A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources

A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources

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Article ID: iaor20123939
Volume: 153
Issue: 3
Start Page Number: 650
End Page Number: 661
Publication Date: Jun 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: allocation: resources
Abstract:

Suppose that a hider possesses a continuously divisible resource that he may distribute around a circle. The resources on a random arc in the circle are lost. The hider has a priori information on the length of the arc and he wants to maximize the probability that the retrieved portion exceeds a critical quantity, which is enough to survive on. We show that there exists an optimal resource distribution, which uses a finite number of point caches of equal size, establishing a conjecture of Kikuta and Ruckle. Our result is related to a conjecture of Samuels’ on‐tail probabilities.

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