A Graph Patrol Problem with Random Attack Times
Lin, Kyle Y.
Atkinson, Michael P.
Chung, Timothy H.
Glazebrook, Kevin D.
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This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and strategic attackers. A random attacker chooses which node to attack according to a probability distribution known to the patroller. A strategic attacker plays a two-person zero-sum game with the patroller. For each case, we give an exact linear program to compute the optimal solution. Because the linear programs quickly become computationally intractable as the problem size grows, we develop index-based heuristics. In the random-attacker case, our heuristic is optimal when there are two nodes, and in a suitably chosen asymptotic regime. In the strategic-attacker case, our heuristic is optimal when there are two nodes if the attack times are deterministic taking integer values. In our numerical experiments, our heuristic typically achieves within 1% of optimality with computation time orders of magnitude less than what is required to compute the optimal policy.
The article of record as published may be found at http://dx.doi.org/10.1287/opre.1120.1149
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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Lin, Kyle Y.; Atkinson, Michael; Glazebrook, Kevin D. (2013-08-12);This paper considers a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. Attackers arrive at each node according to independent Poisson processes and take a random ...
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