A general decomposition theorem for the k-server problem
Information and Computation
A General Decomposition Theorem for the k-Server Problem
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On metric ramsey-type phenomena
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomized k-server algorithms for growth-rate bounded graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
A tight threshold for metric Ramsey phenomena
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Ramsey-type theorems for metric spaces with applications to online problems
Journal of Computer and System Sciences - Special issue on FOCS 2001
A regularization approach to metrical task systems
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
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A lower bound of $\Omega(\sqrt{\log k / \log \log k})$ 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 $\Omega(\log \log k)$ for arbitrary metric spaces [H. J. Karloff, Y. Rabani, and Y. Ravid, SIAM J. Comput., 23 (1994), pp. 293--312] and more closely approaches the conjectured lower bound of $\Omega(\log k)$. For the server problem on k+1 equally spaced points on a line, which corresponds to a natural motion-planning problem, a lower bound of $\Omega(\frac{\log k}{\log \log k})$ is obtained.The results are deduced from a general decomposition theorem for a simpler version of both the k-server and the metrical task system problems, called the "pursuit-evasion game." It is shown that if a metric space $\cal M$ can be decomposed into two spaces $\cal M_L$ and $\cal M_R$ such that the distance between them is sufficiently large compared to their diameter, then the competitive ratio for this game on $\cal M$ can be expressed nearly exactly in terms of the ratios on each of the two subspaces. This yields a divide-and-conquer approach to bounding the competitive ratio of a space.