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/logK); (iii) O(1/√log K})