Polygon search is the problem of nding unpredictable mobile intruders in a polygonal region using one or more mobile searchers with various levels of vision, where both the searcher and intruders are allowed to move freely within the region. In this paper we consider a variant of this problem, termed boundary search, in which a single searcher has to nd the intruders from the boundary of the region. Our main result is that the searcher having one ashlight whose vision is limited to a single ray is just as capable as the searcher having a light bulb that gives 360 vision, that is, any polygon that can be searched by the latter from the boundary can also be searched by the former from the boundary. To our knowledge, the equivalence of these searchers, one having a very limited vision and another having the maximum vision, has never been established for any interesting subclass of the polygon search problem. The proof of the equivalence uses another new result, termed Monotonic Extension Theorem, together with a simple topological argument on a 2-dimensional map called p-map that represents the searcher's state during search. A similar topological argument is used also to partially settle a long-standing conjecture on
Suzuki, et al. introduce another variant of watchman problem termed boundary search where guards are allowed to move only along the boundary of the polygon REF .
Searching a Polygonal Region from the Boundary
International Journal of Computational Geometry and Applications
Mathematics Computer Science