Abstract
We show how under certain conditions one can extend constructions of integrality gaps for semidefinite relaxations into ones that hold for stronger systems: those SDP to which the so-called k-level constraints of the Sherali-Adams hierarchy are added. The value of k above depends on properties of the problem. We present two applications, to the Quadratic Programming problem and to the MaxCutGain problem.
Our technique is inspired by a paper of Raghavendra and Steurer [Raghavendra and Steurer, FOCS 09] and our result gives a doubly exponential improvement for Quadratic Programming on another result by the same authors [Raghavendra and Steurer, FOCS 09]. They provide tight integrality-gap for the system above which is valid up to k = (loglogn)Ω(1) whereas we give such a gap for up to k = n Ω(1).
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Benabbas, S., Magen, A. (2010). Extending SDP Integrality Gaps to Sherali-Adams with Applications to Quadratic Programming and MaxCutGain . In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_23
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DOI: https://doi.org/10.1007/978-3-642-13036-6_23
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