* This file is a part of LEMON, a generic C++ optimization library
* Copyright (C) 2003-2008
* Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
* (Egervary Research Group on Combinatorial Optimization, EGRES).
* Permission to use, modify and distribute this software is granted
* provided that this copyright notice appears in all copies. For
* precise terms see the accompanying LICENSE file.
* This software is provided "AS IS" with no warranty of any kind,
* express or implied, and with no claim as to its suitability for any
@defgroup datas Data Structures
This group describes the several graph structures implemented in LEMON.
@defgroup graphs Graph Structures
\brief Graph structures implemented in LEMON.
The implementation of combinatorial algorithms heavily relies on
efficient graph implementations. LEMON offers data structures which are
planned to be easily used in an experimental phase of implementation studies,
and thereafter the program code can be made efficient by small modifications.
The most efficient implementation of diverse applications require the
usage of different physical graph implementations. These differences
appear in the size of graph we require to handle, memory or time usage
limitations or in the set of operations through which the graph can be
accessed. LEMON provides several physical graph structures to meet
the diverging requirements of the possible users. In order to save on
running time or on memory usage, some structures may fail to provide
some graph features like edge or node deletion.
Alteration of standard containers need a very limited number of
operations, these together satisfy the everyday requirements.
In the case of graph structures, different operations are needed which do
not alter the physical graph, but gives another view. If some nodes or
edges have to be hidden or the reverse oriented graph have to be used, then
this is the case. It also may happen that in a flow implementation
the residual graph can be accessed by another algorithm, or a node-set
is to be shrunk for another algorithm.
LEMON also provides a variety of graphs for these requirements called
\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
in conjunction with other graph representation.
You are free to use the graph structure that fit your requirements
the best, most graph algorithms and auxiliary data structures can be used
with any graph structures.
@defgroup semi_adaptors Semi-Adaptors Classes for Graphs
\brief Graph types between real graphs and graph adaptors.
Graph types between real graphs and graph adaptors. These classes wrap
graphs to give new functionality as the adaptors do it. On the other
hand they are not light-weight structures as the adaptors.
\brief Some special purpose map to make life easier.
LEMON provides several special maps that e.g. combine
new maps from existing ones.
@defgroup graph_maps Graph Maps
\brief Special Graph-Related Maps.
These maps are specifically designed to assign values to the nodes and edges of
\defgroup map_adaptors Map Adaptors
\brief Tools to create new maps from existing ones
Map adaptors are used to create "implicit" maps from other maps.
Most of them are \ref lemon::concepts::ReadMap "ReadMap"s. They can
make arithmetic operations between one or two maps (negation, scaling,
addition, multiplication etc.) or e.g. convert a map to another one
The typical usage of this classes is the passing implicit maps to
algorithms. If a function type algorithm is called then the function
type map adaptors can be used comfortable. For example let's see the
usage of map adaptors with the \c graphToEps() function:
Color nodeColor(int deg) {
return Color(0.5, 0.0, 0.5);
return Color(1.0, 0.5, 1.0);
return Color(0.0, 0.0, 0.0);
Graph::NodeMap<int> degree_map(graph);
graphToEps(graph, "graph.eps")
.coords(coords).scaleToA4().undirected()
.nodeColors(composeMap(functorMap(nodeColor), degree_map))
The \c functorMap() function makes an \c int to \c Color map from the
\e nodeColor() function. The \c composeMap() compose the \e degree_map
and the previous created map. The composed map is proper function to
The usage with class type algorithms is little bit harder. In this
case the function type map adaptors can not be used, because the
function map adaptors give back temporarly objects.
typedef Graph::EdgeMap<double> DoubleEdgeMap;
DoubleEdgeMap length(graph);
DoubleEdgeMap speed(graph);
typedef DivMap<DoubleEdgeMap, DoubleEdgeMap> TimeMap;
TimeMap time(length, speed);
Dijkstra<Graph, TimeMap> dijkstra(graph, time);
dijkstra.run(source, target);
We have a length map and a maximum speed map on a graph. The minimum
time to pass the edge can be calculated as the division of the two
maps which can be done implicitly with the \c DivMap template
class. We use the implicit minimum time map as the length map of the
@defgroup matrices Matrices
\brief Two dimensional data storages.
Two dimensional data storages.
@defgroup paths Path Structures
\brief Path structures implemented in LEMON.
LEMON provides flexible data structures
All of them have similar interfaces, and it can be copied easily with
assignment operator and copy constructor. This make it easy and
efficient to have e.g. the Dijkstra algorithm to store its result in
any kind of path structure.
\sa lemon::concepts::Path
@defgroup auxdat Auxiliary Data Structures
\brief Some data structures implemented in LEMON.
This group describes the data structures implemented in LEMON in
order to make it easier to implement combinatorial algorithms.
