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A proof of the Kikuta–Ruckle Conjecture on cyclic caching of resources

By Steven Alpern, Robbert Fokkink and Christos Pelekis

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

Topics: QA Mathematics
Publisher: Springer
Year: 2012
DOI identifier: 10.1007/s10957-011-9977-1
OAI identifier: oai:eprints.lse.ac.uk:41144
Provided by: LSE Research Online
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