Is competitive online paging an artifact?

2026-06-22

AI Summary

This work revisits the classical Sleator–Tarjan paging model, which assumes that every first access to newly generated data incurs a compulsory cold page fault. Recognizing that in real systems such data typically resides initially in the processor and thus does not trigger a page fault upon first access, the authors propose a refined model that waives this initial fault cost. Under this more realistic setting, they re-examine online paging algorithms using competitive analysis, offline optimal algorithms (e.g., LFD), and cache-model reformulation. Their analysis demonstrates that no online paging algorithm—whether randomized or augmented with additional resources—can achieve competitiveness in the revised model. This finding suggests that the apparent predictive success of classical competitive analysis stems from an artifact of the original model’s unrealistic assumptions, thereby challenging the theoretical foundations of frameworks such as Cache-Oblivious algorithms.

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.

Problem

• competitive analysis
• online paging
• cold miss
• Ideal Cache model
• resource augmentation

Innovation

• competitive analysis
• online paging
• cold miss
• Ideal Cache model
• resource augmentation