Unique Games Over Integers
نویسندگان
چکیده
Consider systems of two-variable linear equations of the form xi−xj = cij , where the cij ’s are integer constants. We show that even if there is an integer solution satisfying at least a (1− )fraction of the equations, it is Unique-Games-hard to find an integer (or even real) solution satisfying at least an -fraction of the equations. Indeed, we show it is Unique-Games-hard even to find an -good solution modulo any integer m ≥ m0( ) of the algorithm’s choosing. ∗Supported by NSF grants CCF-0747250 and CCF-0915893, BSF grant 2008477, and Sloan and Okawa fellowships.
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