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

Author

Listed:
  • Steve Alpern

    (London School of Economics)

  • Robbert Fokkink

    (TU Delft)

  • Christos Pelekis

    (TU Delft)

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.

Suggested Citation

  • Steve Alpern & Robbert Fokkink & Christos Pelekis, 2012. "A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 650-661, June.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:3:d:10.1007_s10957-011-9977-1
    DOI: 10.1007/s10957-011-9977-1
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    References listed on IDEAS

    as
    1. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    2. N. Zoroa & M. J. Fernández-Sáez & P. Zoroa, 1999. "A Game Related to the Number of Hides Game," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 457-473, November.
    3. K. Kikuta & W. H. Ruckle, 1997. "Accumulation Games, Part 1: Noisy Search," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 395-408, August.
    4. W. H. Ruckle & K. Kikuta, 2000. "Continuous Accumulation Games in Continuous Regions," Journal of Optimization Theory and Applications, Springer, vol. 106(3), pages 581-601, September.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Endre Csóka & Thomas Lidbetter, 2016. "The solution to an open problem for a caching game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 23-31, February.

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