In this paper we consider the bicriteria version of the well-known k-server problem in which\udthe cost incurred by an algorithm is evaluated simultaneously with respect to two different edge\udweightings.\udWe show that it is possible to achieve the same competitive ratios of the previously known online\udalgorithms with a dramatic improvement of the running time, i.e., from exponential to polynomial.\udSuch results are obtained by exploiting new polynomial time algorithms able to find offline solutions\udwhose costs differ from the optimal ones only of additive terms independent from the sequence\udof requests.
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