# An optimal local approximation algorithm for max-min linear programs

@inproceedings{Floren2008AnOL, title={An optimal local approximation algorithm for max-min linear programs}, author={Patrik Flor{\'e}en and Joel Kaasinen and Petteri Kaski and Jukka Suomela}, booktitle={ACM Symposium on Parallelism in Algorithms and Architectures}, year={2008} }

In a max-min LP, the objective is to maximise ω subject to <i>A</i><b>x</b> ≤ <b>1</b>, <i>C</i><b>x</b> ≥ ω<b>1</b>, and <b>x</b> ≥ 0 for nonnegative matrices <i>A</i> and <i>C</i>. We present a local algorithm (constant-time distributed algorithm) for approximating max-min LPs. The approximation ratio of our algorithm is the best possible for any local algorithm; there is a matching unconditional lower bound.

## 19 Citations

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It is shown that for any ΔI≤2, ΔK≥2, and ε>0 there exists a local algorithm that achieves the approximation ratio ΔI(1−1/ΔK)+ε, and that this result is the best possible: no local algorithm can achieve the approximability of max-min LPs and min-max LPs.

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The technique of graph unfolding for the design of local approximation algorithms is introduced and it is shown that for every e> 0 there exists a local algorithm achieving theroximation ratio Δ I (1 − 1/Δ K) + e.

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