RhodeCode

LEMON code without an explicit copyright is covered by the following

copyright/license.

Kutatocsoport (Egervary Combinatorial Optimization Research Group,

EGRES).

Permission is hereby granted, free of charge, to any person or organization

obtaining a copy of the software and accompanying documentation covered by

this license (the "Software") to use, reproduce, display, distribute,

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The copyright notices in the Software and this entire statement, including

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must be included in all copies of the Software, in whole or in part, and

all derivative works of the Software, unless such copies or derivative

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a source language processor.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT

SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE

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DEALINGS IN THE SOFTWARE.

===========================================================================

This license is a verbatim copy of the Boost Software License, Version 1.0.

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

///\ingroup demos

///\file

///\brief Argument parser demo

///

/// This example shows how the argument parser can be used.

///

/// \include arg_parser_demo.cc

#include <lemon/arg_parser.h>

using namespace lemon;

int main(int argc, char **argv)

{

  // Initialize the argument parser

  ArgParser ap(argc, argv);

  int i;

  std::string s;

  double d = 1.0;

  bool b, nh;

  bool g1, g2, g3;

  // Add a mandatory integer option with storage reference

  ap.refOption("n", "An integer input.", i, true);

  // Add a double option with storage reference (the default value is 1.0)

  ap.refOption("val", "A double input.", d);

  // Add a double option without storage reference (the default value is 3.14)

  ap.doubleOption("val2", "A double input.", 3.14);

  // Set synonym for -val option

  ap.synonym("vals", "val");

  // Add a string option

  ap.refOption("name", "A string input.", s);

  // Add bool options

  ap.refOption("f", "A switch.", b)

    .refOption("nohelp", "", nh)

    .refOption("gra", "Choice A", g1)

    .refOption("grb", "Choice B", g2)

    .refOption("grc", "Choice C", g3);

  // Bundle -gr* options into a group

  ap.optionGroup("gr", "gra")

    .optionGroup("gr", "grb")

    .optionGroup("gr", "grc");

  // Set the group mandatory

  ap.mandatoryGroup("gr");

  // Set the options of the group exclusive (only one option can be given)

  ap.onlyOneGroup("gr");

  // Add non-parsed arguments (e.g. input files)

  ap.other("infile", "The input file.")

    .other("...");

  // Perform the parsing process

  // (in case of any error it terminates the program)

  ap.parse();

  // Check each option if it has been given and print its value

  std::cout << "Parameters of '" << ap.commandName() << "':\n";

  std::cout << "  Value of -n: " << i << std::endl;

  if(ap.given("val")) std::cout << "  Value of -val: " << d << std::endl;

  if(ap.given("val2")) {

    d = ap["val2"];

    std::cout << "  Value of -val2: " << d << std::endl;

  }

  if(ap.given("name")) std::cout << "  Value of -name: " << s << std::endl;

  if(ap.given("f")) std::cout << "  -f is given\n";

  if(ap.given("nohelp")) std::cout << "  Value of -nohelp: " << nh << std::endl;

  if(ap.given("gra")) std::cout << "  -gra is given\n";

  if(ap.given("grb")) std::cout << "  -grb is given\n";

  if(ap.given("grc")) std::cout << "  -grc is given\n";

  switch(ap.files().size()) {

  case 0:

    std::cout << "  No file argument was given.\n";

    break;

  case 1:

    std::cout << "  1 file argument was given. It is:\n";

    break;

  default:

    std::cout << "  "

              << ap.files().size() << " file arguments were given. They are:\n";

  }

  for(unsigned int i=0;i<ap.files().size();++i)

    std::cout << "    '" << ap.files()[i] << "'\n";

  return 0;

}

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

/// \ingroup demos

/// \file

/// \brief Demo of the graph drawing function \ref graphToEps()

///

/// This demo program shows examples how to use the function \ref

/// graphToEps(). It takes no input but simply creates seven

/// <tt>.eps</tt> files demonstrating the capability of \ref

/// graphToEps(), and showing how to draw directed graphs,

/// how to handle parallel egdes, how to change the properties (like

/// color, shape, size, title etc.) of nodes and arcs individually

/// using appropriate graph maps.

