## Abstract

In this paper we deal with a generalization of the k-server problem (Manasse 1988), 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 number of points in the metric space). For the uniform metric space, we give super exponential 2^{2O(k)}-competitive algorithms for any set of weights. If the servers have one of two possible weights, we give deterministic exponential (k^{O(k)}) competitive algorithms and randomized polynomial Õ(k^{3}) competitive algorithms. We use the MIN operator for both algorithms. This is the first true application of the randomized MIN operator (Fiat 1991). We show that for any metric space there exists some set of weights such that the deterministic competitive ratio must be exponential (k^{Ω(k)}). If the servers are limited to be one of two possible weights then there exist two such weights such that the competitive ratio has a lower bound of 2^{Ω(k)}. With the randomized upper bound above, this shows a clear separation between deterministic and randomized algorithms for the problem of two weights. One can model the problem of storage management for RAM and E^{2}PROM type memories as a weighted server problem with two weights on the uniform metric space.

Original language | English |
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Pages (from-to) | 85-99 |

Number of pages | 15 |

Journal | Theoretical Computer Science |

Volume | 130 |

Issue number | 1 |

DOIs | |

State | Published - 1 Aug 1994 |