,
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embedding and drawing.
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\image html planar.png
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\image latex planar.eps "Plane graph" width=\textwidth
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*/
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/**
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@defgroup matching Matching Algorithms
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@ingroup algs
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\brief Algorithms for finding matchings in graphs and bipartite graphs.
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This group contains algorithm objects and functions to calculate
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matchings in graphs and bipartite graphs. The general matching problem is
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finding a subset of the arcs which does not shares common endpoints.
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There are several different algorithms for calculate matchings in
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graphs.  The matching problems in bipartite graphs are generally
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easier than in general graphs. The goal of the matching optimization
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can be finding maximum cardinality, maximum weight or minimum cost
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matching. The search can be constrained to find perfect or
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maximum cardinality matching.
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The matching algorithms implemented in LEMON:
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- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
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  for calculating maximum cardinality matching in bipartite graphs.
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- \ref PrBipartiteMatching Push-relabel algorithm
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  for calculating maximum cardinality matching in bipartite graphs.
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- \ref MaxWeightedBipartiteMatching
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  Successive shortest path algorithm for calculating maximum weighted
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  matching and maximum weighted bipartite matching in bipartite graphs.
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- \ref MinCostMaxBipartiteMatching
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  Successive shortest path algorithm for calculating minimum cost maximum
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  matching in bipartite graphs.
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- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
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  maximum cardinality matching in general graphs.
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- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
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  maximum weighted matching in general graphs.
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- \ref MaxWeightedPerfectMatching
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  Edmond's blossom shrinking algorithm for calculating maximum weighted
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  perfect matching in general graphs.
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\image html bipartite_matching.png
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\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
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*/
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/**
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@defgroup spantree Minimum Spanning Tree Algorithms
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@ingroup algs
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\brief Algorithms for finding a minimum cost spanning tree in a graph.
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This group describes the algorithms for finding a minimum cost spanning
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tree in a graph.
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*/
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/**
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@defgroup auxalg Auxiliary Algorithms
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@ingroup algs
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\brief Auxiliary algorithms implemented in LEMON.
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This group describes some algorithms implemented in LEMON
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in order to make it easier to implement complex algorithms.
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*/
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/**
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@defgroup approx Approximation Algorithms
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@ingroup algs
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\brief Approximation algorithms.
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This group describes the approximation and heuristic algorithms
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implemented in LEMON.
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*/
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/**
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@defgroup gen_opt_group General Optimization Tools
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\brief This group describes some general optimization frameworks
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implemented in LEMON.
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This group describes some general optimization frameworks
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implemented in LEMON.
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*/
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/**
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@defgroup lp_group Lp and Mip Solvers
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@ingroup gen_opt_group
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\brief Lp and Mip solver interfaces for LEMON.
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This group describes Lp and Mip solver interfaces for LEMON. The
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various LP solvers could be used in the same manner with this
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interface.
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*/
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/**
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@defgroup lp_utils Tools for Lp and Mip Solvers
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@ingroup lp_group
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\brief Helper tools to the Lp and Mip solvers.
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This group adds some helper tools to general optimization framework
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implemented in LEMON.
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*/
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/**
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@defgroup metah Metaheuristics
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@ingroup gen_opt_group
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\brief Metaheuristics for LEMON library.
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This group describes some metaheuristic optimization tools.
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*/
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/**
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@defgroup utils Tools and Utilities
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\brief Tools and utilities for programming in LEMON
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Tools and utilities for programming in LEMON.
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*/
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/**
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@defgroup gutils Basic Graph Utilities
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@ingroup utils
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\brief Simple basic graph utilities.
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This group describes some simple basic graph utilities.
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*/
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/**
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@defgroup misc Miscellaneous Tools
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@ingroup utils
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\brief Tools for development, debugging and testing.
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This group describes several useful tools for development,
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debugging and testing.
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*/
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/**
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@defgroup timecount Time Measuring and Counting
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@ingroup misc
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\brief Simple tools for measuring the performance of algorithms.
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This group describes simple tools for measuring the performance
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of algorithms.
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*/
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/**
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@defgroup exceptions Exceptions
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@ingroup utils
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\brief Exceptions defined in LEMON.
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This group describes the exceptions defined in LEMON.