///

/// \include graph_to_eps_demo.cc

#include<lemon/list_graph.h>

#include<lemon/graph_to_eps.h>

#include<lemon/math.h>

using namespace std;

using namespace lemon;

int main()

{

  Palette palette;

  Palette paletteW(true);

  // Create a small digraph

  ListDigraph g;

  typedef ListDigraph::Node Node;

  typedef ListDigraph::NodeIt NodeIt;

  typedef ListDigraph::Arc Arc;

  typedef dim2::Point<int> Point;

  Node n1=g.addNode();

  Node n2=g.addNode();

  Node n3=g.addNode();

  Node n4=g.addNode();

  Node n5=g.addNode();

  ListDigraph::NodeMap<Point> coords(g);

  ListDigraph::NodeMap<double> sizes(g);

  ListDigraph::NodeMap<int> colors(g);

  ListDigraph::NodeMap<int> shapes(g);

  ListDigraph::ArcMap<int> acolors(g);

  ListDigraph::ArcMap<int> widths(g);

  coords[n1]=Point(50,50);  sizes[n1]=1; colors[n1]=1; shapes[n1]=0;

  coords[n2]=Point(50,70);  sizes[n2]=2; colors[n2]=2; shapes[n2]=2;

  coords[n3]=Point(70,70);  sizes[n3]=1; colors[n3]=3; shapes[n3]=0;

  coords[n4]=Point(70,50);  sizes[n4]=2; colors[n4]=4; shapes[n4]=1;

  coords[n5]=Point(85,60);  sizes[n5]=3; colors[n5]=5; shapes[n5]=2;

  Arc a;

  a=g.addArc(n1,n2); acolors[a]=0; widths[a]=1;

  a=g.addArc(n2,n3); acolors[a]=0; widths[a]=1;

  a=g.addArc(n3,n5); acolors[a]=0; widths[a]=3;

  a=g.addArc(n5,n4); acolors[a]=0; widths[a]=1;

  a=g.addArc(n4,n1); acolors[a]=0; widths[a]=1;

  a=g.addArc(n2,n4); acolors[a]=1; widths[a]=2;

  a=g.addArc(n3,n4); acolors[a]=2; widths[a]=1;

  IdMap<ListDigraph,Node> id(g);

  // Create .eps files showing the digraph with different options

  cout << "Create 'graph_to_eps_demo_out_1_pure.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_1_pure.eps").

    coords(coords).

    title("Sample .eps figure").

    run();

  cout << "Create 'graph_to_eps_demo_out_2.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_2.eps").

    coords(coords).

    title("Sample .eps figure").

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    run();

  cout << "Create 'graph_to_eps_demo_out_3_arr.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_3_arr.eps").

    title("Sample .eps figure (with arrowheads)").

    absoluteNodeSizes().absoluteArcWidths().

    nodeColors(composeMap(palette,colors)).

    coords(coords).

    nodeScale(2).nodeSizes(sizes).

    nodeShapes(shapes).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    drawArrows().arrowWidth(2).arrowLength(2).

    run();

  // Add more arcs to the digraph

  a=g.addArc(n1,n4); acolors[a]=2; widths[a]=1;

  a=g.addArc(n4,n1); acolors[a]=1; widths[a]=2;

  a=g.addArc(n1,n2); acolors[a]=1; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=2; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=3; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=4; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=5; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=6; widths[a]=1;

  a=g.addArc(n1,n2); acolors[a]=7; widths[a]=1;

  cout << "Create 'graph_to_eps_demo_out_4_par.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_4_par.eps").

    title("Sample .eps figure (parallel arcs)").

    absoluteNodeSizes().absoluteArcWidths().

    nodeShapes(shapes).

    coords(coords).

    nodeScale(2).nodeSizes(sizes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.4).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1.5).

    run();

  cout << "Create 'graph_to_eps_demo_out_5_par_arr.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_5_par_arr.eps").

    title("Sample .eps figure (parallel arcs and arrowheads)").

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    coords(coords).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.3).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1).

    drawArrows().arrowWidth(1).arrowLength(1).

    run();

  cout << "Create 'graph_to_eps_demo_out_6_par_arr_a4.eps'" << endl;

  graphToEps(g,"graph_to_eps_demo_out_6_par_arr_a4.eps").

    title("Sample .eps figure (fits to A4)").

    scaleToA4().

