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- W4289552703 abstract "Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies related to global constraints. First, they were not able to support a cardinality constraint, as in, say, the Min-Bisection problem. Second, while the pseudoexpectation of the objective function was shown to have some value $beta$, it did not necessarily actually satisfy the constraint objective = $beta$. In this paper we show how to remedy both deficiencies in the case of random CSPs, by translating emph{global} constraints into emph{local} constraints. Using these ideas, we also show that degree-$Omega(sqrt{n})$ SOS does not provide a $(frac{4}{3} - epsilon)$-approximation for Min-Bisection, and degree-$Omega(n)$ SOS does not provide a $(frac{11}{12} + epsilon)$-approximation for Max-Bisection or a $(frac{5}{4} - epsilon)$-approximation for Min-Bisection. No prior SOS lower bounds for these problems were known." @default.
- W4289552703 created "2022-08-03" @default.
- W4289552703 creator A5051167298 @default.
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- W4289552703 date "2018-09-04" @default.
- W4289552703 modified "2023-10-14" @default.
- W4289552703 title "SOS lower bounds with hard constraints: think global, act local" @default.
- W4289552703 doi "https://doi.org/10.48550/arxiv.1809.01207" @default.
- W4289552703 hasPublicationYear "2018" @default.
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