Abstract
We prove that there exists a randomized online algorithm for the 2-server 3-point problem whose expected competitive ratio is at most 1.5897. This is the first nontrivial upper bound for randomized k-server algorithms in a general metric space whose competitive ratio is well below the corresponding deterministic lower bound (= 2 in the 2-server case).
Highlights
The k-server problem, introduced by Manasse, McGeoch and Sleator [1], is one of the most fundamental online problems
One would imagine that it might be quite straightforward to design randomized algorithms which perform significantly better than deterministic ones for the 2-server problem
Bein et al [13] gave an Hk -competitive randomized algorithm which requires only O(k) memory for k-paging. (Though the techniques in the current paper are inspired by this work, the knowledge state method is not used here.) Lund and Reingold showed that if specific three positions are given, an optimal randomized algorithm for the 2-server problem over those three points can be derived in principle by using linear programming [14]
Summary
Author to whom correspondence should be addressed. Research done while visiting Kyoto University as Kyoto University Visiting Professor. Received: 13 August 2008 / Accepted: September 2008 / Published: September 2008
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