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• W2131906507 abstract "We study the problem of computing the minimum vertex cover on kuniform k-partite hypergraphs when the k-partition is given. On bipartite graphs (k = 2), the minimum vertex cover can be computed in polynomial time. For general k, the problem was studied by Lovasz [23], who gave a k/2 -approximation based on the standard LP relaxation. Subsequent work by Aharoni, Holzman and Krivelevich [1] showed a tight integrality gap of (k/2-o(1)) for the LP relaxation. While this problem was known to be NP-hard for k ≥ 3, the first nontrivial NP-hardness of approximation factor of k/4-e was shown in a recent work by Guruswami and Saket [13]. They also showed that assuming Khot's Unique Games Conjecture yields a k/2- e inapproximability for this problem, implying the optimality of Lovasz's result.In this work, we show that this problem is NP-hard to approximate within k/2 - 1 + 1/2k - e. This hardness factor is off from the optimal by an additive constant of at most 1 for k ≥ 4. Our reduction relies on the Multi-Layered PCP of [8] and uses a gadget - based on biased Long Codes - adapted from the LP integrality gap of [1]. The nature of our reduction requires the analysis of several Long Codes with different biases, for which we prove structural properties of the so called cross-intersecting collections of set families - variants of which have been studied in extremal set theory." @default.
• W2131906507 created "2016-06-24" @default.
• W2131906507 creator A5011759026 @default.
• W2131906507 creator A5067464936 @default.
• W2131906507 date "2011-01-01" @default.
• W2131906507 modified "2023-10-03" @default.
• W2131906507 title "Nearly Optimal NP-Hardness of Vertex Cover on k-Uniform k-Partite Hypergraphs" @default.
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• W2131906507 doi "https://doi.org/10.1007/978-3-642-22935-0_28" @default.
• W2131906507 hasPublicationYear "2011" @default.
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