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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Published in | Computational geometry : theory and applications Vol. 43; no. 1; pp. 23 - 34 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
2010
|
Subjects | |
Online Access | Get full text |
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Abstract | 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). |
---|---|
AbstractList | 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). |
Author | Rudra, Atri Cary, Matthew Vee, Erik Sabharwal, Ashish |
Author_xml | – sequence: 1 givenname: Matthew surname: Cary fullname: Cary, Matthew email: mattcary@google.com organization: Google Inc., 1600 Amphitheatre Parkway, Mountain View, CA 94043, USA – sequence: 2 givenname: Atri surname: Rudra fullname: Rudra, Atri email: atri@cse.buffalo.edu organization: Dept. of Computer Science and Engr., University at Buffalo, SUNY, Buffalo, NY 14260-2000, USA – sequence: 3 givenname: Ashish surname: Sabharwal fullname: Sabharwal, Ashish email: sabhar@cs.cornell.edu organization: Dept. of Computer Science, Cornell University, Ithaca, NY 14853-7501, USA – sequence: 4 givenname: Erik surname: Vee fullname: Vee, Erik email: erikvee@yahoo.com organization: Yahoo! Research, Santa Clara, CA 95054, USA |
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Keywords | Illumination Art gallery problem Floodlights NP-completeness |
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Snippet | 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... |
SourceID | crossref elsevier |
SourceType | Aggregation Database Publisher |
StartPage | 23 |
SubjectTerms | Art gallery problem Floodlights Illumination NP-completeness |
Title | Floodlight illumination of infinite wedges |
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