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(2).nodeSizes(sizes).

    coords(coords).

    nodeShapes(shapes).

    nodeColors(composeMap(palette,colors)).

    arcColors(composeMap(palette,acolors)).

    arcWidthScale(.3).arcWidths(widths).

    nodeTexts(id).nodeTextSize(3).

    enableParallel().parArcDist(1).

    drawArrows().arrowWidth(1).arrowLength(1).

    run();

  // Create an .eps file showing the colors of a default Palette

  ListDigraph h;

  ListDigraph::NodeMap<int> hcolors(h);

  ListDigraph::NodeMap<Point> hcoords(h);

  int cols=int(sqrt(double(palette.size())));

  for(int i=0;i<int(paletteW.size());i++) {

    Node n=h.addNode();

    hcoords[n]=Point(1+i%cols,1+i/cols);

    hcolors[n]=i;

  }

  cout << "Create 'graph_to_eps_demo_out_7_colors.eps'" << endl;

  graphToEps(h,"graph_to_eps_demo_out_7_colors.eps").

    scale(60).

    title("Sample .eps figure (Palette demo)").

    coords(hcoords).

    absoluteNodeSizes().absoluteArcWidths().

    nodeScale(.45).

    distantColorNodeTexts().

    nodeTexts(hcolors).nodeTextSize(.6).

    nodeColors(composeMap(paletteW,hcolors)).

    run();

  return 0;

}

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

///\ingroup demos

///\file

///\brief Demonstrating graph input and output

///

/// This program gives an example of how to read and write a digraph

/// and additional maps from/to a stream or a file using the

/// \ref lgf-format "LGF" format.

///

/// The \c "digraph.lgf" file:

/// \include digraph.lgf

///

/// And the program which reads it and prints the digraph to the

/// standard output:

/// \include lgf_demo.cc

#include <iostream>

#include <lemon/smart_graph.h>

#include <lemon/lgf_reader.h>

#include <lemon/lgf_writer.h>

using namespace lemon;

int main() {

  SmartDigraph g;

  SmartDigraph::ArcMap<int> cap(g);

  SmartDigraph::Node s, t;

  try {

    digraphReader(g, "digraph.lgf"). // read the directed graph into g

      arcMap("capacity", cap).       // read the 'capacity' arc map into cap

      node("source", s).             // read 'source' node to s

      node("target", t).             // read 'target' node to t

      run();

  } catch (Exception& error) { // check if there was any error

    std::cerr << "Error: " << error.what() << std::endl;

    return -1;

  }

  std::cout << "A digraph is read from 'digraph.lgf'." << std::endl;

  std::cout << "Number of nodes: " << countNodes(g) << std::endl;

  std::cout << "Number of arcs: " << countArcs(g) << std::endl;

  std::cout << "We can write it to the standard output:" << std::endl;

  digraphWriter(g).                // write g to the standard output

    arcMap("capacity", cap).       // write cap into 'capacity'

    node("source", s).             // write s to 'source'

    node("target", t).             // write t to 'target'

    run();

  return 0;

}

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

/*!

\page coding_style LEMON Coding Style

\section naming_conv Naming Conventions

In order to make development easier we have made some conventions

according to coding style. These include names of types, classes,

functions, variables, constants and exceptions. If these conventions

are met in one's code then it is easier to read and maintain

it. Please comply with these conventions if you want to contribute

developing LEMON library.

\note When the coding style requires the capitalization of an abbreviation,

only the first letter should be upper case.

\code

XmlReader

\endcode

\warning In some cases we diverge from these rules.

This is primary done because STL uses different naming convention and

in certain cases

it is beneficial to provide STL compatible interface.

\subsection cs-files File Names

The header file names should look like the following.

\code

header_file.h

\endcode

Note that all standard LEMON headers are located in the \c lemon subdirectory,

so you should include them from C++ source like this:

\code

#include <lemon/header_file.h>

\endcode

The source code files use the same style and they have '.cc' extension.

\code

source_code.cc

\endcode

\subsection cs-class Classes and other types

The name of a class or any type should look like the following.

\code

AllWordsCapitalizedWithoutUnderscores

\endcode

\subsection cs-func Methods and other functions

The name of a function should look like the following.

