HaoOrlin< GR, CAP, TOL > Class Template Reference

Detailed Description

template<typename GR, typename CAP, typename TOL>
class lemon::HaoOrlin< GR, CAP, TOL >

This class implements the Hao-Orlin algorithm for finding a minimum value cut in a directed graph \(D=(V,A)\). It takes a fixed node \( source \in V \) and consists of two phases: in the first phase it determines a minimum cut with \( source \) on the source-side (i.e. a set \( X\subsetneq V \) with \( source \in X \) and minimal outgoing capacity) and in the second phase it determines a minimum cut with \( source \) on the sink-side (i.e. a set \( X\subsetneq V \) with \( source \notin X \) and minimal outgoing capacity). Obviously, the smaller of these two cuts will be a minimum cut of \( D \). The algorithm is a modified preflow push-relabel algorithm. Our implementation calculates the minimum cut in \( O(n^2\sqrt{m}) \) time (we use the highest-label rule), or in \(O(nm)\) for unit capacities. A notable use of this algorithm is testing network reliability.

For an undirected graph you can run just the first phase of the algorithm or you can use the algorithm of Nagamochi and Ibaraki, which solves the undirected problem in \( O(nm + n^2 \log n) \) time. It is implemented in the NagamochiIbaraki algorithm class.

Template Parameters

GR	The type of the digraph the algorithm runs on.
CAP	The type of the arc map containing the capacities, which can be any numreric type. The default map type is GR::ArcMap<int>.
TOL	Tolerance class for handling inexact computations. The default tolerance type is Tolerance<CAP::Value>.

#include <lemon/hao_orlin.h>

Public Types
typedef GR	Digraph
	The digraph type of the algorithm.
typedef CAP	CapacityMap
	The capacity map type of the algorithm.
typedef TOL	Tolerance
	The tolerance type of the algorithm.

Public Member Functions
	HaoOrlin (const Digraph &graph, const CapacityMap &capacity, const Tolerance &tolerance=Tolerance())
	Constructor.
HaoOrlin &	tolerance (const Tolerance &tolerance)
	Set the tolerance used by the algorithm.
const Tolerance &	tolerance () const
	Returns a const reference to the tolerance.
Execution Control
The simplest way to execute the algorithm is to use one of the member functions called run(). If you need better control on the execution, you have to call one of the init() functions first, then calculateOut() and/or calculateIn().
void	init ()
	Initialize the internal data structures.
void	init (const Node &source)
	Initialize the internal data structures.
void	calculateOut ()
	Calculate a minimum cut with \( source \) on the source-side.
void	calculateIn ()
	Calculate a minimum cut with \( source \) on the sink-side.
void	run ()
	Run the algorithm.
void	run (const Node &s)
	Run the algorithm.
Query Functions
The result of the HaoOrlin algorithm can be obtained using these functions. run(), calculateOut() or calculateIn() should be called before using them.
Value	minCutValue () const
	Return the value of the minimum cut.
template<typename CutMap >
Value	minCutMap (CutMap &cutMap) const
	Return a minimum cut.

Constructor & Destructor Documentation

HaoOrlin ( const Digraph &  graph, const CapacityMap &  capacity, const Tolerance &  tolerance = Tolerance()  )

inline

Constructor of the algorithm class.

Member Function Documentation

HaoOrlin& tolerance ( const Tolerance &  tolerance )

inline

This function sets the tolerance object used by the algorithm.

Returns

(*this)

const Tolerance& tolerance ( ) const

inline

This function returns a const reference to the tolerance object used by the algorithm.

void init ( )

inline

This function initializes the internal data structures. It creates the maps and some bucket structures for the algorithm. The first node is used as the source node for the push-relabel algorithm.

void init ( const Node &  source )

inline

This function initializes the internal data structures. It creates the maps and some bucket structures for the algorithm. The given node is used as the source node for the push-relabel algorithm.

void calculateOut ( )

inline

This function calculates a minimum cut with \( source \) on the source-side (i.e. a set \( X\subsetneq V \) with \( source \in X \) and minimal outgoing capacity). It updates the stored cut if (and only if) the newly found one is better.

Precondition

init() must be called before using this function.

void calculateIn ( )

inline

This function calculates a minimum cut with \( source \) on the sink-side (i.e. a set \( X\subsetneq V \) with \( source \notin X \) and minimal outgoing capacity). It updates the stored cut if (and only if) the newly found one is better.

Precondition

init() must be called before using this function.

void run ( )

inline

This function runs the algorithm. It chooses source node, then calls init(), calculateOut() and calculateIn().

void run ( const Node &  s )

inline

This function runs the algorithm. It calls init(), calculateOut() and calculateIn() with the given source node.

Value minCutValue ( ) const

inline

This function returns the value of the best cut found by the previously called run(), calculateOut() or calculateIn().

Precondition

run(), calculateOut() or calculateIn() must be called before using this function.

Value minCutMap ( CutMap &  cutMap ) const

inline

This function gives the best cut found by the previously called run(), calculateOut() or calculateIn().

It sets cutMap to the characteristic vector of the found minimum value cut - a non-empty set \( X\subsetneq V \) of minimum outgoing capacity (i.e. cutMap will be true exactly for the nodes of \( X \)).

Parameters

cutMap

A writable node map with bool (or convertible) value type.

Returns

The value of the minimum cut.

Precondition

run(), calculateOut() or calculateIn() must be called before using this function.