Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 d 2  possible input pairs. Then, for some universal constant c,  can, in probabilistic polynomial time, find an assignment whose objective value is, on expectation, within a factor (1- t/d 2 (1- c/d 2  log d)) of optimal.
['Johan Håstad']
I am writing a research paper on a idea Every 2-CSP allows nontrivial approximation
[{"from": "human", "value": "I am writing a research paper on a idea Every 2-CSP allows nontrivial approximation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 d 2  possible input pairs. Then, for some universal constant c,  can, in probabilistic polynomial time, find an assignment whose objective value is, on expectation, within a factor (1- t/d 2 (1- c/d 2  log d)) of optimal."}]