RhodeCode

CMAKE_MINIMUM_REQUIRED(VERSION 2.6)

IF(EXISTS ${CMAKE_SOURCE_DIR}/cmake/version.cmake)

  INCLUDE(${CMAKE_SOURCE_DIR}/cmake/version.cmake)

ELSE(EXISTS ${CMAKE_SOURCE_DIR}/cmake/version.cmake)

  SET(PROJECT_NAME "LEMON")

  SET(PROJECT_VERSION "hg-tip" CACHE STRING "LEMON version string.")

ENDIF(EXISTS ${CMAKE_SOURCE_DIR}/cmake/version.cmake)

PROJECT(${PROJECT_NAME})

SET(CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)

INCLUDE(FindDoxygen)

INCLUDE(FindGhostscript)

FIND_PACKAGE(GLPK 4.33)

FIND_PACKAGE(CPLEX)

FIND_PACKAGE(COIN)

IF(MSVC)

  SET(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} /wd4250 /wd4355 /wd4800 /wd4996")

# Suppressed warnings:

# C4250: 'class1' : inherits 'class2::member' via dominance

# C4355: 'this' : used in base member initializer list

# C4800: 'type' : forcing value to bool 'true' or 'false' (performance warning)

# C4996: 'function': was declared deprecated

ENDIF(MSVC)

INCLUDE(CheckTypeSize)

CHECK_TYPE_SIZE("long long" LEMON_LONG_LONG)

ENABLE_TESTING()

ADD_SUBDIRECTORY(lemon)

IF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

  ADD_SUBDIRECTORY(demo)

  ADD_SUBDIRECTORY(tools)

  ADD_SUBDIRECTORY(doc)

  ADD_SUBDIRECTORY(test)

ENDIF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

IF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

  IF(WIN32)

    SET(CPACK_PACKAGE_NAME ${PROJECT_NAME})

    SET(CPACK_PACKAGE_VENDOR "EGRES")

    SET(CPACK_PACKAGE_DESCRIPTION_SUMMARY

      "LEMON - Library of Efficient Models and Optimization in Networks")

    SET(CPACK_RESOURCE_FILE_LICENSE "${PROJECT_SOURCE_DIR}/LICENSE")

    SET(CPACK_PACKAGE_VERSION ${PROJECT_VERSION})

    SET(CPACK_PACKAGE_INSTALL_DIRECTORY

      "${PROJECT_NAME} ${PROJECT_VERSION}")

    SET(CPACK_PACKAGE_INSTALL_REGISTRY_KEY

      "${PROJECT_NAME} ${PROJECT_VERSION}")

    SET(CPACK_COMPONENTS_ALL headers library html_documentation bin)

    SET(CPACK_COMPONENT_HEADERS_DISPLAY_NAME "C++ headers")

    SET(CPACK_COMPONENT_LIBRARY_DISPLAY_NAME "Dynamic-link library")

    SET(CPACK_COMPONENT_BIN_DISPLAY_NAME "Command line utilities")

    SET(CPACK_COMPONENT_HTML_DOCUMENTATION_DISPLAY_NAME "HTML documentation")

    SET(CPACK_COMPONENT_HEADERS_DESCRIPTION

      "C++ header files")

    SET(CPACK_COMPONENT_LIBRARY_DESCRIPTION

      "DLL and import library")

    SET(CPACK_COMPONENT_BIN_DESCRIPTION

      "Command line utilities")

    SET(CPACK_COMPONENT_HTML_DOCUMENTATION_DESCRIPTION

      "Doxygen generated documentation")

    SET(CPACK_COMPONENT_HEADERS_DEPENDS library)

    SET(CPACK_COMPONENT_HEADERS_GROUP "Development")

    SET(CPACK_COMPONENT_LIBRARY_GROUP "Development")

    SET(CPACK_COMPONENT_HTML_DOCUMENTATION_GROUP "Documentation")

    SET(CPACK_COMPONENT_GROUP_DEVELOPMENT_DESCRIPTION

      "Components needed to develop software using LEMON")

    SET(CPACK_COMPONENT_GROUP_DOCUMENTATION_DESCRIPTION

      "Documentation of LEMON")

    SET(CPACK_ALL_INSTALL_TYPES Full Developer)

    SET(CPACK_COMPONENT_HEADERS_INSTALL_TYPES Developer Full)

