Abstract
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) \(O(1/\sqrt{\log K})\); (ii) O(1/logK); (iii) \(O(1/\sqrt{\log K})\).
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.
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Guruswami, V., Khot, S., O’Donnell, R., Popat, P., Tulsiani, M., Wu, Y. (2010). SDP Gaps for 2-to-1 and Other Label-Cover Variants. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_52
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DOI: https://doi.org/10.1007/978-3-642-14165-2_52
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