The Weighted 2-Server Problem

We consider a generalization of the 2-server problem in which servers have diierent costs. We prove that, in uniform spaces, a version of the Work Function Algorithm is 5-competitive, and that no better ratio is possible. We also give a 5-competitive randomized, memoryless algorithm for uniform spaces, and a matching lower bound. For arbitrary metric spaces, in contrast with the non-weighted case, we prove that there is no memoryless randomized algorithm with nite competitive ratio. We also propose a version of the problem in which a request speciies two points to be covered by the servers, and the algorithm must decide which server to move to which point. For this version, we show a 9-competitive algorithm and we prove that no better ratio is possible.