Metrical Task Systems and the k-Server Problem on HSTs

Abstract

AbstractWe 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 \({\rm exp}(O(\sqrt{\log \log k \log n}))\)-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.KeywordsAllocation ProblemCompetitive RatioDual VariableOnline AlgorithmCompetitive AlgorithmThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.