Randomized Algorithms for Metrical Task Systems

Borodin, Linial, and Saks introduce a general model for online systems in BLS92] called task systems and show a deterministic algorithm which achieves a competitive ratio of 2n ?1 for any metrical task system with n states. We present a randomized algorithm which achieves a competitive ratio of e=(e?1)n?1=(e?1) 1:5820n?0:5820 for this same problem. For the uniform metric space, Borodin, Linial, and Saks present an algorithm which achieves a competitive ratio of 2Hn, and they show a lower bound of Hn for any randomized algorithm. We improve their upper bound for the uniform metric space by showing a randomized algorithm which is ? Hn + O(p log n)-competitive.