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Local edge-connectivity augmentation in hypergraphs is NP-complete |
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| Authors: | Zoltá n Kirá ly |
| Affiliation: | a Department of Computer Science, Eötvös University, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary b Department of Mathematics, University of Reading, Whiteknights, Reading, RG6 6AY, England, United Kingdom c School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, England, United Kingdom |
| 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 γ, for which there exists a set of size-two edges F, with |F|=γ, 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. |
| Keywords: | Hypergraphs Edge-connectivity augmentation NP-completeness |
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