The zookeeper route problem

Abstract The { S , T }-route problem inside a polygon P with a set S of of sights (edge segments) and a set T of point threats is to find a route such that each point in S is visible from at least one point in the route and the route is not visible to any of the points in T [7]. The requirement that exposure to the threats is not allowed at all is usually too severe and solutions do not exist in many cases, especially those arising in typical applications where the sights and threats overlap (e.g., defense applications). An alternative way to model the risk posed by the threats is to enclose each threat location in a polygonal envelope (within which the risk is unacceptably high) resulting in the zookeeper route problem. We are given a polygon P and a collection P ′ of convex polygons inside P and we want to find a shortest route that visits (without entering) the polygons in P ′ (e.g., design a route for a zookeeper that wants to feed animals in enclosures). We show that the general zookeeper route problem is NP-hard, we present necessary and sufficient conditions for the existence of a zookeeper route and give an O( n 2 ) algorithm for the case where P is a simple polygon and the polygons in P ′ are attached to the boundary of P .