    SET(CPACK_COMPONENT_LIBRARY_INSTALL_TYPES Developer Full)

    SET(CPACK_COMPONENT_HTML_DOCUMENTATION_INSTALL_TYPES Full)

    SET(CPACK_GENERATOR "NSIS")

    SET(CPACK_NSIS_MUI_ICON "${PROJECT_SOURCE_DIR}/cmake/nsis/lemon.ico")

    SET(CPACK_NSIS_MUI_UNIICON "${PROJECT_SOURCE_DIR}/cmake/nsis/uninstall.ico")

    #SET(CPACK_PACKAGE_ICON "${PROJECT_SOURCE_DIR}/cmake/nsis\\\\installer.bmp")

    SET(CPACK_NSIS_INSTALLED_ICON_NAME "bin\\\\lemon.ico")

    SET(CPACK_NSIS_DISPLAY_NAME "${CPACK_PACKAGE_INSTALL_DIRECTORY} ${PROJECT_NAME}")

    SET(CPACK_NSIS_HELP_LINK "http:\\\\\\\\lemon.cs.elte.hu")

    SET(CPACK_NSIS_URL_INFO_ABOUT "http:\\\\\\\\lemon.cs.elte.hu")

    SET(CPACK_NSIS_CONTACT "lemon-user@lemon.cs.elte.hu")

    SET(CPACK_NSIS_CREATE_ICONS_EXTRA "

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    SET(CPACK_NSIS_DELETE_ICONS_EXTRA "

      !insertmacro MUI_STARTMENU_GETFOLDER Application $MUI_TEMP

      Delete \\\"$SMPROGRAMS\\\\$MUI_TEMP\\\\Documentation.lnk\\\"

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    INCLUDE(CPack)

  ENDIF(WIN32)

ENDIF(${CMAKE_SOURCE_DIR} STREQUAL ${PROJECT_SOURCE_DIR})

ACLOCAL_AMFLAGS = -I m4

AM_CXXFLAGS = $(WARNINGCXXFLAGS)

AM_CPPFLAGS = -I$(top_srcdir) -I$(top_builddir)

LDADD = $(top_builddir)/lemon/libemon.la

EXTRA_DIST = \

	AUTHORS \

	LICENSE \

	m4/lx_check_cplex.m4 \

	m4/lx_check_glpk.m4 \

	m4/lx_check_soplex.m4 \

	CMakeLists.txt \

	cmake/FindGhostscript.cmake \

	cmake/FindGLPK.cmake \

	cmake/version.cmake.in \

	cmake/version.cmake \

	cmake/nsis/lemon.ico \

	cmake/nsis/uninstall.ico

pkgconfigdir = $(libdir)/pkgconfig

lemondir = $(pkgincludedir)

bitsdir = $(lemondir)/bits

conceptdir = $(lemondir)/concepts

pkgconfig_DATA =

lib_LTLIBRARIES =

lemon_HEADERS =

bits_HEADERS =

concept_HEADERS =

noinst_HEADERS =

noinst_PROGRAMS =

bin_PROGRAMS =

check_PROGRAMS =

dist_bin_SCRIPTS =

TESTS =

XFAIL_TESTS =

include lemon/Makefile.am

include test/Makefile.am

include doc/Makefile.am

include tools/Makefile.am

DIST_SUBDIRS = demo

demo:

	$(MAKE) $(AM_MAKEFLAGS) -C demo

MRPROPERFILES = \

	aclocal.m4 \

	config.h.in \

	config.h.in~ \

	configure \

	Makefile.in \

	build-aux/config.guess \

	build-aux/config.sub \

	build-aux/depcomp \

	build-aux/install-sh \

	build-aux/ltmain.sh \

	build-aux/missing \

	doc/doxygen.log

mrproper:

	$(MAKE) $(AM_MAKEFLAGS) maintainer-clean

	-rm -f $(MRPROPERFILES)

dist-bz2: dist

	zcat $(PACKAGE)-$(VERSION).tar.gz | \

	bzip2 --best -c > $(PACKAGE)-$(VERSION).tar.bz2

distcheck-bz2: distcheck

	zcat $(PACKAGE)-$(VERSION).tar.gz | \

	bzip2 --best -c > $(PACKAGE)-$(VERSION).tar.bz2

.PHONY: demo mrproper dist-bz2 distcheck-bz2

SET(COIN_ROOT_DIR "" CACHE PATH "COIN root directory")

