A new upper bound on the work function algorithm for the k-server problem

The k -server problem was introduced by Manasse et al. (in: Proceedings of the 20th annual ACM symposium on theory of computing, Chicago, Illinois, USA, pp 322–333, 1988), and is one of the most famous and well-studied online problems. Koutsoupias and Papadimitriou (J ACM 42(5):971–983, 1995) showed...

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Bibliographic Details
Published in:Journal of combinatorial optimization Vol. 39; no. 2; pp. 509 - 518
Main Authors: Zhang, Wenming, Cheng, Yongxi
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2020
Springer Nature B.V
Subjects:
Algorithms
Combinatorics
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Metric space
Operations Research/Decision Theory
Optimization
Theory of Computation
Upper bounds
Work functions
Work function
server problem
Competitive analysis
On-line algorithms
ISSN:1382-6905, 1573-2886
Online Access:Get full text
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Summary:The k -server problem was introduced by Manasse et al. (in: Proceedings of the 20th annual ACM symposium on theory of computing, Chicago, Illinois, USA, pp 322–333, 1988), and is one of the most famous and well-studied online problems. Koutsoupias and Papadimitriou (J ACM 42(5):971–983, 1995) showed that the work function algorithm ( WFA ) has a competitive ratio of at most 2 k - 1 for the k -server problem. In this paper, by proposing a potential function that is different from the one in Koutsoupias and Papadimitriou (1995), we show that the WFA has a competitive ratio of at most n - 1 , where n is the number of points in the metric space. When n < 2 k , this ratio is less than 2 k - 1 .
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ISSN:1382-6905
1573-2886
DOI:10.1007/s10878-019-00493-z