A Concentration Inequality for the Facility Location Problem

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

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005