Randomized algorithms for metrical task systems

Abstract

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 any metrical task system of n states. 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 H n for any randomized algorithm. We improve their upper bound for the uniform metric space by showing a randomized algorithm which is (Hn/ln2+1≈1.4427H n +1)-competitive.