org.jgrapht.alg.flow

## Class GusfieldEquivalentFlowTree<V,E>

• Type Parameters:
V - the graph vertex type
E - the graph edge type
All Implemented Interfaces:
FlowAlgorithm<V,E>, MaximumFlowAlgorithm<V,E>

public class GusfieldEquivalentFlowTree<V,E>
extends Object
implements MaximumFlowAlgorithm<V,E>
This class computes an Equivalent Flow Tree (EFT) using the algorithm proposed by Dan Gusfield. EFTs can be used to efficiently calculate the maximum flow for all pairs of vertices. The algorithm is described in: Gusfield, D, Very simple methods for all pairs network flow analysis. SIAM Journal on Computing, 19(1), p142-155, 1990
In an undirected graph, there exist $frac{n(n-1)}{2}$ different vertex pairs. This class computes the maximum flow between each of these pairs efficiently by performing exactly $(n-1)$ minimum $s-t$ cut computations. If your application requires fewer than $(n-1)$ flow calculations, consider computing the maximum flows manually through MaximumFlowAlgorithm.

The runtime complexity of this class is $O((V-1)Q)$, where $Q$ is the runtime complexity of the algorithm used to compute $s-t$ cuts in the graph. By default, this class uses the PushRelabelMFImpl implementation to calculate minimum $s-t$ cuts. This class has a runtime complexity of $O(V^3)$, resulting in a $O(V^4)$ runtime complexity for the overal algorithm.

Note: this class performs calculations in a lazy manner. The EFT is not calculated until the first invocation of getMaximumFlowValue(Object, Object) or getEquivalentFlowTree(). Moreover, this class only calculates the value of the maximum flow between a source-destination pair; it does not calculate the corresponding flow per edge. If you need to know the exact flow through an edge, use one of the alternative MaximumFlowAlgorithm implementations.

Warning: EFTs do not allow you to calculate minimum cuts for all pairs of vertex! For that, Gomory-Hu cut trees are required! Use the GusfieldGomoryHuCutTree implementation instead.

This class does not support changes to the underlying graph. The behavior of this class is undefined when the graph is modified after instantiating this class.

Author:
Joris Kinable
• ### Constructor Detail

• #### GusfieldEquivalentFlowTree

public GusfieldEquivalentFlowTree(Graph<V,E> network)
Constructs a new GusfieldEquivalentFlowTree instance.
Parameters:
network - input graph
• #### GusfieldEquivalentFlowTree

public GusfieldEquivalentFlowTree(Graph<V,E> network,
double epsilon)
Constructs a new GusfieldEquivalentFlowTree instance.
Parameters:
network - input graph
epsilon - precision
• #### GusfieldEquivalentFlowTree

public GusfieldEquivalentFlowTree(Graph<V,E> network,
MinimumSTCutAlgorithm<V,E> minimumSTCutAlgorithm)
Constructs a new GusfieldEquivalentFlowTree instance.
Parameters:
network - input graph
minimumSTCutAlgorithm - algorithm used to compute the minimum $s-t$ cuts
• ### Method Detail

• #### getEquivalentFlowTree

public SimpleWeightedGraph<V,DefaultWeightedEdge> getEquivalentFlowTree()
Returns the Equivalent Flow Tree as an actual tree (graph). Note that this tree is not necessarily unique. The edge weights represent the flow values/cut weights. This method runs in $O(n)$ time
Returns:
Equivalent Flow Tree
• #### getMaximumFlowValue

public double getMaximumFlowValue(V source,
V sink)
Returns the Maximum flow between source and sink. The algorithm is only executed once; successive invocations of this method will return in $O(1)$ time.
Specified by:
getMaximumFlowValue in interface MaximumFlowAlgorithm<V,E>
Parameters:
source - source vertex
sink - sink vertex
Returns:
the Maximum flow between source and sink.
• #### getFlowDirection

public V getFlowDirection(E e)
Unsupported operation
Specified by:
getFlowDirection in interface FlowAlgorithm<V,E>
Parameters:
e - edge
Returns:
nothing