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- W1591801237 abstract "We study constraint satisfaction problems on the domain { − 1,1}, where the given constraints are homogeneous linear threshold predicates. That is, predicates of the form sgn(w 1 x 1 + ⋯ + w n x n ) for some positive integer weights w 1, ..., w n . Despite their simplicity, current techniques fall short of providing a classification of these predicates in terms of approximability. In fact, it is not easy to guess whether there exists a homogeneous linear threshold predicate that is approximation resistant or not. The focus of this paper is to identify and study the approximation curve of a class of threshold predicates that allow for non-trivial approximation. Arguably the simplest such predicate is the majority predicate sgn(x 1 + ⋯ + x n ), for which we obtain an almost complete understanding of the asymptotic approximation curve, assuming the Unique Games Conjecture. Our techniques extend to a more general class of “majority-like” predicates and we obtain parallel results for them. In order to classify these predicates, we introduce the notion of Chow-robustness that might be of independent interest." @default.
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- W1591801237 date "2010-01-01" @default.
- W1591801237 modified "2023-10-16" @default.
- W1591801237 title "Approximating Linear Threshold Predicates" @default.
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- W1591801237 doi "https://doi.org/10.1007/978-3-642-15369-3_9" @default.
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