@defgroup algs Algorithms
\brief This group describes the several algorithms
This group describes the several algorithms
@defgroup search Graph Search
\brief This group contains the common graph
This group contains the common graph
search algorithms like Bfs and Dfs.
@defgroup shortest_path Shortest Path algorithms
\brief This group describes the algorithms
for finding shortest paths.
This group describes the algorithms for finding shortest paths in
@defgroup max_flow Maximum Flow algorithms
\brief This group describes the algorithms for finding maximum flows.
This group describes the algorithms for finding maximum flows and
The maximum flow problem is to find a flow between a single-source and
single-target that is maximum. Formally, there is \f$G=(V,A)\f$
directed graph, an \f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity
function and given \f$s, t \in V\f$ source and target node. The
maximum flow is the solution of the next optimization problem:
\f[ 0 \le f_a \le c_a \f]
\f[ \sum_{v\in\delta^{-}(u)}f_{vu}=\sum_{v\in\delta^{+}(u)}f_{uv} \quad u \in V \setminus \{s,t\}\f]
\f[ \max \sum_{v\in\delta^{+}(s)}f_{uv} - \sum_{v\in\delta^{-}(s)}f_{vu}\f]
The lemon contains several algorithms for solve maximum flow problems:
- \ref lemon::EdmondsKarp "Edmonds-Karp"
- \ref lemon::Preflow "Goldberg's Preflow algorithm"
- \ref lemon::DinitzSleatorTarjan "Dinitz's blocking flow algorithm with dynamic tree"
- \ref lemon::GoldbergTarjan "Preflow algorithm with dynamic trees"
In most cases the \ref lemon::Preflow "preflow" algorithm provides the
fastest method to compute the maximum flow. All impelementations
provides functions for query the minimum cut, which is the dual linear
programming probelm of the maximum flow.
@defgroup min_cost_flow Minimum Cost Flow algorithms
\brief This group describes the algorithms
for finding minimum cost flows and circulations.
This group describes the algorithms for finding minimum cost flows and
@defgroup min_cut Minimum Cut algorithms
\brief This group describes the algorithms for finding minimum cut in
This group describes the algorithms for finding minimum cut in graphs.
The minimum cut problem is to find a non-empty and non-complete
\f$X\f$ subset of the vertices with minimum overall capacity on
outgoing arcs. Formally, there is \f$G=(V,A)\f$ directed graph, an
\f$c_a:A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
cut is the solution of the next optimization problem:
\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}\sum_{uv\in A, u\in X, v\not\in X}c_{uv}\f]
The lemon contains several algorithms related to minimum cut problems:
- \ref lemon::HaoOrlin "Hao-Orlin algorithm" for calculate minimum cut
- \ref lemon::NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
calculate minimum cut in undirected graphs
- \ref lemon::GomoryHuTree "Gomory-Hu tree computation" for calculate all
pairs minimum cut in undirected graphs
If you want to find minimum cut just between two distinict nodes,
please see the \ref max_flow "Maximum Flow page".
@defgroup graph_prop Connectivity and other graph properties
\brief This group describes the algorithms
for discover the graph properties
This group describes the algorithms for discover the graph properties
like connectivity, bipartiteness, euler property, simplicity, etc...
\image html edge_biconnected_components.png
\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
@defgroup planar Planarity embedding and drawing
\brief This group contains algorithms for planarity embedding and drawing
This group contains algorithms for planarity checking, embedding and drawing.
\image latex planar.eps "Plane graph" width=\textwidth
@defgroup matching Matching algorithms
\brief This group describes the algorithms
for find matchings in graphs and bipartite graphs.
This group provides some algorithm objects and function to calculate
matchings in graphs and bipartite graphs. The general matching problem is
finding a subset of the edges which does not shares common endpoints.
There are several different algorithms for calculate matchings in
graphs. The matching problems in bipartite graphs are generally
easier than in general graphs. The goal of the matching optimization
can be the finding maximum cardinality, maximum weight or minimum cost
matching. The search can be constrained to find perfect or
maximum cardinality matching.
Lemon contains the next algorithms:
- \ref lemon::MaxBipartiteMatching "MaxBipartiteMatching" Hopcroft-Karp
augmenting path algorithm for calculate maximum cardinality matching in
- \ref lemon::PrBipartiteMatching "PrBipartiteMatching" Push-Relabel
algorithm for calculate maximum cardinality matching in bipartite graphs
- \ref lemon::MaxWeightedBipartiteMatching "MaxWeightedBipartiteMatching"
Successive shortest path algorithm for calculate maximum weighted matching
and maximum weighted bipartite matching in bipartite graph
- \ref lemon::MinCostMaxBipartiteMatching "MinCostMaxBipartiteMatching"
Successive shortest path algorithm for calculate minimum cost maximum
matching in bipartite graph
- \ref lemon::MaxMatching "MaxMatching" Edmond's blossom shrinking algorithm
for calculate maximum cardinality matching in general graph
- \ref lemon::MaxWeightedMatching "MaxWeightedMatching" Edmond's blossom
shrinking algorithm for calculate maximum weighted matching in general
- \ref lemon::MaxWeightedPerfectMatching "MaxWeightedPerfectMatching"
Edmond's blossom shrinking algorithm for calculate maximum weighted
perfect matching in general graph
\image html bipartite_matching.png
\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
@defgroup spantree Minimum Spanning Tree algorithms
\brief This group contains the algorithms for finding a minimum cost spanning
This group contains the algorithms for finding a minimum cost spanning
@defgroup auxalg Auxiliary algorithms
\brief Some algorithms implemented in LEMON.
