A randomized algorithm for two servers in cross polytope spaces

Authors:
Wolfgang Bein;Kazuo Iwama;Jun Kawahara;Lawrence L. Larmore;James A. Oravec
Affiliations:
School of Computer Science, Center for the Advanced Study of Algorithms, University of Nevada, Las Vegas, NV 89154, United States;School of Informatics, Kyoto University, Kyoto 606-8501, Japan;School of Informatics, Kyoto University, Kyoto 606-8501, Japan;School of Computer Science, Center for the Advanced Study of Algorithms, University of Nevada, Las Vegas, NV 89154, United States;School of Computer Science, University of Nevada, Las Vegas, NV 89154, United States
Venue:
Theoretical Computer Science
Year:
2011

Citing 13
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Abstract

It has been a long-standing open problem to determine the exact randomized competitiveness of the 2-server problem, that is, the minimum competitiveness of any randomized online algorithm for the 2-server problem. For deterministic algorithms the best competitive ratio that can be obtained is 2 and no randomized algorithm is known that improves this ratio for general spaces. For the line, Bartal et al. (1998) [2] give a 15578 competitive algorithm, but their algorithm is specific to the geometry of the line. We consider here the 2-server problem over Cross Polytope Spaces M"2"4. We obtain an algorithm with competitive ratio of 1912, and show that this ratio is best possible. This algorithm gives the second non-trivial example of metric spaces with better than2-competitive ratio. The algorithm uses a design technique called the knowledge state technique - a method not specific to M"2"4.