Target tracking on triangulation graphs

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. The guards are confined to move along the diagonals of a polygon, and are deployed according to the strategy proposed in [1] that provides an upper bound of ⌊ n/4 ⌋ mobile guards to cover a simply-connected polygonal environment. We introduce the concept of critical regions to generate event-triggered strategies for the guards. Based on these strategies, we present sufficient conditions for ⌊ n/4 ⌋ guards to track an unpredictable mobile intruder forever.