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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 \Gamma 1 for any metrical task system with n states. We present a randomized algorithm which achieves a competitive ratio of e=(e\Gamma1)n\Gamma1=(e\Gamma1) 1:5820n\Gamma0:5820 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 \Gamma, |
