Tree patrolling conjecture for the E-patrolling strategy

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Let QQ be a tree network, let α>0\alpha>0 be the attack duration, let EE denote the set used to define the EE-patrolling strategy, let μ\mu denote the measure of QQ, and let v∗v^* be the value of the continuous patrolling game on QQ. Tree patrolling conjecture. For any α\alpha, the EE-patrolling strategy is optimal and

v∗=αμ+λ(E).v^* = \frac{\alpha}{\mu+\lambda(E)}.

The EE-patrolling strategy was previously known to be optimal for trees satisfying the Leaf Condition. The paper's abstract states that it proves this conjecture, so the conjecture is resolved by the source.

References

Primary source

Thuy Bui and Thomas Lidbetter, “Optimal Patrolling Strategies for Trees and Complete Networks”, arXiv:2210.15045 (2023).

Additional references

2 papers in this index state this conjecture (2020–2022). The statement above is taken from the most recent of them; the others are arXiv:2008.07369.

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