  We present a local algorithm (constant-time distributed algorithm) for
approximating max-min LPs. The objective is to maximise $\omega$ subject to $Ax
\le 1$, $Cx \ge \omega 1$, 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.
