Facility Location Problem in Differential Privacy Model Revisited

NeurIPS 2019  ·  Yunus Esencayi, Marco Gaboardi, Shi Li, Di Wang ·

In this paper we study the uncapacitated facility location problem in the model of differential privacy (DP) with uniform facility cost. Specifically, we first show that, under the hierarchically well-separated tree (HST) metrics and the super-set output setting that was introduced in Gupta et. al., there is an $\epsilon$-DP algorithm that achieves an $O(\frac{1}{\epsilon})$(expected multiplicative) approximation ratio; this implies an $O(\frac{\log n}{\epsilon})$ approximation ratio for the general metric case, where $n$ is the size of the input metric. These bounds improve the best-known results given by Gupta et. al. In particular, our approximation ratio for HST-metrics is independent of $n$, and the ratio for general metrics is independent of the aspect ratio of the input metric. On the negative side, we show that the approximation ratio of any $\epsilon$-DP algorithm is lower bounded by $\Omega(\frac{1}{\sqrt{\epsilon}})$, even for instances on HST metrics with uniform facility cost, under the super-set output setting. The lower bound shows that the dependence of the approximation ratio for HST metrics on $\epsilon$ can not be removed or greatly improved. Our novel methods and techniques for both the upper and lower bound may find additional applications.

PDF Abstract NeurIPS 2019 PDF NeurIPS 2019 Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here