SDP Gaps for 2-to-1 and Other Label-Cover Variants

In this paper we present semidefinite programming (SDP) gap instances for the following variants of the Label-Cover problem, closely related to the Unique Games Conjecture: (i) 2-to-1 Label-Cover; (ii) 2-to-2 Label-Cover; (iii) α-constraint Label-Cover. All of our gap instances have perfect SDP solutions. For alphabet size K, the integral optimal solutions have value: (i) O(1/ √ log K); (ii) O(1/ log K); (iii) O(1/ √ log K). Prior to this work, there were no known SDP gap instances for any of these problems with perfect SDP value and integral optimum tending to 0.

• Type: Conference
• Year: 2010
• Where: ICALP
• Authors: Venkatesan Guruswami, Subhash Khot, Ryan O'Donnell, Preyas Popat, Madhur Tulsiani, Yi Wu
• Keywords: Gap Instances, ICALP 2010, Log K, Perfect Sdp, Programming Languages