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Network reinforcement

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Abstract

We give an algorithm for the following problem: given a graph G=(V,E) with edge-weights and a nonnegative integer k, find a minimum cost set of edges that contains k disjoint spanning trees. This also solves the following reinforcement problem: given a network, a number k and a set of candidate edges, each of them with an associated cost, find a minimum cost set of candidate edges to be added to the network so it contains k disjoint spanning trees. The number k is seen as a measure of the invulnerability of a network. Our algorithm has the same asymptotic complexity as |V| applications of the minimum cut algorithm of Goldberg & Tarjan.

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  1. IBM T. J. Watson research Center, P. O. Box 218, Yorktown Heights, NY, 10598, USA

    Francisco Barahona

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  1. Francisco Barahona
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Correspondence to Francisco Barahona.

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Received: April, 2004

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Barahona, F. Network reinforcement. Math. Program. 105, 181–200 (2006). https://doi.org/10.1007/s10107-005-0648-6

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  • DOI: https://doi.org/10.1007/s10107-005-0648-6

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