Visibility Problems for Manhattan Towers

Abstract

SUMMARY A Manhattan tower is a monotone orthogonal polyhedron lying in the halfspace z ≥ 0 such that (i) its intersection with the xy-plane is a simply connected orthogonal polygon, and (ii) the horizontal cross section at higher levels is nested in that for lower levels. Here, a monotone polyhedron meets each vertical line in a single segment or not at all. We study the computational complexity of finding the minimum number of guards which can observe the side and upper surfaces of a Manhattan tower. It is shown that the vertex-guarding, edge-guarding, and face-guarding problems for Manhattan towers are NP-hard.