SEARCHING A POLYGONAL REGION FROM THE BOUNDARY

Polygon search is the problem of finding mobile intruders who move unpredictably in a polygonal region, using one or more mobile searchers. Different levels of vision are assumed to model the ability of the searchers. In this paper we mainly consider a special case of this problem, termed boundary search, in which a single searcher has to find the intruders from the boundary of the region. Our main result is that a single searcher whose vision is limited to the ray of a single flashlight is just as capable as a single 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. The proof of the equivalence uses another new result, termed Monotonic Extension Theorem, together with a two-dimensional diagram called the planar boundary visibility map that represents the status of the search as a function of time. We partially settle a long-standing conjecture on the equivalence of the abilities of two types of searchers, one having two flashlights and the other having full 360° vision, for the general (non-boundary) polygon search problem.

SEARCHING FOR A MOBILE INTRUDER IN A CORRIDOR —THE OPEN EDGE VARIANT OF THE POLYGON SEARCH PROBLEM

The polygon search problem is the problem of searching for mobile intruders in a simple polygon by a single mobile searcher having various degrees of visibility. This paper considers the “open edge” variant of the problem in which the given polygon P must be searched without allowing undetected intruders to reach a given edge u, under an additional assumption that any number of intruders can leave and enter P through another edge v at any time. One may view P as representing a corridor with two open exits u and v, and the task of the searcher is to force all the intruders out of P through v (but not u). We present a simple necessary condition for a polygon to be searchable in this manner by the searcher having a light bulb, and then show that the same condition is sufficient for the polygon to be searchable by the searcher having two flashlights. The time complexity of generating a search schedule is also discussed.