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|
|Title of host publication||Algorithms, ESA 1998 - 6th Annual European Symposium, Proceedings|
|Number of pages||12|
|ISBN (Print)||3540648488, 9783540648482|
|State||Published - 1998|
|Event||6th Annual European Symposium on Algorithms, ESA 1998 - Venice, Italy|
Duration: 24 Aug 1998 → 26 Aug 1998
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||6th Annual European Symposium on Algorithms, ESA 1998|
|Period||24/08/98 → 26/08/98|
Bibliographical noteFunding 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.