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 1, . . . , n at n sites p1, . . . , pn in a plane such that a given infinite wedge W of angle located at point q is completely illuminated by the floodlights. We prove that this problem is NPhard, closing an open problem posed by Demaine and O'Rourke (CCCG 2001). In fact, we show that the problem is NP-complete even when i = for all 1 i n (the uniform case) and = n i=1 i (the tight case). Key words: illumination, art gallery problem, floodlights, NP-completeness

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Matthew Cary, Atri Rudra, Ashish Sabharwal, Erik Vee
• Keywords: Applied Computing, COMGEO 2010, Floodlight Illumination Problem, Floodlights Illuminating Infinite, One-to-one Placement