Buying a Constant Competitive Ratio for Paging

We consider a variant of the online paging problem where the online algorithm may buy additional cache slots at a certain cost. The overall cost incurred equals the total cost for the cache plus the number of page faults. This problem and our results are a generalization of both, the classical paging problem and the ski rental problem. We derive the following three tight results: (1) For the case where the cache cost depends linearly on the cache size, we give a λ-competitive online algorithm where λ ≈ 3.14619 is a solution of λ = 2 + ln λ. This competitive ratio λ is best possible. (2) For the case where the cache cost grows like a polynomial of degree d in the cache size, we give an online algorithm whose competitive ratio behaves like d/lnd + o(d/lnd). No online algorithm can reach a competitive ratio better than d/lnd. (3) We exactly characterize the class of cache cost functions for which there exist online algorithms with finite competitive ratios