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Some Mathematical Facts About Optimal Cache Replacement
Pierre Michaud
Source abstract
This article exposes and proves some mathematical facts about optimal cache replacement that were previously unknown or not proved rigorously. An explicit formula is obtained, giving OPT hits and misses as a function of past references. Several mathematical facts are derived from this formula, including a proof that OPT miss curves are always convex, and a new algorithm called OPT tokens , for reasoning about optimal replacement.
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