We consider guarding a city of k vertical buildings, each having a rectangular base, by placing guards only at vertices. The aim is to use the smallest number of guards. The problem is a 2.5D variant of the traditional art gallery problem, and finds applications in urban security.
We give upper and lower bounds on the number of guards needed for a few versions of the problem. Specifically, we prove that $\lfloor\frac{2(k-1)}{3}\rfloor + 1$ guards are always sufficient and sometimes necessary to guard all roofs, and guards are always sufficient to guard the roofs, walls, and the ground, while each roof has at least one guard on it.