Adaptive k-center and diameter estimation in sliding windows

In this paper we present novel streaming algorithms for the k-center and the diameter estimation problems for general metric spaces under the sliding window model. The key idea behind our algorithms is to maintain a small coreset which, at any time, allows to compute a solution to the problem under consideration for the current window, whose quality can be made arbitrarily close to the one of the best solution attainable by running a polynomial-time sequential algorithm on the entire window. Remarkably, the size of our coresets is independent of the window length and can be upper bounded by a function of the target number of centers (for the k-center problem), of the desired accuracy, and of the characteristics of the current window, namely its doubling dimension and aspect ratio. One of the major strengths of our algorithms is that they adapt obliviously to these two latter characteristics. We also provide experimental evidence of the practical viability of the algorithms and their superiority over the current state of the art.