Gomory-Hu tree with the Gusfield's algorithm

Description

Given a connected weighted and undirected graph, the ghTreeGusfield function builds a Gomory-Hu tree with the Gusfield's algorithm.

Usage

1
ghTreeGusfield(nodes, arcs)

Arguments

nodes

vector containing the nodes of the graph, identified by a number that goes from 1 to the order of the graph.

arcs

matrix with the list of arcs of the graph. Each row represents one arc. The first two columns contain the two endpoints of each arc and the third column contains their weights.

Details

The Gomory-Hu tree was introduced by R. E. Gomory and T. C. Hu in 1961. Given a connected weighted and undirected graph, the Gomory-Hu tree is a weighted tree that contains the minimum s-t cuts for all s-t pairs of nodes in the graph. Gomory and Hu also developed an algorithm to find it that involves maximum flow searchs and nodes contractions.

In 1990, Dan Gusfield proposed a new algorithm that can be used to find a Gomory-Hu tree without nodes contractions and simplifies the implementation.

Value

ghTreeGusfield returns a list with:

tree.nodes

vector containing the nodes of the Gomory-Hu tree.

tree.arcs

matrix containing the list of arcs of the Gomory-Hu tree.

stages

number of stages required.

References

R. E. Gomory, T. C. Hu. Multi-terminal network flows. Journal of the Society for Industrial and Applied Mathematics, vol. 9, 1961.

Dan Gusfield (1990). "Very Simple Methods for All Pairs Network Flow Analysis". SIAM J. Comput. 19 (1): 143-155.

See Also

A more general function getMinimumCutTree.

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