No Small Linear Program Approximates Vertex Cover within a Factor 2 - e

The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regevproved that the problem is NP-hard to approximate within a factor2 - ∈, assuming the Unique Games Conjecture (UGC). This is tight because the problem has an easy 2-approximation algorithm. Without resorting to the UGC, the best in approximability result for the problem is due to Dinur and Safra: vertex cover is NP-hard to approximate within a factor 1.3606. We prove the following unconditional result about linear programming (LP)relaxations of the problem: every LP relaxation that approximates vertex cover within a factor of 2-∈ has super-polynomially many inequalities. As a direct consequence of our methods, we also establish that LP relaxations (as well as SDP relaxations) that approximate the independent set problem within any constant factor have super-polynomially many inequalities. © 2015 IEEE.


Editor(s):
Guruswami, Venkatesan
Published in:
IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, Berkeley, CA, USA, 17-20 October, 2015, 1123-1142
Year:
2015
Publisher:
IEEE Computer Society
ISBN:
978-1-4673-8191-8
Laboratories:




 Record created 2017-05-10, last modified 2018-03-17


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