EdmondsKarp< GR, CAP, TR > Class Template Reference

Detailed Description

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

This class provides an implementation of the Edmonds-Karp algorithm producing a flow of maximum value in a digraph [6], [1], [12]. The Edmonds-Karp algorithm is slower than the Preflow algorithm, but it has an advantage of the step-by-step execution control with feasible flow solutions. The source node, the target node, the capacity of the arcs and the starting flow value of the arcs should be passed to the algorithm through the constructor.

The time complexity of the algorithm is \( O(nm^2) \) in worst case. Always try the Preflow algorithm instead of this if you just want to compute the optimal flow.

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 EdmondsKarpDefaultTraits<GR, CAP>. In most cases, this parameter should not be set directly, consider to use the named template parameters instead.

#include <lemon/edmonds_karp.h>

Classes
struct	SetFlowMap

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::Tolerance	Tolerance
	The type of the tolerance.

Public Member Functions
	EdmondsKarp (const Digraph &digraph, const CapacityMap &capacity, Node source, Node target)
	The constructor of the class.
	~EdmondsKarp ()
EdmondsKarp &	capacityMap (const CapacityMap &map)
	Sets the capacity map.
EdmondsKarp &	flowMap (FlowMap &map)
	Sets the flow map.
EdmondsKarp &	source (const Node &node)
	Sets the source node.
EdmondsKarp &	target (const Node &node)
	Sets the target node.
EdmondsKarp &	tolerance (const Tolerance &tolerance)
	Sets the tolerance used by algorithm.
const Tolerance &	tolerance () const
	Returns a const reference to the tolerance.
Execution control
The simplest way to execute the algorithm is to use run(). If you need better control on the initial solution or the execution, you have to call one of the init() functions first, then start() or multiple times the augment() function.
void	init ()
	Initializes the algorithm.
template<typename FlowMap >
void	init (const FlowMap &flowMap)
	Initializes the algorithm using the given flow map.
template<typename FlowMap >
bool	checkedInit (const FlowMap &flowMap)
	Initializes the algorithm using the given flow map.
bool	augment ()
	Augments the solution along a shortest path.
void	start ()
	Executes the algorithm.
void	run ()
	Runs the algorithm.
Query Functions
The result of the Edmonds-Karp algorithm can be obtained using these functions. Either run() or start() 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

EdmondsKarp ( 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.

~EdmondsKarp ( )

inline

Destructor.

Member Function Documentation

EdmondsKarp& capacityMap ( const CapacityMap &  map )

inline

Sets the capacity map.

Returns

(*this)

EdmondsKarp& 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)

EdmondsKarp& source ( const Node &  node )

inline

Sets the source node.

Returns

(*this)

EdmondsKarp& target ( const Node &  node )

inline

Sets the target node.

Returns

(*this)

EdmondsKarp& tolerance ( const Tolerance &  tolerance )

inline

Sets the tolerance used by 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.

void init ( const FlowMap &  flowMap )

inline

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

bool checkedInit ( const FlowMap &  flowMap )

inline

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

Returns

false when the given flowMap does not contain a feasible flow.

bool augment ( )

inline

Augments the solution along a shortest path. This function searches a shortest path between the source and the target in the residual digraph by the Bfs algoritm. Then it increases the flow on this path with the minimal residual capacity on the path. If there is no such path, it gives back false.

Returns

false when the augmenting did not success, i.e. the current flow is a feasible and optimal solution.

void start ( )

inline

Executes the algorithm by performing augmenting phases until the optimal solution is reached.

Precondition

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

void run ( )

inline

Runs the Edmonds-Karp algorithm.

Note

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

ek.init();
ek.start();

Value flowValue ( ) const

inline

Returns the value of the maximum flow found by 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.

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.

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.

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.

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.