RhodeCode

 * (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

*/

/**

@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

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) {

  ReverseDigraph<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.

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.

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.

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

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) {

  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.

*/

/**

@defgroup paths Path Structures

@ingroup datas

\brief %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.

order to make it easier to implement combinatorial algorithms.

*/

/**

@defgroup algs Algorithms

implemented in LEMON.

implemented in LEMON.

*/

/**

@defgroup search Graph Search

@ingroup algs

\brief Common graph search algorithms.

\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.

 - \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.

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.

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]

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.

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.

  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

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

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

  maximum cardinality matching in general graphs.

- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating

  maximum weighted matching in general graphs.

- \ref MaxWeightedPerfectMatching

  Edmond's blossom shrinking algorithm for calculating maximum weighted

  perfect matching in general graphs.

\image html bipartite_matching.png

\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth

*/

/**

@defgroup spantree Minimum Spanning Tree Algorithms

@ingroup algs

\brief Algorithms for finding a minimum cost spanning tree in a graph.

tree in a graph.

*/

/**

@defgroup auxalg Auxiliary Algorithms

@ingroup algs

\brief Auxiliary algorithms implemented in LEMON.

in order to make it easier to implement complex algorithms.

*/

/**

@defgroup approx Approximation Algorithms

@ingroup algs

\brief Approximation algorithms.

implemented in LEMON.

*/

/**

@defgroup gen_opt_group General Optimization Tools

implemented in LEMON.

implemented in LEMON.

*/

/**

@defgroup lp_group Lp and Mip Solvers

@ingroup gen_opt_group

\brief Lp and Mip solver interfaces for LEMON.

various LP solvers could be used in the same manner with this

interface.

*/

/**

@defgroup lp_utils Tools for Lp and Mip Solvers

@ingroup lp_group

\brief Helper tools to the Lp and Mip solvers.

This group adds some helper tools to general optimization framework

implemented in LEMON.

*/

/**

@defgroup metah Metaheuristics

@ingroup gen_opt_group

\brief Metaheuristics for LEMON library.

*/

/**

@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

@ingroup utils

\brief Simple basic graph utilities.

*/

/**

@defgroup misc Miscellaneous Tools

@ingroup utils

\brief Tools for development, debugging and testing.

debugging and testing.

*/

/**

@defgroup timecount Time Measuring and Counting

@ingroup misc

\brief Simple tools for measuring the performance of algorithms.

of algorithms.

*/

/**

@defgroup exceptions Exceptions

@ingroup utils

\brief Exceptions defined in LEMON.

*/

/**

@defgroup io_group Input-Output

\brief Graph Input-Output methods

and graph related data. Now it supports the \ref lgf-format

"LEMON Graph Format", the \c DIMACS format and the encapsulated

postscript (EPS) format.

*/

/**

@defgroup lemon_io LEMON Graph Format

@ingroup io_group

\brief Reading and writing LEMON Graph Format.

\ref lgf-format "LEMON Graph Format".

*/

/**

@defgroup eps_io Postscript Exporting

@ingroup io_group

\brief General \c EPS drawer and graph exporter

graph exporting tools.

*/

/**

@defgroup dimacs_group DIMACS format

@ingroup io_group

\brief Read and write files in DIMACS format

Tools to read a digraph from or write it to a file in DIMACS format data.

*/

/**

@defgroup nauty_group NAUTY Format

@ingroup io_group

\brief Read \e Nauty format

Tool to read graphs from \e Nauty format data.

*/

/**

@defgroup concept Concepts

\brief Skeleton classes and concept checking classes

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 to 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

@ingroup concept

\brief Skeleton and concept checking classes for graph structures

graph structures and helper classes used to implement these.

*/

/**

@defgroup map_concepts Map Concepts

@ingroup concept

\brief Skeleton and concept checking classes for maps

*/

/**

\anchor demoprograms

@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.

It order to compile them, use <tt>--enable-demo</tt> configure option when

build the library.

*/

/**

@defgroup tools Standalone Utility Applications

with graphs.

<b>

LEMON is an <a class="el" href="http://opensource.org/">open&nbsp;source</a>

project.

You are free to use it in your commercial or

non-commercial applications under very permissive

\ref license "license terms".

</b>

\subsection howtoread How to read the documentation

If you want to get a quick start and see the most important features then

take a look at our \ref quicktour

"Quick Tour to LEMON" which will guide you along.

If you know what you are looking for then try to find it under the

If you are a user of the old (0.x) series of LEMON, please check out the

\ref migration "Migration Guide" for the backward incompatibilities.

*/

    typedef GraphAdaptorExtender<UndirectorBase<DGR> > Parent;

  protected:

    Undirector() { }

  public:

    /// \brief Constructor

    ///

    /// Creates an undirected graph from the given digraph.

    Undirector(DGR& digraph) {

      initialize(digraph);

    }

    /// \brief Arc map combined from two original arc maps

    ///

    /// This map adaptor class adapts two arc maps of the underlying

    /// digraph to get an arc map of the undirected graph.

    class CombinedArcMap {

    public:

      /// The key type of the map

      typedef typename Parent::Arc Key;

      /// The value type of the map

      /// Constructor

        : _forward(&forward), _backward(&backward) {}

      /// Sets the value associated with the given key.

      void set(const Key& e, const Value& a) {

        if (Parent::direction(e)) {

          _forward->set(e, a);

        } else {

          _backward->set(e, a);

        }

      }

      /// Returns the value associated with the given key.

