Technical Report CS0524

Title: Self-Organizing Lists and Independent References - A Statistical Synergy
Authors: M. Hofri and H. Shachnai
Abstract: Let R1...,Rn be a linear list of n elements. We assume the independent reference model, with a fixed but unknown access probability vector. The problem of dynamically reorganizing the list, on the basis of accrued references, with the objective of minimizing the expected access-cost is surveyed. The Counter Scheme (CS) is known to be asymptotically optimal for this purpose. This paper concentrates on the CS, with the aim of reducing its storage requirements. We start with a detailed exposition of its cost function. We then point out that it interacts with the access model to produce some remarkable synergistic effects. These make it possible to use very effective 'truncated versions' of the CS, which have very modest space requirements. The versions we consider are: (i) The 'Limited-Counters Scheme', which bounds each of the frequency counters to a maximal value c. (ll) The original CS, with a bound on the number of references during which the Scheme is active. The bound is chosen so as to achieve a desired level of performance compared with the optimal policy.
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