Uniform metrical task systems with a limited number of states

Abstract

We give a randomized algorithm (the “Wedge Algorithm”) of competitiveness 3 2 H k − 1 2 k for any metrical task system on a uniform space of k points, for any k ⩾ 2 , where H k = ∑ i = 1 k 1 i , the kth harmonic number. This algorithm has better competitiveness than the Irani–Seiden algorithm if k is smaller than 10 8. The algorithm is better by a factor of 2 if k < 47 .