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*/
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/**
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@defgroup io_group Input-Output
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\brief Graph Input-Output methods
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This group describes the tools for importing and exporting graphs
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and graph related data. Now it supports the \ref lgf-format
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"LEMON Graph Format", the \c DIMACS format and the encapsulated
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postscript (EPS) format.
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*/
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/**
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@defgroup lemon_io LEMON Graph Format
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@ingroup io_group
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\brief Reading and writing LEMON Graph Format.
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   515
This group describes methods for reading and writing
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\ref lgf-format "LEMON Graph Format".
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*/
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/**
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@defgroup eps_io Postscript Exporting
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@ingroup io_group
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\brief General \c EPS drawer and graph exporter
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This group describes general \c EPS drawing methods and special
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   525
graph exporting tools.
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   526
*/
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   527
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   528
/**
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@defgroup dimacs_group DIMACS format
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@ingroup io_group
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   531
\brief Read and write files in DIMACS format
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   532
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   533
Tools to read a digraph from or write it to a file in DIMACS format data.
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   534
*/
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   535
kpeter@403
   536
/**
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   537
@defgroup nauty_group NAUTY Format
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   538
@ingroup io_group
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   539
\brief Read \e Nauty format
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   540
kpeter@363
   541
Tool to read graphs from \e Nauty format data.
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   542
*/
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   543
kpeter@363
   544
/**
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@defgroup concept Concepts
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\brief Skeleton classes and concept checking classes
alpar@40
   547
alpar@40
   548
This group describes the data/algorithm skeletons and concept checking
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classes implemented in LEMON.
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   550
alpar@40
   551
The purpose of the classes in this group is fourfold.
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   552
kpeter@318
   553
- These classes contain the documentations of the %concepts. In order
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   554
  to avoid document multiplications, an implementation of a concept
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   555
  simply refers to the corresponding concept class.
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   556
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   557
- These classes declare every functions, <tt>typedef</tt>s etc. an
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  implementation of the %concepts should provide, however completely
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   559
  without implementations and real data structures behind the
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  interface. On the other hand they should provide nothing else. All
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  the algorithms working on a data structure meeting a certain concept
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  should compile with these classes. (Though it will not run properly,
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   563
  of course.) In this way it is easily to check if an algorithm
alpar@40
   564
  doesn't use any extra feature of a certain implementation.
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   565
alpar@40
   566
- The concept descriptor classes also provide a <em>checker class</em>
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   567
  that makes it possible to check whether a certain implementation of a
alpar@40
   568
  concept indeed provides all the required features.
alpar@40
   569
alpar@40
   570
- Finally, They can serve as a skeleton of a new implementation of a concept.
alpar@40
   571
*/
alpar@40
   572
alpar@40
   573
/**
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   574
@defgroup graph_concepts Graph Structure Concepts
alpar@40
   575
@ingroup concept
alpar@40
   576
\brief Skeleton and concept checking classes for graph structures
alpar@40
   577
kpeter@50
   578
This group describes the skeletons and concept checking classes of LEMON's
alpar@40
   579
graph structures and helper classes used to implement these.
alpar@40
   580
*/
alpar@40
   581
kpeter@314
   582
/**
kpeter@314
   583
@defgroup map_concepts Map Concepts
kpeter@314
   584
@ingroup concept
kpeter@314
   585
\brief Skeleton and concept checking classes for maps
kpeter@314
   586
kpeter@314
   587
This group describes the skeletons and concept checking classes of maps.
alpar@40
   588
*/
alpar@40
   589
alpar@40
   590
/**
alpar@40
   591
\anchor demoprograms
alpar@40
   592
kpeter@422
   593
@defgroup demos Demo Programs
alpar@40
   594
alpar@40
   595
Some demo programs are listed here. Their full source codes can be found in
alpar@40
   596
the \c demo subdirectory of the source tree.
alpar@40
   597
alpar@41
   598
It order to compile them, use <tt>--enable-demo</tt> configure option when
alpar@41
   599
build the library.
alpar@40
   600
*/
alpar@40
   601
alpar@40
   602
/**
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   603
@defgroup tools Standalone Utility Applications
alpar@40
   604
alpar@209
   605
Some utility applications are listed here.
alpar@40
   606
alpar@40
   607
The standard compilation procedure (<tt>./configure;make</tt>) will compile
alpar@209
   608
them, as well.
alpar@40
   609
*/
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   610
kpeter@422
   611
}