The k-server problem with advice in d dimensions and on the sphere

Abstract

We study the impact of additional information on the hardness of the k-server problem on different metric spaces. To this end, we consider the well-known model of computing with advice. In particular, we design an algorithm for the d-dimensional Euclidean space, which generalizes a known result for the Euclidean plane. As another relevant setting, we investigate a metric space with positive curvature; in particular, the sphere. Both algorithms have constant strict competitive ratios while reading a constant number of advice bits with every request, independent of the number k of servers, and solely depending on parameters of the underlying metric structure.