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 θ=∑i=1n ^αi (the tight case).