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# A Decomposition Theorem for Task Systems and Bounds for Randomized Server Problems

@article{Blum2000ADT, title={A Decomposition Theorem for Task Systems and Bounds for Randomized Server Problems}, author={Avrim Blum and Howard J. Karloff and Yuval Rabani and Michael E. Saks}, journal={SIAM J. Comput.}, year={2000}, volume={30}, pages={1624-1661} }

- Published 2000 in SIAM J. Comput.
DOI:10.1137/S0097539799351882

A lower bound of Ω( √ log k/ log log k) is proved for the competitive ratio of randomized algorithms for the k-server problem against an oblivious adversary. The bound holds for arbitrary metric spaces (having at least k+1 points) and provides a new lower bound for the metrical task system problem as well. This improves the previous best lower bound of Ω(log log k) for arbitrary metric spaces [H.J. Karloff, Y. Rabani, and Y. Ravid, SIAM J. Comput., 23 (1994), pp. 293–312] and more closely… CONTINUE READING

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