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- W2397736010 abstract "We study the problem of computing the minimum vertex cover on $k$-uniform $k$-partite hypergraphs when the $k$-partition is given. On bipartite graphs (k=2), the minimum vertex cover can be computed in polynomial time. For $k ge 3,$ this problem is known to be NP-hard. For general $k$, the problem was studied by Lovasz, who gave a $frac{k}{2}$-approximation based on the standard LP relaxation. Subsequent work by Aharoni, Holzman, and Krivelevich showed a tight integrality gap of $(frac{k}{2} - o(1))$ for the LP relaxation. We further investigate the inapproximability of minimum vertex cover on $k$-uniform $k$-partite hypergraphs and present the following results (here $varepsilon > 0$ is an arbitrarily small constant): NP-hardness of obtaining an approximation factor of $(frac{k}{4} - varepsilon)$ for even $k$ and $(frac{k}{4} - frac{1}{4k} - varepsilon)$ for odd $k$, NP-hardness of obtaining a nearly optimal approximation factor of $(frac{k}{2}-1+frac{1}{2k}-varepsilon)$, and an optimal uniqu..." @default.
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- W2397736010 date "2013-01-01" @default.
- W2397736010 modified "2023-10-04" @default.
- W2397736010 title "Inapproximability of Minimum Vertex Cover on k-uniform k-partite Hypergraphs." @default.
- W2397736010 hasPublicationYear "2013" @default.
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