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Optimizing periodic patrols against short attacks on the line and other networks

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  • Alpern, Steve
  • Lidbetter, Thomas
  • Papadaki, Katerina

Abstract

On a given network, a Patroller and Attacker play the following win–lose game: The Patroller adopts a periodic walk on the network while the Attacker chooses a node and two consecutive periods (to attack there). The Patroller wins if he successfully intercepts the attack, that is, if he occupies the attacked node in one of the two periods of the attack. We solve this game in mixed strategies for line graphs, the first class of graphs to be solved for the periodic patrolling game. We also solve the game for arbitrary graphs when the period is even.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:3:p:1065-1073
    DOI: 10.1016/j.ejor.2018.08.050
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    References listed on IDEAS

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    Cited by:

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    2. Darlington, Matthew & Glazebrook, Kevin D. & Leslie, David S. & Shone, Rob & Szechtman, Roberto, 2023. "A stochastic game framework for patrolling a border," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1146-1158.
    3. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    4. Caraballo, Luis E. & Díaz-Báñez, José M. & Fabila-Monroy, Ruy & Hidalgo-Toscano, Carlos, 2022. "Stochastic strategies for patrolling a terrain with a synchronized multi-robot system," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1099-1116.

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