Competitive algorithms for the weighted server problem

@article{Fiat1993CompetitiveAF,
  title={Competitive algorithms for the weighted server problem},
  author={Amos Fiat and Moty Ricklin},
  journal={[1993] The 2nd Israel Symposium on Theory and Computing Systems},
  year={1993},
  pages={294-303}
}
  • A. Fiat, Moty Ricklin
  • Published 7 June 1993
  • Computer Science, Mathematics
  • [1993] The 2nd Israel Symposium on Theory and Computing Systems
The authors deal with a generalization of the k-server problem, in which the servers are unequal. In the weighted server model each of the servers is assigned a positive weight. The cost associated with moving a server equals the product of the distance traversed and the server weight. A weighted k-server algorithm is called competitive if the competitive ratio depends only upon the number of servers. (i.e., the competitive ratio is independent of the weights associated with the servers and the… 

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References

SHOWING 1-10 OF 20 REFERENCES
The K-Server Problem with Distinguishable Servers
TLDR
A survey of existing results in the field of on-line k-server algorithms and some new findings is given and a variation of the k- server problem in which the servers have different costs is discussed.
New results on server problems
TLDR
A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.
Competitive k-Server Algorithms
TLDR
Deterministic competitive k-server algorithms are given for all k and all metric spaces and the competitive ratio can be proved is exponential in the number of servers, settling the k- server conjecture.
The harmonic online K-server algorithm is competitive
TLDR
The Harmonic algorithm for the online K-server problem is shown to be competitive against an adaptive online adversary for K 22 and the best competitive ratios that have been published so far for online algorithms over a general metric space when K >2 are shown.
Competitive Paging Algorithms
Competitive algorithms for on-line problems
TLDR
This paper presents several general results concerning competitive algorithms, as well as results on specific on-line problems.
Competitive algorithms for layered graph traversal
TLDR
For traversing layered graphs consisting of w disjoint paths tied together at a common source, the authors give a randomized online algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor.
Shortest Paths Without a Map
Competitive snoopy caching
TLDR
This work presents new on-line algorithms to be used by the caches of snoopy cache multiprocessor systems to decide which blocks to retain and which to drop in order to minimize communication over the bus.
An optimal on-line algorithm for metrical task system
TLDR
A general model for the processing of sequences of tasks is introduced, and a general on-line decision algorithm is developed, which is shown that, for an important class of special cases, this algorithm is optimal among all on- line algorithms.
...
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