A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources |
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Authors: | Steve Alpern Robbert Fokkink Christos Pelekis |
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Institution: | 1.Department of Applied Mathematics,London School of Economics,London,UK;2.Institute of Applied Mathematics,TU Delft,Delft,The Netherlands |
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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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