We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The objective is to maximise ω subject to Ax≤1, Cx≥ω1, and x≥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.
@article{arxiv.0809.1489,
title = {An optimal local approximation algorithm for max-min linear programs},
author = {Patrik Floréen and Joel Kaasinen and Petteri Kaski and Jukka Suomela},
journal= {arXiv preprint arXiv:0809.1489},
year = {2012}
}