Differentially Private Approximation Algorithms

Consider the following problem: given a metric space, some of whose points are "clients," select a set of at most k facility locations to minimize the average distance from the clients to their nearest facility. This is just the well-studied k-median problem, for which many approximation algorithms and hardness results are known. Note that the objective function encourages opening facilities in areas where there are many clients, and given a solution, it is often possible to get a good idea of where the clients are located. This raises the following quandary: what if the locations of the clients are sensitive information that we would like to keep private? Is it even possible to design good algorithms for this problem that preserve the privacy of the clients? In this paper, we initiate a systematic study of algorithms for discrete optimization problems in the framework of differential privacy (which formalizes the idea of protecting the privacy of individual input elements)....

• Type: Conference
• Year: 2010
• Where: SODA
• Authors: Anupam Gupta, Katrina Ligett, Frank McSherry, Aaron Roth, Kunal Talwar
• Keywords: Discrete Algorithms, Logarithmic Additive Approximation, Non-trivial Approximation, SODA 2010, Submodular Maximization Problem