COMPETITIVE ALGORITHMS FOR THE WEIGHTED SERVER PROBLEM

In this paper we deal with a generalization of the k-server problem (M anasse et al. 1988), in which the servers are unequal. In the weighted server model each of the servers is assigned a positive weight. The c ost associated with moving a server equals the product of the distance traversed and the server weight. A weighted k-server algorithm is cal led 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 spa ce). 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)) c ompetitive algorithms and randomized polynomial O(k3) competitive algo rithms. We use the MIN operator for both algorithms. This is the first true application of the randomized MIN operator (Fiat et al. 1991). W e show that for any metric space there exists some set of weights such that the deterministic competitive ratio must be exponential (k(OMEGA (k))). If the servers are limited to be one of two possible weights th en there exist two such weights such that the competitive ratio has a lower bound of 2OMEGA(k). With the randomized upper bound above, this shows a clear separation between deterministic and randomized algorith ms for the problem of two weights. One can model the problem of storag e management for RAM and E2PROM type memories as a weighted server pro blem with two weights on the uniform metric space.