Optimal prediction for prefetching in the worst case
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
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Response time delays caused by I/O is a major problem in many systems and database applications. Prefetching and cache-replacement methods are attracting renewed attention because of their success in avoiding costly I/Os. Prefetching can be looked upon as a type of online sequential prediction, where the predictions must be accurate as well as made in a computationally efficient way. Unlike other online problems, prefetching cannot admit a competitive analysis, since the optimal offline prefetcher incurs no cost when it knows the future page requests. Previous analytical work on prefetching [ViK] consisted of modeling the user as a probabilistic Markov source. In this paper, we look at the much stronger form of worst-case analysis and derive a randomized algorithm that we prove analytically {\em converges almost surely to the optimal fault rate in the worst case for every sequence of page requests\/} with respect to the important class of finite state prefetchers. In particular, we make no assumption about how the sequence of page requests is generated. This analysis model can be looked upon as a generalization of the competitive framework, in that it compares an online algorithm in a worst-case manner over all sequences against a powerful yet non-clairvoyant opponent. We simultaneously achieve the computational goal of implementing our prefetcher in optimal constant expected time per prefetched page, using the optimal dynamic discrete random variate generator of [MVN].