Abstract
We prove that Minimum Vertex Cover on k-uniform hypergraphs is NP-hard to approximate within Ω(k 1 − ε). The result follows by a new reduction and a PCP characterization of NP by Håstad and Khot [11]. We also give an alternate construction of a PCP with the required properties. We also show that Minimum Vertex Cover on 3-uniform hypergraphs is NP-hard to approximate within 3/2 − ε. Of independent interest may be a 3 query PCP for NP with perfect completeness where answers are from a domain of size d and where the soundness is 2/d.
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Holmerin, J. (2002). Improved Inapproximability Results for Vertex Cover on k-Uniform Hypergraphs. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_86
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DOI: https://doi.org/10.1007/3-540-45465-9_86
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