A Note on Parametric Network Flows

Edward Minieka
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Edward Minieka: University of Illinois, Chicago

Management Science, 1973, vol. 19, issue 5, 585-587

Abstract: In their paper [Doulliez, P. J., M. R. Rao. 1971. Maximal flow in a multi-terminal network with any one are subject to failure. Management Sci. 18 (1, September) 48-58.], Doulliez and Rao present algorithms that solve two flow problems for a single source, multi-terminal network. The first problem that they solve is the construction of a flow that maximizes the value of t, where the demand at each sink is a nondecreasing, linear function of t. Given such a flow, the second problem that they solve is the construction of a flow that maximizes the value of t when the capacity of an arc is reduced. This paper supplies a finiteness proof for the first algorithm and sketches a finiteness proof for the second algorithm. The proofs are based on the well-known fact that a network possesses only a finite number of different spanning trees.

Date: 1973
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