Better algorithms for unfair metrical task systems and applications

Abstract

Unfair metrical task systems are a generalization of online metrical task systems. In this paper we introduce new techniques to combine algorithms for unfair metrical task systems and apply these techniques to obtain improved randomized online algorithms for metrical task systems on arbitrary metric spaces. 1. Introduction. Metrical task systems (MTSs), introduced by Borodin, Linial, and Saks (11), can be described as follows: A server in some internal state receives tasks that have a service cost associated with each of the internal states. The server may switch states, paying a cost given by a metric space defined on the state space, and then pays the service cost associated with the new state. MTSs have been the subject of a great deal of study. A large part of the research into online algorithms can be viewed as a study of some particular MTS. In modelling some of these problems as MTSs, the set of permissible tasks is constrained to fit the particulars of the problem. In this paper we consider the original definition of MTSs, where the set of tasks can be arbitrary. A deterministic algorithm for any n-state MTS with a competitive ratio of 2n − 1