GomoryHu< GR, CAP > Class Template Reference

Detailed Description

template<typename GR, typename CAP>
class lemon::GomoryHu< GR, CAP >

The Gomory-Hu tree is a tree on the node set of a given graph, but it may contain edges which are not in the original graph. It has the property that the minimum capacity edge of the path between two nodes in this tree has the same weight as the minimum cut in the graph between these nodes. Moreover the components obtained by removing this edge from the tree determine the corresponding minimum cut. Therefore once this tree is computed, the minimum cut between any pair of nodes can easily be obtained.

The algorithm calculates n-1 distinct minimum cuts (currently with the Preflow algorithm), thus it has \(O(n^3\sqrt{m})\) overall time complexity. It calculates a rooted Gomory-Hu tree. The structure of the tree and the edge weights can be obtained using predNode(), predValue() and rootDist(). The functions minCutMap() and minCutValue() calculate the minimum cut and the minimum cut value between any two nodes in the graph. You can also list (iterate on) the nodes and the edges of the cuts using MinCutNodeIt and MinCutEdgeIt.

Template Parameters

GR	The type of the undirected graph the algorithm runs on.
CAP	The type of the edge map containing the capacities. The default map type is GR::EdgeMap<int>.

#include <lemon/gomory_hu.h>

Classes
class	MinCutEdgeIt
	Iterate on the edges of a minimum cut. More...
class	MinCutNodeIt
	Iterate on the nodes of a minimum cut. More...

Public Types
typedef GR	Graph
	The graph type of the algorithm.
typedef CAP	Capacity
	The capacity map type of the algorithm.
typedef Capacity::Value	Value
	The value type of capacities.

Public Member Functions
	GomoryHu (const Graph &graph, const Capacity &capacity)
	Constructor.
	~GomoryHu ()
Execution Control
void	run ()
	Run the Gomory-Hu algorithm.
Query Functions
The results of the algorithm can be obtained using these functions. run() should be called before using them. See also MinCutNodeIt and MinCutEdgeIt.
Node	predNode (const Node &node) const
	Return the predecessor node in the Gomory-Hu tree.
Value	predValue (const Node &node) const
	Return the weight of the predecessor edge in the Gomory-Hu tree.
int	rootDist (const Node &node) const
	Return the distance from the root node in the Gomory-Hu tree.
Value	minCutValue (const Node &s, const Node &t) const
	Return the minimum cut value between two nodes.
template<typename CutMap >
Value	minCutMap (const Node &s, const Node &t, CutMap &cutMap) const
	Return the minimum cut between two nodes.

Constructor & Destructor Documentation

GomoryHu ( const Graph &  graph, const Capacity &  capacity  )

inline

Constructor.

Parameters

graph	The undirected graph the algorithm runs on.
capacity	The edge capacity map.

~GomoryHu ( )

inline

Destructor.

Member Function Documentation

void run ( )

inline

This function runs the Gomory-Hu algorithm.

Node predNode ( const Node &  node ) const

inline

This function returns the predecessor node of the given node in the Gomory-Hu tree. If node is the root of the tree, then it returns INVALID.

Precondition

run() must be called before using this function.

Value predValue ( const Node &  node ) const

inline

This function returns the weight of the predecessor edge of the given node in the Gomory-Hu tree. If node is the root of the tree, the result is undefined.

Precondition

run() must be called before using this function.

int rootDist ( const Node &  node ) const

inline

This function returns the distance of the given node from the root node in the Gomory-Hu tree.

Precondition

run() must be called before using this function.

Value minCutValue ( const Node &  s, const Node &  t  ) const

inline

This function returns the minimum cut value between the nodes s and t. It finds the nearest common ancestor of the given nodes in the Gomory-Hu tree and calculates the minimum weight edge on the paths to the ancestor.

Precondition

run() must be called before using this function.

Value minCutMap ( const Node &  s, const Node &  t, CutMap &  cutMap  ) const

inline

This function returns the minimum cut between the nodes s and t in the cutMap parameter by setting the nodes in the component of s to true and the other nodes to false.

For higher level interfaces see MinCutNodeIt and MinCutEdgeIt.

Parameters

s	The base node.
t	The node you want to separate from node s.
cutMap	The cut will be returned in this map. It must be a bool (or convertible) ReadWriteMap on the graph nodes.

Returns

The value of the minimum cut between s and t.

Precondition

run() must be called before using this function.