Metrical task systems and the k-server problem on HSTs

Abstract

We consider the randomized k-server problem, and give improved results for various metric spaces. In particular, we extend a recent result of Coté et al [15] for well-separated binary Hierarchically Separated Trees (HSTs) to well-separated d-ary HSTs for poly-logarithmic values of d. One application of this result is an -competitive algorithm for k-server on n uniformly spaced points on a line. This substantially improves upon the prior guarantee of O( min (k,n 2/3) for this metric [16]. These results are based on obtaining a refined guarantee for the unfair metrical task systems problem on an HST. Prior to our work, such a guarantee was only known for the case of a uniform metric [5,7,18]. Our results are based on the primal-dual approach for online algorithms. Previous primal-dual approaches in the context of k-server and MTS [2,4,3] worked only for uniform or weighted star metrics, and the main technical contribution here is to extend many of these techniques to work directly on HSTs. © 2010 Springer-Verlag Berlin Heidelberg.