\code

firstWordLowerCaseRestCapitalizedWithoutUnderscores

\endcode

\subsection cs-funcs Constants, Macros

The names of constants and macros should look like the following.

\code

ALL_UPPER_CASE_WITH_UNDERSCORES

\endcode

\subsection cs-loc-var Class and instance member variables, auto variables

The names of class and instance member variables and auto variables

(=variables used locally in methods) should look like the following.

\code

all_lower_case_with_underscores

\endcode

\subsection pri-loc-var Private member variables

Private member variables should start with underscore

\code

_start_with_underscores

\endcode

\subsection cs-excep Exceptions

When writing exceptions please comply the following naming conventions.

\code

ClassNameEndsWithException

\endcode

or

\code

ClassNameEndsWithError

\endcode

\section header-template Template Header File

Each LEMON header file should look like this:

\include template.h

*/

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

/**

\dir demo

\brief A collection of demo applications.

This directory contains several simple demo applications, mainly

for educational purposes.

*/

/**

\dir doc

\brief Auxiliary (and the whole generated) documentation.

This directory contains some auxiliary pages and the whole generated

documentation.

*/

/**

\dir test

\brief Test programs.

This directory contains several test programs that check the consistency

of the code.

*/

/**

\dir tools

\brief Some useful executables.

This directory contains the sources of some useful complete executables.

*/

/**

\dir lemon

\brief Base include directory of LEMON.

This is the base directory of LEMON includes, so each include file must be

prefixed with this, e.g.

\code

#include<lemon/list_graph.h>

#include<lemon/dijkstra.h>

\endcode

*/

/**

\dir concepts

\brief Concept descriptors and checking classes.

This directory contains the concept descriptors and concept checking tools.

For more information see the \ref concept "Concepts" module.

*/

/**

\dir bits

\brief Auxiliary tools for implementation.

maps and some other classes.

As a user you typically don't have to deal with these files.

*/

/* -*- mode: C++; indent-tabs-mode: nil; -*-

 *

 * This file is a part of LEMON, a generic C++ optimization library.

 *

 * 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

 * purpose.

 *

 */

namespace lemon {

/**

@defgroup datas Data Structures

This group describes the several data structures implemented in LEMON.

*/

/**

@defgroup graphs Graph Structures

@ingroup datas

\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 arc/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

arcs 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 representations.

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 structure.

<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".

*/

/**

@defgroup graph_adaptors Adaptor Classes for graphs

@ingroup graphs

\brief This group contains several adaptor classes for digraphs and graphs

The main parts of LEMON are the different graph structures, generic

graph algorithms, graph concepts which couple these, and graph

adaptors. While the previous notions are more or less clear, the

latter one needs further explanation. Graph adaptors are graph classes

which serve for considering graph structures in different ways.

A short example makes this much clearer.  Suppose that we have an

instance \c g of a directed graph type say ListDigraph and an algorithm

\code

template <typename Digraph>

int algorithm(const Digraph&);

\endcode

is needed to run on the reverse oriented graph.  It may be expensive

(in time or in memory usage) to copy \c g with the reversed

arcs.  In this case, an adaptor class is used, which (according

to LEMON digraph concepts) works as a digraph.  The adaptor uses the

original digraph structure and digraph operations when methods of the

reversed oriented graph are called.  This means that the adaptor have

minor memory usage, and do not perform sophisticated algorithmic

actions.  The purpose of it is to give a tool for the cases when a

graph have to be used in a specific alteration.  If this alteration is

obtained by a usual construction like filtering the arc-set or

considering a new orientation, then an adaptor is worthwhile to use.

To come back to the reverse oriented graph, in this situation

\code

template<typename Digraph> class ReverseDigraph;

\endcode

template class can be used. The code looks as follows

\code

ListDigraph g;

ReverseDigraph<ListGraph> rg(g);

int result = algorithm(rg);

\endcode

After running the algorithm, the original graph \c g is untouched.

This techniques gives rise to an elegant code, and based on stable

graph adaptors, complex algorithms can be implemented easily.

In flow, circulation and bipartite matching problems, the residual

graph is of particular importance. Combining an adaptor implementing

this, shortest path algorithms and minimum mean cycle algorithms,

a range of weighted and cardinality optimization algorithms can be

obtained. For other examples, the interested user is referred to the

detailed documentation of particular adaptors.