FIND_PATH(COIN_INCLUDE_DIR coin/CoinUtilsConfig.h

INCLUDE(FindPackageHandleStandardArgs)

FIND_PACKAGE_HANDLE_STANDARD_ARGS(COIN DEFAULT_MSG

  COIN_INCLUDE_DIR

  COIN_CBC_LIBRARY

  COIN_CBC_SOLVER_LIBRARY

  COIN_CGL_LIBRARY

  COIN_CLP_LIBRARY

  COIN_COIN_UTILS_LIBRARY

  COIN_OSI_LIBRARY

  COIN_OSI_CBC_LIBRARY

  COIN_OSI_CLP_LIBRARY

  COIN_OSI_VOL_LIBRARY

  COIN_VOL_LIBRARY

)

IF(COIN_FOUND)

  SET(COIN_INCLUDE_DIRS ${COIN_INCLUDE_DIR})

  SET(COIN_LIBRARIES "${COIN_CBC_LIBRARY};${COIN_CBC_SOLVER_LIBRARY};${COIN_CGL_LIBRARY};${COIN_CLP_LIBRARY};${COIN_COIN_UTILS_LIBRARY};${COIN_OSI_LIBRARY};${COIN_OSI_CBC_LIBRARY};${COIN_OSI_CLP_LIBRARY};${COIN_OSI_VOL_LIBRARY};${COIN_VOL_LIBRARY}")

  SET(COIN_CLP_LIBRARIES "${COIN_CLP_LIBRARY};${COIN_COIN_UTILS_LIBRARY}")

  SET(COIN_CBC_LIBRARIES ${COIN_LIBRARIES})

ENDIF(COIN_FOUND)

MARK_AS_ADVANCED(

  COIN_INCLUDE_DIR

  COIN_CBC_LIBRARY

  COIN_CBC_SOLVER_LIBRARY

  COIN_CGL_LIBRARY

  COIN_CLP_LIBRARY

  COIN_COIN_UTILS_LIBRARY

  COIN_OSI_LIBRARY

  COIN_OSI_CBC_LIBRARY

  COIN_OSI_CLP_LIBRARY

  COIN_OSI_VOL_LIBRARY

  COIN_VOL_LIBRARY

)

IF(COIN_FOUND)

  SET(LEMON_HAVE_LP TRUE)

  SET(LEMON_HAVE_MIP TRUE)

  SET(LEMON_HAVE_CLP TRUE)

  SET(LEMON_HAVE_CBC TRUE)

ENDIF(COIN_FOUND)

FIND_PATH(CPLEX_INCLUDE_DIR

  ilcplex/cplex.h

FIND_LIBRARY(CPLEX_LIBRARY

INCLUDE(FindPackageHandleStandardArgs)

FIND_PACKAGE_HANDLE_STANDARD_ARGS(CPLEX DEFAULT_MSG CPLEX_LIBRARY CPLEX_INCLUDE_DIR)

FIND_PATH(CPLEX_BIN_DIR

  cplex91.dll

IF(CPLEX_FOUND)

  SET(CPLEX_INCLUDE_DIRS ${CPLEX_INCLUDE_DIR})

  SET(CPLEX_LIBRARIES ${CPLEX_LIBRARY})

ENDIF(CPLEX_FOUND)

MARK_AS_ADVANCED(CPLEX_LIBRARY CPLEX_INCLUDE_DIR CPLEX_BIN_DIR)

IF(CPLEX_FOUND)

  SET(LEMON_HAVE_LP TRUE)

  SET(LEMON_HAVE_MIP TRUE)

  SET(LEMON_HAVE_CPLEX TRUE)

ENDIF(CPLEX_FOUND)

SET(GLPK_REGKEY "[HKEY_LOCAL_MACHINE\\SOFTWARE\\GnuWin32\\Glpk;InstallPath]")

GET_FILENAME_COMPONENT(GLPK_ROOT_PATH ${GLPK_REGKEY} ABSOLUTE)

FIND_PATH(GLPK_INCLUDE_DIR

  glpk.h

INCLUDE(FindPackageHandleStandardArgs)

IF(GLPK_FOUND)

  SET(GLPK_INCLUDE_DIRS ${GLPK_INCLUDE_DIR})

  SET(GLPK_LIBRARIES ${GLPK_LIBRARY})

  SET(GLPK_BIN_DIR ${GLPK_ROOT_PATH}/bin)

ENDIF(GLPK_FOUND)

MARK_AS_ADVANCED(GLPK_LIBRARY GLPK_INCLUDE_DIR GLPK_BIN_DIR)

IF(GLPK_FOUND)

  SET(LEMON_HAVE_LP TRUE)

  SET(LEMON_HAVE_MIP TRUE)

  SET(LEMON_HAVE_GLPK TRUE)

ENDIF(GLPK_FOUND)

/**

@defgroup graph_maps Graph Maps

@ingroup maps

\brief Special graph-related maps.