This group describes the algorithms in LEMON in order to make
it easier to implement complex algorithms.
@defgroup approx Approximation algorithms
\brief Approximation algorithms
Approximation and heuristic algorithms
@defgroup gen_opt_group General Optimization Tools
\brief This group describes some general optimization frameworks
This group describes some general optimization frameworks
@defgroup lp_group Lp and Mip solvers
\brief Lp and Mip solver interfaces for LEMON.
This group describes Lp and Mip solver interfaces for LEMON. The
various LP solvers could be used in the same manner with this
@defgroup lp_utils Tools for Lp and Mip solvers
\brief This group adds some helper tools to the Lp and Mip solvers
This group adds some helper tools to general optimization framework
@defgroup metah Metaheuristics
\brief Metaheuristics for LEMON library.
This group contains some metaheuristic optimization tools.
@defgroup utils Tools and Utilities
\brief Tools and Utilities for Programming in LEMON
Tools and Utilities for Programming in LEMON
@defgroup gutils Basic Graph Utilities
\brief This group describes some simple basic graph utilities.
This group describes some simple basic graph utilities.
@defgroup misc Miscellaneous Tools
Here you can find several useful tools for development,
@defgroup timecount Time measuring and Counting
Here you can find simple tools for measuring the performance
@defgroup graphbits Tools for Graph Implementation
\brief Tools to Make It Easier to Make Graphs.
This group describes the tools that makes it easier to make graphs and
the maps that dynamically update with the graph changes.
@defgroup exceptions Exceptions
This group contains the exceptions thrown by LEMON library
@defgroup io_group Input-Output
\brief Several Graph Input-Output methods
Here you can find tools for importing and exporting graphs
and graph related data. Now it supports the LEMON format, the
\c DIMACS format and the encapsulated postscript format.
@defgroup lemon_io Lemon Input-Output
\brief Reading and writing LEMON format
Methods for reading and writing LEMON format. More about this
format you can find on the \ref graph-io-page "Graph Input-Output"
@defgroup section_io Section readers and writers
\brief Section readers and writers for lemon Input-Output.
Here you can find which section readers and writers can attach to
the LemonReader and LemonWriter.
@defgroup item_io Item Readers and Writers
\brief Item readers and writers for lemon Input-Output.
The Input-Output classes can handle more data type by example
as map or attribute value. Each of these should be written and
read some way. The module make possible to do this.
@defgroup eps_io Postscript exporting
\brief General \c EPS drawer and graph exporter
This group contains general \c EPS drawing methods and special
@defgroup concept Concepts
\brief Skeleton classes and concept checking classes
This group describes the data/algorithm skeletons and concept checking
classes implemented in LEMON.
The purpose of the classes in this group is fourfold.
- These classes contain the documentations of the concepts. In order
to avoid document multiplications, an implementation of a concept
simply refers to the corresponding concept class.
- These classes declare every functions, <tt>typedef</tt>s etc. an
implementation of the concepts should provide, however completely
without implementations and real data structures behind the
interface. On the other hand they should provide nothing else. All
the algorithms working on a data structure meeting a certain concept
should compile with these classes. (Though it will not run properly,
of course.) In this way it is easily to check if an algorithm
doesn't use any extra feature of a certain implementation.
- The concept descriptor classes also provide a <em>checker class</em>
that makes it possible check whether a certain implementation of a
concept indeed provides all the required features.
- Finally, They can serve as a skeleton of a new implementation of a concept.
@defgroup graph_concepts Graph Structure Concepts
\brief Skeleton and concept checking classes for graph structures
This group contains the skeletons and concept checking classes of LEMON's
graph structures and helper classes used to implement these.
@defgroup experimental Experimental Structures and Algorithms
This group contains some Experimental structures and algorithms.
The stuff here is subject to change.
@defgroup demos Demo programs
Some demo programs are listed here. Their full source codes can be found in
the \c demo subdirectory of the source tree.
The standard compilation procedure (<tt>./configure;make</tt>) will compile
@defgroup tools Standalone utility applications
Some utility applications are listed here.
The standard compilation procedure (<tt>./configure;make</tt>) will compile
