Abstract
Priority patrolling is a particular case of the patrolling problem where few locations have higher priority than others, and a patrolling agent must visit these locations more frequently. This letter provides three results on the priority patrol problem. First, we study the minimum time interval between two visits to a priority node, which we term the Time Period. We show that there doesn’t exist a feasible patrol strategy for a time period less than a particular threshold. Next, we prove that a patrol strategy with recurring circuits always exists for this problem. Lastly, we provide an algorithm to obtain a patrol strategy with constant factor approximation to the time period. We validated the results on grid graphs of various sizes, connectivity, and the number and placement of priority nodes in the graph.
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