This group contains 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 contains 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 contains two dimensional data storages implemented in LEMON.

*/

/**

@defgroup paths Path Structures

@ingroup datas

\brief %Path structures implemented in LEMON.

This group contains 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 contains some data structures implemented in LEMON in

order to make it easier to implement combinatorial algorithms.

*/

/**

@defgroup algs Algorithms

\brief This group contains the several algorithms

implemented in LEMON.

This group contains the several algorithms

implemented in LEMON.

*/

/**

@defgroup search Graph Search

@ingroup algs

\brief Common graph search algorithms.

This group contains 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 contains 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 contains 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_{sv\in A} f(sv) - \sum_{vs\in A} f(vs) \f]

\f[ \sum_{uv\in A} f(uv) = \sum_{vu\in A} f(vu)

    \quad \forall u\in V\setminus\{s,t\} \f]

\f[ 0 \leq f(uv) \leq cap(uv) \quad \forall uv\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 contains 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 (lower and upper bounds)

and arc costs.

upper bounds for the flow values on the arcs, for which

signed supply values of the nodes.

If \f$sup(u)>0\f$, then \f$u\f$ is a supply node with \f$sup(u)\f$

supply, if \f$sup(u)<0\f$, then \f$u\f$ is a demand node with

\f$-sup(u)\f$ demand.

of the following optimization problem.

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

\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \geq

    sup(u) \quad \forall u\in V \f]

\f[ lower(uv) \leq f(uv) \leq upper(uv) \quad \forall uv\in A \f]

The sum of the supply values, i.e. \f$\sum_{u\in V} sup(u)\f$ must be

zero or negative in order to have a feasible solution (since the sum

of the expressions on the left-hand side of the inequalities is zero).

It means that the total demand must be greater or equal to the total

supply and all the supplies have to be carried out from the supply nodes,

but there could be demands that are not satisfied.

If \f$\sum_{u\in V} sup(u)\f$ is zero, then all the supply/demand

constraints have to be satisfied with equality, i.e. all demands

have to be satisfied and all supplies have to be used.

If you need the opposite inequalities in the supply/demand constraints

(i.e. the total demand is less than the total supply and all the demands

have to be satisfied while there could be supplies that are not used),

then you could easily transform the problem to the above form by reversing

the direction of the arcs and taking the negative of the supply values

(e.g. using \ref ReverseDigraph and \ref NegMap adaptors).

However \ref NetworkSimplex algorithm also supports this form directly

for the sake of convenience.

A feasible solution for this problem can be found using \ref Circulation.

Note that the above formulation is actually more general than the usual

definition of the minimum cost flow problem, in which strict equalities

are required in the supply/demand contraints, i.e.

\f[ \sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) =

    sup(u) \quad \forall u\in V. \f]

However if the sum of the supply values is zero, then these two problems

are equivalent. So if you need the equality form, you have to ensure this

additional contraint for the algorithms.

The dual solution of the minimum cost flow problem is represented by node 

potentials \f$\pi: V\rightarrow\mathbf{Z}\f$.

is optimal if and only if for some \f$\pi: V\rightarrow\mathbf{Z}\f$

node potentials the following \e complementary \e slackness optimality

conditions hold.

 - For all \f$uv\in A\f$ arcs:

   - if \f$cost^\pi(uv)>0\f$, then \f$f(uv)=lower(uv)\f$;

   - if \f$lower(uv)<f(uv)<upper(uv)\f$, then \f$cost^\pi(uv)=0\f$;

   - if \f$cost^\pi(uv)<0\f$, then \f$f(uv)=upper(uv)\f$.

   - if \f$\sum_{uv\in A} f(uv) - \sum_{vu\in A} f(vu) \neq sup(u)\f$,

     then \f$\pi(u)=0\f$.

