An optimal local approximation algorithm for max-min linear programs

We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The objective is to maximise $ω$ subject to $Ax \le 1$, $Cx \ge ω1$, and $x \ge 0$ for nonnegative matrices $A$ and $C$. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.

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