Characterizing the flow equivalent trees of a network

Authors:
David Hartvigsen
Affiliations:
354, Mendoza College of Business, University of Notre Dame, Notre Dame, IN
Venue:
Discrete Applied Mathematics
Year:
2003

Citing 3
Cited 0

Combinatorial optimization

Combinatorial optimization
Building chain and cactus representations of all minimum cuts from Hao-Orlin in the same asymptotic run time

Journal of Algorithms
Combinatorial Algorithms

Combinatorial Algorithms

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Abstract

Consider a connected graph G with positive edge capacities. Gomory and Hu (J. SIAM 9 (1961) 551) showed that there always exists a tree T with positive edge capacities, on the same node set as G, such that the max flow value between any pair of nodes in G is the same as the max flow value between the corresponding pair of nodes in T. Such a tree is called a flow equivalent tree for G and need not be unique. In this paper, we present a "compact" (i.e., polynomial size) characterization of the collection of all flow equivalent trees for a graph G. We also present a polynomial time algorithm for recognizing such representations.