Buying a Constant Competitive Ratio for Paging

Abstract

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.

Supported by the Hungarian National Foundation for Scientific Research, Grant T030074

Supported by the START program Y43-MAT of the Austrian Ministry of Science.

Supported by the Research Competitiveness Subprogram of the Louisiana Board of Regents.