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Unique Games Over Integers

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journal contribution
posted on 01.09.1993, 00:00 authored by Ryan O'Donnell, Yi Wu, Yuan Zhou
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 −ε)- fraction of the equations, it is Unique-Games-hard to find an integer (or even real) solution satisfying at least an ε-fraction of the equations. Indeed, we show it is Unique-Games-hard even to find an ε-good solution modulo any integer m ≥ m0(ε) of the algorithm’s choosing




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