Preflow< GR, CAP, TR > Class Template Reference

Detailed Description

template<typename GR, typename CAP, typename TR>
class lemon::Preflow< GR, CAP, TR >

This class provides an implementation of Goldberg-Tarjan's preflow push-relabel algorithm producing a flow of maximum value in a digraph [6], [1], [15]. The preflow algorithms are the fastest known maximum flow algorithms. The current implementation uses a mixture of the "highest label" and the "bound decrease" heuristics. The worst case time complexity of the algorithm is \(O(n^2\sqrt{m})\).

The algorithm consists of two phases. After the first phase the maximum flow value and the minimum cut is obtained. The second phase constructs a feasible maximum flow on each arc.

Warning

This implementation cannot handle infinite or very large capacities (e.g. the maximum value of CAP::Value).

Template Parameters

GR	The type of the digraph the algorithm runs on.
CAP	The type of the capacity map. The default map type is GR::ArcMap<int>.
TR	The traits class that defines various types used by the algorithm. By default, it is PreflowDefaultTraits<GR, CAP>. In most cases, this parameter should not be set directly, consider to use the named template parameters instead.

#include <lemon/preflow.h>

Classes
struct	SetElevator
	Named parameter for setting Elevator type More...
struct	SetFlowMap
	Named parameter for setting FlowMap type More...
struct	SetStandardElevator
	Named parameter for setting Elevator type with automatic allocation More...

Public Types
typedef TR	Traits
	The traits class of the algorithm.
typedef Traits::Digraph	Digraph
	The type of the digraph the algorithm runs on.
typedef Traits::CapacityMap	CapacityMap
	The type of the capacity map.
typedef Traits::Value	Value
	The type of the flow values.
typedef Traits::FlowMap	FlowMap
	The type of the flow map.
typedef Traits::Elevator	Elevator
	The type of the elevator.
typedef Traits::Tolerance	Tolerance
	The type of the tolerance.

Public Member Functions
	Preflow (const Digraph &digraph, const CapacityMap &capacity, Node source, Node target)
	The constructor of the class.
	~Preflow ()
Preflow &	capacityMap (const CapacityMap &map)
	Sets the capacity map.
Preflow &	flowMap (FlowMap &map)
	Sets the flow map.
Preflow &	source (const Node &node)
	Sets the source node.
Preflow &	target (const Node &node)
	Sets the target node.
Preflow &	elevator (Elevator &elevator)
	Sets the elevator used by algorithm.
const Elevator &	elevator () const
	Returns a const reference to the elevator.
Preflow &	tolerance (const Tolerance &tolerance)
	Sets 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 preflow algorithm is to use run() or runMinCut(). If you need better control on the initial solution or the execution, you have to call one of the init() functions first, then startFirstPhase() and if you need it startSecondPhase().
void	init ()
	Initializes the internal data structures.
template<typename FlowMap >
bool	init (const FlowMap &flowMap)
	Initializes the internal data structures using the given flow map.
void	startFirstPhase ()
	Starts the first phase of the preflow algorithm.
void	startSecondPhase ()
	Starts the second phase of the preflow algorithm.
void	run ()
	Runs the preflow algorithm.
void	runMinCut ()
	Runs the preflow algorithm to compute the minimum cut.
Query Functions
The results of the preflow algorithm can be obtained using these functions. Either one of the run*() functions or one of the start*() functions should be called before using them.
Value	flowValue () const
	Returns the value of the maximum flow.
Value	flow (const Arc &arc) const
	Returns the flow value on the given arc.
const FlowMap &	flowMap () const
	Returns a const reference to the flow map.
bool	minCut (const Node &node) const
	Returns true when the node is on the source side of the minimum cut.
template<typename CutMap >
void	minCutMap (CutMap &cutMap) const
	Gives back a minimum value cut.

Constructor & Destructor Documentation

Preflow ( const Digraph &  digraph, const CapacityMap &  capacity, Node  source, Node  target  )

inline

The constructor of the class.

