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

Steve Alpern (), Robbert Fokkink () and Christos Pelekis ()
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Steve Alpern: London School of Economics
Robbert Fokkink: TU Delft
Christos Pelekis: TU Delft

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 3, No 7, 650-661

Abstract: 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.

Keywords: Resource allocation; Tail probability; Farey numbers (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-011-9977-1

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