Is competitive online paging an artifact?

Abstract

In any real system a newly computed datum begins its existence in the processor rather than in external memory, and thus does not inevitably incur a cold miss. This was captured by early I/O models, but not by the Sleator-Tarjan one that has come to underpin competitive analysis of paging. If one corrects the Sleator-Tarjan model by charging no cost for the first access to newly computed data, optimal offline algorithms such as LFD remain optimal, but no online paging algorithm can be competitive, even if randomized, even with arbitrary resource augmentation, even against request sequences that are not tailored against it but are instead representative of widely used computational techniques. The proofs are simple, and appear robust against any reasonable assumption/model adjustment, including virtually all tools developed to make competitive analysis less pessimistic. In other words, while competitive analysis does predict the good performance exhibited in practice by online paging algorithms such as LRU, these predictions seem just a fortuitous artifact of an incorrect assumption that has crept into the underlying model several decades ago. And there are implications beyond paging, too: for example, the same issue undermines the Ideal Cache model on which the popular Cache-Oblivious and Cache-Adaptive algorithmic frameworks are based.