The first general decomposition theorem for the k-server problem is presented. Whereas all previous theorems are for the case of a finite metric with k + 1 points, the theorem given here allows an arbitrary number of points in the underlying metric space. This theorem implies O(polylog(k))-competitive randomized algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces, and takes a first step towards a general O(polylog(k))- competitive algorithm. The only other cases for which polylogarithmic competitive randomized algorithms are known are the uniform metric space, and the weighted cache metric space with two weights.
CITATION STYLE
Seiden, S. S. (2001). A general decomposition theorem for the k-server problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2161, pp. 86–97). Springer Verlag. https://doi.org/10.1007/3-540-44676-1_7
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