Here \f$cost^\pi(uv)\f$ denotes the \e reduced \e cost of the arc

\f[ cost^\pi(uv) = cost(uv) + \pi(u) - \pi(v).\f]

if an optimal flow is found.

LEMON contains several algorithms for solving minimum cost flow problems.

 - \ref NetworkSimplex Primal Network Simplex algorithm with various

   pivot strategies.

 - \ref CostScaling Push-Relabel and Augment-Relabel algorithms based on

   cost scaling.

 - \ref CapacityScaling Successive Shortest %Path algorithm with optional

   capacity scaling.

 - \ref CancelAndTighten The Cancel and Tighten algorithm.

 - \ref CycleCanceling Cycle-Canceling algorithms.

Most of these implementations support the general inequality form of the

minimum cost flow problem, but CancelAndTighten and CycleCanceling

only support the equality form due to the primal method they use.

In general NetworkSimplex is the most efficient implementation,

but in special cases other algorithms could be faster.

For example, if the total supply and/or capacities are rather small,

CapacityScaling is usually the fastest algorithm (without effective scaling).

*/

/**

@defgroup min_cut Minimum Cut Algorithms

@ingroup algs

\brief Algorithms for finding minimum cut in graphs.

This group contains 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 GomoryHu "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_properties Connectivity and Other Graph Properties

@ingroup algs

\brief Algorithms for discovering the graph properties

This group contains 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 contains 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 the algorithms for calculating

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

finding a subset of the edges for which each node has at most one incident

edge.

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.

The matching algorithms implemented in LEMON:

- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm

  for calculating maximum cardinality matching in bipartite graphs.

- \ref PrBipartiteMatching Push-relabel algorithm

  for calculating maximum cardinality matching in bipartite graphs.

- \ref MaxWeightedBipartiteMatching

  Successive shortest path algorithm for calculating maximum weighted

  matching and maximum weighted bipartite matching in bipartite graphs.

- \ref MinCostMaxBipartiteMatching

  Successive shortest path algorithm for calculating minimum cost maximum

  matching in bipartite graphs.

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

  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.

This group contains the algorithms for finding a minimum cost spanning

tree in a graph.

*/

/**

@defgroup auxalg Auxiliary Algorithms

@ingroup algs

\brief Auxiliary algorithms implemented in LEMON.

This group contains some algorithms implemented in LEMON

in order to make it easier to implement complex algorithms.

*/

/**

@defgroup approx Approximation Algorithms

@ingroup algs

\brief Approximation algorithms.

This group contains the approximation and heuristic algorithms

implemented in LEMON.

*/

/**

@defgroup gen_opt_group General Optimization Tools

\brief This group contains some general optimization frameworks

implemented in LEMON.

This group contains some general optimization frameworks

implemented in LEMON.

*/

/**

@defgroup lp_group Lp and Mip Solvers

@ingroup gen_opt_group

\brief Lp and Mip solver interfaces for LEMON.

This group contains Lp and Mip solver interfaces for LEMON. The

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.

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

@ingroup utils

\brief Simple basic graph utilities.

This group contains some simple basic graph utilities.

EXTRA_DIST += \

	lemon/lemon.pc.in \

	lemon/CMakeLists.txt

pkgconfig_DATA += lemon/lemon.pc

lib_LTLIBRARIES += lemon/libemon.la

lemon_libemon_la_SOURCES = \

	lemon/arg_parser.cc \

	lemon/base.cc \

	lemon/color.cc \

	lemon/lp_base.cc \

	lemon/lp_skeleton.cc \

	lemon/random.cc \

	lemon/bits/windows.cc

lemon_libemon_la_CXXFLAGS = \

	$(AM_CXXFLAGS) \

	$(GLPK_CFLAGS) \

	$(CPLEX_CFLAGS) \

	$(SOPLEX_CXXFLAGS) \

	$(CLP_CXXFLAGS) \

	$(CBC_CXXFLAGS)

lemon_libemon_la_LDFLAGS = \

	$(GLPK_LIBS) \

	$(CPLEX_LIBS) \

	$(SOPLEX_LIBS) \

	$(CLP_LIBS) \

	$(CBC_LIBS)

