NagamochiIbaraki< GR, CM, TR > Class Template Reference

Detailed Description

template<typename GR, typename CM, typename TR>
class lemon::NagamochiIbaraki< GR, CM, TR >

Calculates the minimum cut in an undirected graph with the Nagamochi-Ibaraki algorithm. The algorithm separates the graph's nodes into two partitions with the minimum sum of edge capacities between the two partitions. The algorithm can be used to test the network reliability, especially to test how many links have to be destroyed in the network to split it to at least two distinict subnetworks.

The complexity of the algorithm is \( O(nm\log(n)) \) but with Fibonacci heap it can be decreased to \( O(nm+n^2\log(n)) \). When the edges have unit capacities, BucketHeap can be used which yields \( O(nm) \) time complexity.

Warning

The value type of the capacity map should be able to hold any cut value of the graph, otherwise the result can overflow.

Note

This capacity is supposed to be integer type.

#include <lemon/nagamochi_ibaraki.h>

Classes
struct	SetHeap
	Named parameter for setting heap and cross reference type More...
struct	SetStandardHeap
	Named parameter for setting heap and cross reference type with automatic allocation More...
struct	SetUnitCapacity

Public Types
typedef Traits::Graph	Graph
	The type of the underlying graph.
typedef Traits::CapacityMap	CapacityMap
	The type of the capacity map.
typedef Traits::CapacityMap::Value	Value
	The value type of the capacity map.
typedef Traits::Heap	Heap
	The heap type used by the algorithm.
typedef Traits::HeapCrossRef	HeapCrossRef
	The cross reference type used for the heap.

Public Member Functions
	NagamochiIbaraki (const Graph &graph, const CapacityMap &capacity)
	Constructor.
	NagamochiIbaraki (const Graph &graph)
	Constructor.
	~NagamochiIbaraki ()
NagamochiIbaraki &	heap (Heap &hp, HeapCrossRef &cr)
	Sets the heap and the cross reference used by algorithm.
Execution control
The simplest way to execute the algorithm is to use one of the member functions called run(). If you need more control on the execution, first you must call init() and then call the start() or proper times the processNextPhase() member functions.
void	init ()
bool	processNextPhase ()
	Processes the next phase.
void	start ()
	Executes the algorithm.
void	run ()
	Runs NagamochiIbaraki algorithm.
Query Functions
The result of the NagamochiIbaraki algorithm can be obtained using these functions. Before the use of these functions, either run() or start() must be called.
Value	minCutValue () const
	Returns the min cut value.
template<typename CutMap >
Value	minCutMap (CutMap &cutMap) const
	Returns a min cut in a NodeMap.

Constructor & Destructor Documentation

NagamochiIbaraki ( const Graph &  graph, const CapacityMap &  capacity  )

inline

Parameters

graph	The graph the algorithm runs on.
capacity	The capacity map used by the algorithm.

NagamochiIbaraki ( const Graph &  graph )

inline

This constructor can be used only when the Traits class defines how can the local capacity map be instantiated. If the SetUnitCapacity used the algorithm automatically constructs the capacity map.

Parameters

graph

The graph the algorithm runs on.

~NagamochiIbaraki ( )

inline

Destructor.

Member Function Documentation

NagamochiIbaraki& heap ( Heap &  hp, HeapCrossRef &  cr  )

inline

Sets the heap and the cross reference used by algorithm. If you don't use this function before calling run(), it will allocate one. The destuctor deallocates this automatically allocated heap and cross reference, of course.

Returns

(*this)

void init ( )

inline

Initializes the internal data structures.

bool processNextPhase ( )

inline

Processes the next phase in the algorithm. It must be called at most one less the number of the nodes in the graph.

Returns

True when the algorithm finished.

void start ( )

inline

Executes the algorithm.

Precondition

init() must be called

void run ( )

inline

This method runs the Min cut algorithm

Note

mc.run(s) is just a shortcut of the following code.

mc.init();
mc.start();

Value minCutValue ( ) const

inline

Returns the min cut value if the algorithm finished. After the first processNextPhase() it is a value of a valid cut in the graph.

Value minCutMap ( CutMap &  cutMap ) const

inline

It sets the nodes of one of the two partitions to true and the other partition to false.

Parameters

cutMap

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