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- W4294039073 abstract "A valued constraint satisfaction problem (VCSP) instance $(V,Pi,w)$ is a set of variables $V$ with a set of constraints $Pi$ weighted by $w$. Given a VCSP instance, we are interested in a re-weighted sub-instance $(V,Pi'subset Pi,w')$ such that preserves the value of the given instance (under every assignment to the variables) within factor $1pmepsilon$. A well-studied special case is cut sparsification in graphs, which has found various applications. We show that a VCSP instance consisting of a single boolean predicate $P(x,y)$ (e.g., for cut, $P=mbox{XOR}$) can be sparsified into $O(|V|/epsilon^2)$ constraints if and only if the number of inputs that satisfy $P$ is anything but one (i.e., $|P^{-1}(1)| neq 1$). Furthermore, this sparsity bound is tight unless $P$ is a relatively trivial predicate. We conclude that also systems of 2SAT (or 2LIN) constraints can be sparsified." @default.
- W4294039073 created "2022-09-01" @default.
- W4294039073 creator A5037378898 @default.
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- W4294039073 date "2015-09-06" @default.
- W4294039073 modified "2023-09-26" @default.
- W4294039073 title "Sparsification of Two-Variable Valued CSPs" @default.
- W4294039073 doi "https://doi.org/10.48550/arxiv.1509.01844" @default.
- W4294039073 hasPublicationYear "2015" @default.
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