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 - l)n - l/(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 2Hn for any randomized algorithm. We improve their upper bound for the uniform metric space by showing a randomized algorithm which is (Hn/In 2 +1 ≈ 1.4427Hn +1)-competitive.