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}
}
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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