Improvements on the k-center Problem for Uncertain Data

Abstract

In real applications, there are situations where we need to model some problems based on uncertain data. This leads us to define an uncertain model for some classical geometric optimization problems and propose algorithms to solve them. The assigned version of the k-center problem for n uncertain points in a metric space is studied in this paper. The main approach is to replace each uncertain point with a clever choice of a certain point. We argue that the k-center solution for these certain replacements of our uncertain points, is a good constant approximation factor for the original uncertain k-center problem. This approach enables us to present fast and simple algorithms that give 10-approximation solution for the k-center problem in any metric space and when the ambient space is Euclidean, it can be improved to (3+ε)-approximation for any ε>0. These algorithms improve both the approximation factor and the running time of the previously known algorithms. Also, our algorithms are suitable for applying in the case of streaming and big data.