Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;

Authors:
Jonas Holmerin
Affiliations:
Royal Institute of Technology, Stockholm, Sweden
Venue:
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Year:
2002

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Abstract

(MATH) We prove that Minimu Vertex Cover on 4-regular hyper-graphs (or in other words, Minimum Hitting Set where all sets have size exactly 4), is hard to approximate within $2 - &egr;. We also prove that the maximization version, in which we are allowed to pick B = pn elements in an n-vertex hyper-graph, and are asked to cover as many edges as possible, is hard to approximate within 1/(1 — (1—p)4) - &egr; when p &rhoe; 1/2 and within ((1—p)4 + p4)/(1 &mdadsh; (1—p)4) — &egr; when p ξ 1/2. From this follows that the general problem when B is part of the input is hard to approximate within 16/15 - &egr;.