Randomized algorithms for metrical task systems

Abstract

Borodin et al. (1992) introduce a general model for online systems in [3] called task systems and show a deterministic algorithm which achieves a competitive ratio of 2 n − 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) ≈ 1.5820 n − 0.5820 for this same problem. For the uniform metric space, Borodin et al. present an algorithm which achieves a competitive ratio of 2 H n , 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 ( H n + O(√ log n))-competitive.