The behavior of graph adaptors can be very different. Some of them keep

capabilities of the original graph while in other cases this would be

meaningless. This means that the concepts that they are models of depend

on the graph adaptor, and the wrapped graph(s).

If an arc of \c rg is deleted, this is carried out by deleting the

corresponding arc of \c g, thus the adaptor modifies the original graph.

But for a residual graph, this operation has no sense.

Let us stand one more example here to simplify your work.

RevGraphAdaptor has constructor

\code

ReverseDigraph(Digraph& digraph);

\endcode

This means that in a situation, when a <tt>const ListDigraph&</tt>

reference to a graph is given, then it have to be instantiated with

<tt>Digraph=const ListDigraph</tt>.

\code

int algorithm1(const ListDigraph& g) {

  RevGraphAdaptor<const ListDigraph> rg(g);

  return algorithm2(rg);

}

\endcode

*/

/**

@defgroup semi_adaptors Semi-Adaptor Classes for Graphs

@ingroup graphs

\brief Graph types between real graphs and graph adaptors.

This group describes some 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.

*/

/**

@defgroup maps Maps

@ingroup datas

\brief Map structures implemented in LEMON.

This group describes the map structures implemented in LEMON.

LEMON provides several special purpose maps and map adaptors that e.g. combine

new maps from existing ones.

<b>See also:</b> \ref map_concepts "Map Concepts".

*/

/**

@defgroup graph_maps Graph Maps

@ingroup maps

\brief Special graph-related maps.

This group describes maps that are specifically designed to assign

values to the nodes and arcs/edges of graphs.

If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,

\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".

*/

/**

\defgroup map_adaptors Map Adaptors

\ingroup maps

\brief Tools to create new maps from existing ones

This group describes map adaptors that are used to create "implicit"

maps from other maps.

Most of them are \ref concepts::ReadMap "read-only maps".

They can make arithmetic and logical operations between one or two maps

(negation, shifting, addition, multiplication, logical 'and', 'or',

'not' etc.) or e.g. convert a map to another one of different Value type.

The typical usage of this classes is 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.

\code

  Color nodeColor(int deg) {

    if (deg >= 2) {

      return Color(0.5, 0.0, 0.5);

    } else if (deg == 1) {

      return Color(1.0, 0.5, 1.0);

    } else {

      return Color(0.0, 0.0, 0.0);

    }

  }

  Digraph::NodeMap<int> degree_map(graph);

  graphToEps(graph, "graph.eps")

    .coords(coords).scaleToA4().undirected()

    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))

    .run();

\endcode

The \c functorToMap() function makes an \c int to \c Color map from the

\c nodeColor() function. The \c composeMap() compose the \c degree_map

and the previously created map. The composed map is a proper function to

get the color of each node.

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 temporary objects.

\code

  Digraph graph;

  typedef Digraph::ArcMap<double> DoubleArcMap;

  DoubleArcMap length(graph);

  DoubleArcMap speed(graph);

  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;

  TimeMap time(length, speed);

  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);

  dijkstra.run(source, target);

\endcode

We have a length map and a maximum speed map on the arcs of a digraph.

The minimum time to pass the arc 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

\c Dijkstra algorithm.

*/

/**

@defgroup matrices Matrices

@ingroup datas

\brief Two dimensional data storages implemented in LEMON.

This group describes two dimensional data storages implemented in LEMON.

*/

/**

@defgroup paths Path Structures

@ingroup datas

\brief %Path structures implemented in LEMON.

This group describes the path structures implemented in LEMON.

LEMON provides flexible data structures to work with paths.

All of them have similar interfaces and they can be copied easily with

assignment operators and copy constructors. This makes 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

@ingroup datas

\brief Auxiliary data structures implemented in LEMON.

This group describes some 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

implemented in LEMON.

This group describes the several algorithms

implemented in LEMON.

*/

/**

@defgroup search Graph Search

@ingroup algs

\brief Common graph search algorithms.

This group describes the common graph search algorithms, namely

\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).

*/

/**

@defgroup shortest_path Shortest Path Algorithms

@ingroup algs

\brief Algorithms for finding shortest paths.

