The k-Server Problem and Fractional Analysis
نویسنده
چکیده
The k-server problem, introduced by Manasse, McGeoch and Sleator [29, 30] is a fundamental online problem where k mobile servers are required to serve a sequence of requests on a metric space, with the minimum possible movement cost. Despite the conjectured existence of a Θ(log k)-competitive randomized algorithm, the best known upper bound for arbitrary metric spaces is 2k − 1. Even for one of the simplest cases, the Euclidean metric on the interval [0, 1], nothing better than k is known. In this work, we first give a survey of the k-server problem, and then introduce a fractional version in order to provide a different perspective on randomized algorithms for this problem. In this version, servers can move fractionally instead of moving as a unit, and in the process, servicing a request requires providing one unit server at the point of request. We show that on the line and circle, the randomized version of the problem is equivalent to the fractional version. We also classify the cases for which these versions are not equivalent by presenting a fractional algorithm which cannot be simulated by any randomized algorithm. Furthermore, we investigate and analyze some algorithms on the line using the fractional setting.
منابع مشابه
Online Algorithms and the k - server problem — June 14 , 2011
Finally, we wrap-up this lecture with our new result which achieves a competitive factor of Õ(log k log n) for the k-server problem on n nodes1. This is joint work with Nikhil Bansal, Niv Buchbinder, and Aleksander Madry. Our basic approach is based on the framework of [CMP08]. The key idea in our work is that instead of using the allocation problem (as suggested by [CMP08]), we use the fractio...
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