Abstract.
We use semidefinite programming to prove that any constraint satisfaction problem in two variables over any domain allows an efficient approximation algorithm that does better than picking a random assignment. Specifically we consider the case when each variable can take values in [d] and that each constraint rejects t out of the d 2 possible input pairs. Then, for some universal constant c, we can, in probabilistic polynomial time, find an assignment whose objective value is, in expectation, within a factor \(1- \frac{t} {d^{2}} +\frac{ct} {d^{4}log d}\) of optimal, improving on the trivial bound of \(1- \frac{t} {d^{2}}\).
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Manuscript received 27 September 2007
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Håstad, J. Every 2-csp Allows Nontrivial Approximation. comput. complex. 17, 549–566 (2008). https://doi.org/10.1007/s00037-008-0256-y
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DOI: https://doi.org/10.1007/s00037-008-0256-y