On multicriteria online problems

In this paper we consider multicriteria formulations of classical online problems where an algorithm must simultaneously perform well with respect to two different cost measures. The one of the possible optimal offline strategies according to a given selection function. We consider a parametric family of functions based on their monotonicity properties which covers all the possible selections. Then, we provide a universal multicriteria algorithm that can be applied to different online problems. For the multicriteria k-server formulation, for each function class, such an algorithm achieves competitive ratios that are only an O(logW) multiplicative factor away from the corresponding lower bounds that we determine for the class, where W is the maximum edge weight. We then show how to extend our results to other multicriteria online problems sharing similar properties. © Springer-Verlag Berlin Heidelberg 2000.