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arXiv · 2210.15045

Optimal Patrolling Strategies for Trees and Complete Networks

Thuy Bui·Thomas Lidbetter
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Abstract

We present solutions to a continuous patrolling game played on network. In this zero-sum game, an Attacker chooses a time and place to attack a network for a fixed amount of time. A Patroller patrols the network with the aim of intercepting the attack with maximum probability. Our main result is the proof of a recent conjecture on the optimal patrolling strategy for trees. The conjecture asserts that a particular patrolling strategy called the E-patrolling strategy is optimal for all tree networks. The conjecture was previously known to be true in a limited class of special cases. The E-patrolling strategy has the advantage of being straightforward to calculate and implement. We prove the conjecture by presenting $\varepsilon$-optimal strategies for the Attacker which provide upper bounds for the value of the game that come arbitrarily close to the lower bound provided by the E-patrolling strategy. We also solve the patrolling game in some cases for complete networks.

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Thuy Bui, Thomas Lidbetter. 2023-01-30. Optimal Patrolling Strategies for Trees and Complete Networks. https://arxiv.org/abs/2210.15045

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