Every 2-CSP allows nontrivial approximation

Authors:
Johan Håstad
Affiliations:
Royal Institute of Technology, Stockholm, Sweden
Venue:
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Year:
2005

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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 provably better than picking a random assignment. To be more precise assume that each variable can take values in [d] and that each constraint rejects t out of the d2 possible input pairs. Then, for some universal constant c, we can, in probabilistic polynomial time, find an assignment whose objective value is, on expectation, within a factor (1- t/d2(1- c/d2 log d)) of optimal.