Parameters

digraph	The digraph the algorithm runs on.
capacity	The capacity of the arcs.
source	The source node.
target	The target node.

~Preflow ( )

inline

Destructor.

Member Function Documentation

Preflow& capacityMap ( const CapacityMap &  map )

inline

Sets the capacity map.

Returns

(*this)

Preflow& flowMap ( FlowMap &  map )

inline

Sets the flow map. If you don't use this function before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated map, of course.

Returns

(*this)

Preflow& source ( const Node &  node )

inline

Sets the source node.

Returns

(*this)

Preflow& target ( const Node &  node )

inline

Sets the target node.

Returns

(*this)

Preflow& elevator ( Elevator &  elevator )

inline

Sets the elevator used by algorithm. If you don't use this function before calling run() or init(), an instance will be allocated automatically. The destructor deallocates this automatically allocated elevator, of course.

Returns

(*this)

const Elevator& elevator ( ) const

inline

Returns a const reference to the elevator.

Precondition

Either run() or init() must be called before using this function.

Preflow& tolerance ( const Tolerance &  tolerance )

inline

Sets the tolerance object used by the algorithm.

Returns

(*this)

const Tolerance& tolerance ( ) const

inline

Returns a const reference to the tolerance object used by the algorithm.

void init ( )

inline

Initializes the internal data structures and sets the initial flow to zero on each arc.

bool init ( const FlowMap &  flowMap )

inline

Initializes the internal data structures and sets the initial flow to the given flowMap. The flowMap should contain a flow or at least a preflow, i.e. at each node excluding the source node the incoming flow should greater or equal to the outgoing flow.

Returns

false if the given flowMap is not a preflow.

void startFirstPhase ( )

inline

The preflow algorithm consists of two phases, this method runs the first phase. After the first phase the maximum flow value and a minimum value cut can already be computed, although a maximum flow is not yet obtained. So after calling this method flowValue() returns the value of a maximum flow and minCut() returns a minimum cut.

Precondition

One of the init() functions must be called before using this function.

void startSecondPhase ( )

inline

The preflow algorithm consists of two phases, this method runs the second phase. After calling one of the init() functions and startFirstPhase() and then startSecondPhase(), flowMap() returns a maximum flow, flowValue() returns the value of a maximum flow, minCut() returns a minimum cut

Precondition

One of the init() functions and startFirstPhase() must be called before using this function.

void run ( )

inline

Runs the preflow algorithm.

Note

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

pf.init();
pf.startFirstPhase();
pf.startSecondPhase();

void runMinCut ( )

inline

Runs the preflow algorithm to compute the minimum cut.

Note

pf.runMinCut() is just a shortcut of the following code.

pf.init();
pf.startFirstPhase();

Value flowValue ( ) const

inline

Returns the value of the maximum flow by returning the excess of the target node. This value equals to the value of the maximum flow already after the first phase of the algorithm.

Precondition

Either run() or init() must be called before using this function.

Value flow ( const Arc &  arc ) const

inline

Returns the flow value on the given arc. This method can be called after the second phase of the algorithm.

Precondition

Either run() or init() must be called before using this function.

const FlowMap& flowMap ( ) const

inline

Returns a const reference to the arc map storing the found flow. This method can be called after the second phase of the algorithm.

Precondition

Either run() or init() must be called before using this function.

bool minCut ( const Node &  node ) const

inline

Returns true when the node is on the source side of the found minimum cut. This method can be called both after running startFirstPhase() and startSecondPhase().

Precondition

Either run() or init() must be called before using this function.

void minCutMap ( CutMap &  cutMap ) const

inline

Sets cutMap to the characteristic vector of a minimum value cut. cutMap should be a writable node map with bool (or convertible) value type.

This method can be called both after running startFirstPhase() and startSecondPhase(). The result after the second phase could be slightly different if inexact computation is used.

Note

This function calls minCut() for each node, so it runs in O(n) time.

Precondition

Either run() or init() must be called before using this function.