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A search problem on a bipartite network

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  • Baston, Vic
  • Kikuta, Kensaku

Abstract

A searcher starting from a given node in a connected network can move along the edges and, when at a node can (but does not have to) search that node; moving on an edge involves a travelling cost and searching a node involves a search cost. The searcher wants to find an immobile object located at one of the nodes other than the searcher’s starting node and, for each node, knows the probability that it is located there. The object is found if and only if the searcher is at the node where the object is hidden and searches there. How can the searcher find the object at minimum cost? We analyze this problem when the network is complete bipartite, where the set of nodes is partitioned to two.

Suggested Citation

  • Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:1:p:227-237
    DOI: 10.1016/j.ejor.2019.02.029
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    References listed on IDEAS

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    1. Cheng-Shang Chang & Wanjiun Liao & Ching-Min Lien, 2015. "On the Multichannel Rendezvous Problem: Fundamental Limits, Optimal Hopping Sequences, and Bounded Time-to-Rendezvous," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 1-23, February.
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    6. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    7. 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.
    8. Alpern, Steven & Lidbetter, Thomas, 2015. "Optimal trade-off between speed and acuity when searching for a small object," LSE Research Online Documents on Economics 61504, London School of Economics and Political Science, LSE Library.
    9. Steven M. Shechter & Farhad Ghassemi & Yasin Gocgun & Martin L. Puterman, 2015. "Technical Note—Trading Off Quick versus Slow Actions in Optimal Search," Operations Research, INFORMS, vol. 63(2), pages 353-362, April.
    10. 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.
    11. 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.
    12. Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.
    13. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.
    14. Alpern, Steve & Lidbetter, Thomas & Papadaki, Katerina, 2019. "Optimizing periodic patrols against short attacks on the line and other networks," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1065-1073.
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    Cited by:

    1. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    2. Alpern, Steve & Lidbetter, Thomas, 2020. "Search and Delivery Man Problems: When are depth-first paths optimal?," European Journal of Operational Research, Elsevier, vol. 285(3), pages 965-976.

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