Note: Local edge-connectivity augmentation in hypergraphs is NP-complete

Authors:
Zoltán Király;Ben Cosh;Bill Jackson
Affiliations:
Department of Computer Science, Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary;Department of Mathematics, University of Reading, Whiteknights, Reading, RG6 6AY, England, United Kingdom;School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, England, United Kingdom
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

We consider a local edge-connectivity hypergraph augmentation problem. Specifically, we are given a hypergraph G=(V,E) and a subpartition of V. We are asked to find the smallest possible integer @c, for which there exists a set of size-two edges F, with |F|=@c, such that in G^'=(V,E@?F), the local edge-connectivity between any pair of vertices lying in the same part of the subpartition is at least a given value k. Using a transformation from the bin-packing problem, we show that the associated decision problem is NP-complete, even when k=2.