Floodlight illumination of infinite wedges

The floodlight illumination problem asks whether there exists a one-to-one placement of n floodlights illuminating infinite wedges of angles α1,…,αn at n sites p1,…,pn in a plane such that a given infinite wedge W of angle θ located at point q is completely illuminated by the floodlights. We prove that this problem is NP-hard, closing an open problem posed by Demaine and O'Rourke (CCCG 2001). In fact, we show that the problem is NP-complete even when αi=α for all 1⩽i⩽n (the uniform case) and (the tight case).