Randomly Supported Independence and Resistance
SIAM Journal on Computing
Beating the Random Ordering Is Hard: Every Ordering CSP Is Approximation Resistant
SIAM Journal on Computing
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
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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 $$1- \frac{t} {d^{2}}$$.