Abstract
In this paper, we present a randomized polynomial-time approximation algorithm for MAX k-CSP d . In MAX k-CSP d , we are given a set of predicates of arity k over an alphabet of size d. Our goal is to find an assignment that maximizes the number of satisfied constraints.
Our algorithm has approximation factor Ω(kd/d k) (when k ≥ Ω(logd)). This bound is asymptotically optimal assuming the Unique Games Conjecture. The best previously known algorithm has approximation factor Ω(klogd/d k).
We also give an approximation algorithm for the boolean MAX k-CSP2 problem with a slightly improved approximation guarantee.
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Makarychev, K., Makarychev, Y. (2012). Approximation Algorithm for Non-boolean MAX k-CSP. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_22
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DOI: https://doi.org/10.1007/978-3-642-32512-0_22
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