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Initial point search on weighted trees

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  • Kensaku Kikuta
  • William H. Ruckle

Abstract

An initial point search game on a weighted graph involves a searcher who wants to minimize search and travel costs seeking a hider who wants to maximize these costs. The searcher starts from a specified vertex 0 and searches each vertex in some order. The hider chooses a nonzero vertex and remains there. We solve the game in which the graph is a simple tree, and use this solution to solve a search game on a tree in which each branch is itself a weighted graph with a certain property, and the searcher is obliged to search the entire branch before departing. © 1994 John Wiley & Sons, Inc.

Suggested Citation

  • Kensaku Kikuta & William H. Ruckle, 1994. "Initial point search on weighted trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(6), pages 821-831, October.
    • Handle: RePEc:wly:navres:v:41:y:1994:i:6:p:821-831
    DOI: 10.1002/1520-6750(199410)41:63.0.CO;2-Y
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    References listed on IDEAS

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    1. Udo Lössner & Ingo Wegener, 1982. "Discrete Sequential Search with Positive Switch Cost," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 426-440, August.
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    Cited by:

    1. 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.
    2. Vic Baston & Kensaku Kikuta, 2015. "Search games on a network with travelling and search costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 347-365, May.
    3. Steve Alpern & Thomas Lidbetter, 2015. "Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object," Operations Research, INFORMS, vol. 63(1), pages 122-133, February.
    4. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    5. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    6. Steve Alpern, 2011. "A New Approach to Gal’s Theory of Search Games on Weakly Eulerian Networks," Dynamic Games and Applications, Springer, vol. 1(2), pages 209-219, June.
    7. Andrey Garnaev & Kensaku Kikuta, 2014. "Screening and hiding versus search," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 255-265, December.
    8. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.

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