if HAVE_GLPK

lemon_libemon_la_SOURCES += lemon/glpk.cc

endif

if HAVE_CPLEX

lemon_libemon_la_SOURCES += lemon/cplex.cc

endif

if HAVE_SOPLEX

lemon_libemon_la_SOURCES += lemon/soplex.cc

endif

if HAVE_CLP

lemon_libemon_la_SOURCES += lemon/clp.cc

endif

if HAVE_CBC

lemon_libemon_la_SOURCES += lemon/cbc.cc

endif

lemon_HEADERS += \

	lemon/adaptors.h \

	lemon/arg_parser.h \

	lemon/assert.h \

	lemon/bfs.h \

	lemon/bin_heap.h \

	lemon/circulation.h \

	lemon/clp.h \

	lemon/color.h \

	lemon/concept_check.h \

	lemon/connectivity.h \

	lemon/counter.h \

	lemon/core.h \

	lemon/cplex.h \

	lemon/dfs.h \

	lemon/dijkstra.h \

	lemon/dim2.h \

	lemon/dimacs.h \

	lemon/edge_set.h \

	lemon/elevator.h \

	lemon/error.h \

	lemon/euler.h \

	lemon/full_graph.h \

	lemon/glpk.h \

	lemon/gomory_hu.h \

	lemon/graph_to_eps.h \

	lemon/grid_graph.h \

	lemon/hypercube_graph.h \

	lemon/kruskal.h \

	lemon/hao_orlin.h \

	lemon/lgf_reader.h \

	lemon/lgf_writer.h \

	lemon/list_graph.h \

	lemon/lp.h \

	lemon/lp_base.h \

	lemon/lp_skeleton.h \

	lemon/list_graph.h \

	lemon/maps.h \

	lemon/matching.h \

	lemon/math.h \

	lemon/min_cost_arborescence.h \

	lemon/nauty_reader.h \

	lemon/network_simplex.h \

	lemon/path.h \

	lemon/preflow.h \

	lemon/radix_sort.h \

	lemon/random.h \

	lemon/smart_graph.h \

	lemon/soplex.h \

	lemon/suurballe.h \

	lemon/time_measure.h \

	lemon/tolerance.h \

	lemon/unionfind.h \

	lemon/bits/windows.h

bits_HEADERS += \

	lemon/bits/alteration_notifier.h \

	lemon/bits/array_map.h \

	lemon/bits/base_extender.h \

	lemon/bits/bezier.h \

	lemon/bits/default_map.h \

	lemon/bits/edge_set_extender.h \

	lemon/bits/enable_if.h \

	lemon/bits/graph_adaptor_extender.h \

	lemon/bits/graph_extender.h \

	lemon/bits/map_extender.h \

	lemon/bits/path_dump.h \

	lemon/bits/solver_bits.h \

	lemon/bits/traits.h \

	lemon/bits/variant.h \

	lemon/bits/vector_map.h

concept_HEADERS += \

	lemon/concepts/digraph.h \

	lemon/concepts/graph.h \

	lemon/concepts/graph_components.h \

	lemon/concepts/heap.h \

	lemon/concepts/maps.h \

	lemon/concepts/path.h

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

 *

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

 *

 * Copyright (C) 2003-2009

 * 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.

 *

 */

#ifndef LEMON_CIRCULATION_H

#define LEMON_CIRCULATION_H

#include <lemon/tolerance.h>

#include <lemon/elevator.h>

#include <limits>

///\ingroup max_flow

///\file

///\brief Push-relabel algorithm for finding a feasible circulation.

///

namespace lemon {

  /// \brief Default traits class of Circulation class.

  ///

  /// Default traits class of Circulation class.

  ///

  /// \tparam GR Type of the digraph the algorithm runs on.

  /// \tparam LM The type of the lower bound map.

  /// \tparam UM The type of the upper bound (capacity) map.

  /// \tparam SM The type of the supply map.

  template <typename GR, typename LM,

            typename UM, typename SM>

  struct CirculationDefaultTraits {

    /// \brief The type of the digraph the algorithm runs on.

    typedef GR Digraph;

    /// \brief The type of the lower bound map.

    ///

    /// The type of the map that stores the lower bounds on the arcs.

    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.

    typedef LM LowerMap;

    /// \brief The type of the upper bound (capacity) map.

    ///

    /// The type of the map that stores the upper bounds (capacities)

    /// on the arcs.

    /// It must conform to the \ref concepts::ReadMap "ReadMap" concept.

    typedef UM UpperMap;

    /// \brief The type of supply map.

    ///