2020/08/13 by Steve Alpern, Alpern, Steve, Bui, Thuy +4
Computer Science · Engineering · #Advanced Graph Theory Research #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Guidance and Control Systems #Infrastructure Resilience and Vulnerability Analysis #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2008.07369
openalex publication_date 2020/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a patrolling game played on a network Q, considered as a metric space. The Attacker chooses a point of Q (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed path on Q and intercepts the attack (and wins) if she visits the attacked point during the attack time interval. This zero-sum game models the problem of protecting roads or pipelines from an adversarial attack. The payoff to the maximizing Patroller is the probability that the attack is intercepted. Our results include the following: (i) a solution to the game for any network Q, as long as the time required to carry out the attack is sufficiently short, (ii) a solution to the game for all tree networks that satisfy a certain condition on their extremities, and (iii) a solution to the game for any attack duration for stars with one long arc and the remaining arcs equal in length. We present a conjecture on the solution of the game for arbitrary trees and establish it in certain cases.