This group describes the algorithms for finding shortest paths in digraphs.

 - \ref Dijkstra algorithm for finding shortest paths from a source node

   when all arc lengths are non-negative.

 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths

   from a source node when arc lenghts can be either positive or negative,

   but the digraph should not contain directed cycles with negative total

   length.

 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms

   for solving the \e all-pairs \e shortest \e paths \e problem when arc

   lenghts can be either positive or negative, but the digraph should

   not contain directed cycles with negative total length.

 - \ref Suurballe A successive shortest path algorithm for finding

   arc-disjoint paths between two nodes having minimum total length.

*/

/**

@defgroup max_flow Maximum Flow Algorithms

@ingroup algs

\brief Algorithms for finding maximum flows.

This group describes the algorithms for finding maximum flows and

feasible circulations.

The \e maximum \e flow \e problem is to find a flow of maximum value between

a single source and a single target. Formally, there is a \f$G=(V,A)\f$

digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and

\f$s, t \in V\f$ source and target nodes.

A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the

following optimization problem.

\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]

\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)

    \qquad \forall v\in V\setminus\{s,t\} \f]

\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]

LEMON contains several algorithms for solving maximum flow problems:

- \ref EdmondsKarp Edmonds-Karp algorithm.

- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.

- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.

- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.

In most cases the \ref Preflow "Preflow" algorithm provides the

fastest method for computing a maximum flow. All implementations

provides functions to also query the minimum cut, which is the dual

problem of the maximum flow.

*/

/**

@defgroup min_cost_flow Minimum Cost Flow Algorithms

@ingroup algs

\brief Algorithms for finding minimum cost flows and circulations.

This group describes the algorithms for finding minimum cost flows and

circulations.

The \e minimum \e cost \e flow \e problem is to find a feasible flow of

minimum total cost from a set of supply nodes to a set of demand nodes

in a network with capacity constraints and arc costs.

Formally, let \f$G=(V,A)\f$ be a digraph,

\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and

upper bounds for the flow values on the arcs,

\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow

on the arcs, and

\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values

of the nodes.

A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of

the following optimization problem.

\f[ \min\sum_{a\in A} f(a) cost(a) \f]

\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =

    supply(v) \qquad \forall v\in V \f]

\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]

LEMON contains several algorithms for solving minimum cost flow problems:

 - \ref CycleCanceling Cycle-canceling algorithms.

 - \ref CapacityScaling Successive shortest path algorithm with optional

   capacity scaling.

 - \ref CostScaling Push-relabel and augment-relabel algorithms based on

   cost scaling.

 - \ref NetworkSimplex Primal network simplex algorithm with various

   pivot strategies.

*/

/**

@defgroup min_cut Minimum Cut Algorithms

@ingroup algs

\brief Algorithms for finding minimum cut in graphs.

This group describes the algorithms for finding minimum cut in graphs.

The \e minimum \e cut \e problem is to find a non-empty and non-complete

\f$X\f$ subset of the nodes with minimum overall capacity on

outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a

\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum

cut is the \f$X\f$ 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}cap(uv) \f]

LEMON contains several algorithms related to minimum cut problems:

- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut

  in directed graphs.

- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for

  calculating minimum cut in undirected graphs.

- \ref GomoryHuTree "Gomory-Hu tree computation" for calculating

  all-pairs minimum cut in undirected graphs.

If you want to find minimum cut just between two distinict nodes,

see the \ref max_flow "maximum flow problem".

*/

/**

@defgroup graph_prop Connectivity and Other Graph Properties

@ingroup algs

\brief Algorithms for discovering the graph properties

This group describes the algorithms for discovering 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

@ingroup algs

\brief Algorithms for planarity checking, embedding and drawing

This group describes the algorithms for planarity checking,

embedding and drawing.

\image html planar.png

\image latex planar.eps "Plane graph" width=\textwidth

*/

/**

@defgroup matching Matching Algorithms

@ingroup algs

\brief Algorithms for finding matchings in graphs and bipartite graphs.

This group contains algorithm objects and functions to calculate

matchings in graphs and bipartite graphs. The general matching problem is

finding a subset of the arcs 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 finding maximum cardinality, maximum weight or minimum cost

matching. The search can be constrained to find perfect or

maximum cardinality matching.