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arXiv · 2012.04488

A Concentration Inequality for the Facility Location Problem

Sandeep Silwal
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Abstract

We give a concentration inequality for a stochastic version of the facility location problem. We show the objective $C_n = \min_{F \subseteq [0,1]^2}|F|+\sum_{x\in X}\min_{f\in F}\|x-f\|$ is concentrated in an interval of length $O(n^{1/6})$ and $\E[C_n]=\Theta(n^{2/3})$ if the input $X$ consists of i.i.d. uniform points in the unit square. Our main tool is to use a geometric quantity, previously used in the design of approximation algorithms for the facility location problem, to analyze a martingale process. Many of our techniques generalize to other settings.

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Sandeep Silwal. 2020-12-08. A Concentration Inequality for the Facility Location Problem. https://arxiv.org/abs/2012.04488

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