Datensatz

Zusammenfassung

The {\em 1-searcher} is a mobile guard whose visibility is limited to a ray emanating from his position, where the direction of the ray can be changed continuously with bounded angular rotation speed. Given a polygonal region $\poly$ with a specified boundary point $d$, is it possible for a 1-searcher to eventually {\em see} a mobile intruder that is arbitrarily faster than the searcher within $\poly$, before the intruder reaches $d$? We decide this question in $O(n\log n)$-time for an $n$-sided polygon. Our main result is a simple characterization of the class of polygons (with a boundary point $d$) that admits such a search strategy. We also present a simple $O(n^2)$-time algorithm for constructing a search schedule, if one exists. Finally, we compare the search capability of a 1-searcher with that of two guards.