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 α 1 , … , α n at n sites p 1 , … , p n in a plane such that a given infinite wedge W of angle θ located at point q is completely illuminated by the floodlights...

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Bibliographic Details
Published inComputational geometry : theory and applications Vol. 43; no. 1; pp. 23 - 34
Main Authors Cary, Matthew, Rudra, Atri, Sabharwal, Ashish, Vee, Erik
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2010
Subjects
Art gallery problem
Floodlights
Illumination
NP-completeness
Illumination
Art gallery problem
Floodlights
NP-completeness
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Summary:The floodlight illumination problem asks whether there exists a one-to-one placement of n floodlights illuminating infinite wedges of angles α 1 , … , α n at n sites p 1 , … , p n 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 α i = α for all 1 ⩽ i ⩽ n (the uniform case) and θ = ∑ i = 1 n α i (the tight case).
ISSN:0925-7721
DOI:10.1016/j.comgeo.2007.01.004