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… CONTINUE READING