Partial Searchlight Scheduling is Strongly PSPACE-complete

The problem of searching a polygonal region for an unpredictably moving intruder by a set of stationary guards, each carrying an orientable laser, is known as the Searchlight Scheduling Problem. Determining the computational complexity of deciding if the polygon can be searched by a given set of guards is a long-standing open problem. Here we propose a generalization called the Partial Searchlight Scheduling Problem, in which only a given subregion of the environment has to be searched, as opposed to the entire area. We prove that the corresponding decision problem is strongly PSPACEcomplete, both in general and restricted to orthogonal polygons where the region to be searched is a rectangle. Our technique is to reduce from the “edge-to-edge” problem for nondeterministic constraint logic machines, after showing that the computational power of such machines does not change if we allow “asynchronous” edge reversals (as opposed to “sequential”).