Abstract
In the k-server problem we wish to minimize, in an online fashion, the movement cost of k servers in response to a sequence of requests. For 2 servers, it is known that the optimal deterministic algorithm has competitive ratio 2, and it has been a long-standing open problem whether it is possible to improve this ratio using randomization. We give a positive answer to this problem when the underlying metric space is a real line, by providing a randomized online algorithm for this case with competitive ratio at most 155 78 ≈ 1:987. This is the rst algorithm for 2 servers with competitive ratio smaller than 2 in a non-uniform metricspace with more than three points. We consider a more general problem called the (k; l)-server problem, in which a request is served using l out of k available servers. We show that the randomized 2-server problem can be reduced to the deterministic (2l; l)-server problem. We prove a lower bound of 2 on the competitive ratio of the (4; 2)-server problem. This implies that one unbiase random bit is not sufficient to improve the ratio of 2 for the 2-server problem. Then we give a 155 78 competitive algorithm for the (6; 3)-server problem on the real line. Our algorithm is simple and memoryless. The solution has been obtained using linear programming techniques that may have applications for other online problems.
| Original language | American English |
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| Title of host publication | Algorithms, ESA 1998 - 6th Annual European Symposium, Proceedings |
| Publisher | Springer Verlag |
| Pages | 247-258 |
| Number of pages | 12 |
| ISBN (Print) | 3540648488, 9783540648482 |
| DOIs | |
| State | Published - 1998 |
| Externally published | Yes |
| Event | 6th Annual European Symposium on Algorithms, ESA 1998 - Venice, Italy Duration: 24 Aug 1998 → 26 Aug 1998 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 1461 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Conference
| Conference | 6th Annual European Symposium on Algorithms, ESA 1998 |
|---|---|
| Country/Territory | Italy |
| City | Venice |
| Period | 24/08/98 → 26/08/98 |
Bibliographical note
Funding Information:1This research was partially conducted while the author was at International Computer Science Institute, University of California, Berkeley. 2Research supported by NSF Grant CCR-9503498. This research was partially conducted when the author was visiting International Computer Science Institute, University of California, Berkeley. 3Research supported by NSF Grant CCR-9503441.