An optimal local approximation algorithm for max-min linear programs

Authors:
Patrik Floréen;Joel Kaasinen;Petteri Kaski;Jukka Suomela
Affiliations:
University of Helsinki, Helsinki, Finland;University of Helsinki, Helsinki, Finland;University of Helsinki, Helsinki, Finland;University of Helsinki, Helsinki, Finland
Venue:
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Year:
2009

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Abstract

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0 for nonnegative matrices A and C. 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.