An optimal local approximation algorithm for max-min linear programs

TL;DR

This paper introduces a constant-time distributed local algorithm that optimally approximates max-min linear programs, achieving the best possible approximation ratio with a proven lower bound.

Contribution

It provides the first local algorithm with optimal approximation ratio for max-min LPs, matching the theoretical lower bound.

Findings

Achieves the best possible approximation ratio for local algorithms

Establishes a matching lower bound proving optimality

Demonstrates effectiveness in distributed settings

Abstract

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.