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- W1465199488 abstract "MAX-2-SAT and MAX-2-CSP are important NP-hard optimization problems generalizing many graph problems. Despite many efforts, the only known algorithm (due to Williams) solving them in less than 2 n steps uses exponential space. Scott and Sorkin give an algorithm with $2^{n(1-frac{2}{d+1})}$ time and polynomial space for these problems, where d is the average variable degree. We improve this bound to $O^*(2^{n(1-frac{10/3}{d+1})})$ for MAX-2-SAT and $O^*(2^{n(1-frac{3}{d+1})})$ for MAX-2-CSP. We also prove stronger upper bounds for d bounded from below. E.g., for d ≥ 10 the bounds improve to $O^*(2^{n(1-frac{3.469}{d+1})})$ and $O^*(2^{n(1-frac{3.221}{d+1})})$ , respectively. As a byproduct we get a simple proof of an $O^*(2^frac{m}{5.263})$ upper bound for MAX-2-CSP, where m is the number of constraints. This matches the best known upper bound w.r.t. m due to Gaspers and Sorkin." @default.
- W1465199488 created "2016-06-24" @default.
- W1465199488 creator A5062090877 @default.
- W1465199488 date "2012-01-01" @default.
- W1465199488 modified "2023-09-24" @default.
- W1465199488 title "New Upper Bounds for MAX-2-SAT and MAX-2-CSP w.r.t. the Average Variable Degree" @default.
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- W1465199488 doi "https://doi.org/10.1007/978-3-642-28050-4_9" @default.
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