      ConstReturnValue operator[](const Key& e) const {

        if (Parent::direction(e)) {

          return (*_forward)[e];

        } else {

          return (*_backward)[e];

        }

      }

      /// Returns a reference to the value associated with the given key.

      ReturnValue operator[](const Key& e) {

        if (Parent::direction(e)) {

          return (*_forward)[e];

        } else {

          return (*_backward)[e];

        }

      }

    protected:

    };

    /// \brief Returns a combined arc map

    ///

    /// This function just returns a combined arc map.

    }

  };

  /// \brief Returns a read-only Undirector adaptor

  ///

  /// This function just returns a read-only \ref Undirector adaptor.

  /// \ingroup graph_adaptors

  /// \relates Undirector

  template<typename DGR>

  Undirector<const DGR> undirector(const DGR& digraph) {

    return Undirector<const DGR>(digraph);

  }

  template <typename GR, typename DM>

    static Arc arc(const DigraphNode& n) {

      return Parent::arc(n);

    }

    /// \brief Returns the arc that corresponds to the given original arc.

    ///

    /// Returns the arc in the adaptor that corresponds to the given

    /// original arc.

    static Arc arc(const DigraphArc& a) {

      return Parent::arc(a);

    }

    /// \brief Node map combined from two original node maps

    ///

    /// This map adaptor class adapts two node maps of the original digraph

    /// to get a node map of the split digraph.

    class CombinedNodeMap {

    public:

      /// The key type of the map

      typedef Node Key;

      /// The value type of the map

      /// Constructor

        : _in_map(in_map), _out_map(out_map) {}

      /// Returns the value associated with the given key.

      Value operator[](const Key& key) const {

        if (SplitNodesBase<const DGR>::inNode(key)) {

          return _in_map[key];

        } else {

          return _out_map[key];

        }

      }

      /// Returns a reference to the value associated with the given key.

      Value& operator[](const Key& key) {

        if (SplitNodesBase<const DGR>::inNode(key)) {

          return _in_map[key];

        } else {

          return _out_map[key];

        }

      }

      /// Sets the value associated with the given key.

      void set(const Key& key, const Value& value) {

        if (SplitNodesBase<const DGR>::inNode(key)) {

          _in_map.set(key, value);

        } else {

          _out_map.set(key, value);

        }

      }

    private:

    };

    /// \brief Returns a combined node map

    ///

    /// This function just returns a combined node map.

    }

    /// \brief Arc map combined from an arc map and a node map of the

    /// original digraph.

    ///

    /// This map adaptor class adapts an arc map and a node map of the

    /// original digraph to get an arc map of the split digraph.

    class CombinedArcMap {

    public:

      /// The key type of the map

      typedef Arc Key;

      /// The value type of the map

      /// Constructor

        : _arc_map(arc_map), _node_map(node_map) {}

      /// Returns the value associated with the given key.

      Value operator[](const Key& arc) const {

        if (SplitNodesBase<const DGR>::origArc(arc)) {

          return _arc_map[arc];

        } else {

          return _node_map[arc];

        }

      }

      /// Returns a reference to the value associated with the given key.

      Value& operator[](const Key& arc) {

        if (SplitNodesBase<const DGR>::origArc(arc)) {

          return _arc_map[arc];

        } else {

          return _node_map[arc];

        }

      }

      /// Sets the value associated with the given key.

      void set(const Arc& arc, const Value& val) {

        if (SplitNodesBase<const DGR>::origArc(arc)) {

          _arc_map.set(arc, val);

        } else {

          _node_map.set(arc, val);

        }

      }

    private:

    };

    /// \brief Returns a combined arc map

    ///

    /// This function just returns a combined arc map.

    template <typename ArcMap, typename NodeMap>

    static CombinedArcMap<ArcMap, NodeMap>

    combinedArcMap(ArcMap& arc_map, NodeMap& node_map) {

      return CombinedArcMap<ArcMap, NodeMap>(arc_map, node_map);

    }

    template <typename ArcMap, typename NodeMap>

    static CombinedArcMap<const ArcMap, NodeMap>

    combinedArcMap(const ArcMap& arc_map, NodeMap& node_map) {

      return CombinedArcMap<const ArcMap, NodeMap>(arc_map, node_map);

    }

#define LEMON_BIN_HEAP_H

///\ingroup auxdat

///\file

///\brief Binary Heap implementation.

#include <vector>

#include <utility>

#include <functional>

namespace lemon {

  ///\ingroup auxdat

  ///

  ///\brief A Binary Heap implementation.

  ///

  ///

  ///to handle the cross references.

  ///

  ///\sa FibHeap

  ///\sa Dijkstra

  class BinHeap {

  public:

    ///\e

    ///\e

    ///\e

    typedef typename ItemIntMap::Key Item;

    ///\e

    typedef std::pair<Item,Prio> Pair;

    ///\e

    /// \brief Type to represent the items states.

    ///

    /// Each Item element have a state associated to it. It may be "in heap",

    /// "pre heap" or "post heap". The latter two are indifferent from the

    /// heap's point of view, but may be useful to the user.

    ///

    enum State {