NDLI: Guarding polyominoes

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Guarding polyominoes

Content Provider	ACM Digital Library
Author	Irfan, Mohammad T. Iwerks, Justin Kim, Joondong Biedl, Therese Mitchell, Joseph S.B.
Abstract	We explore the art gallery problem for the special case that the domain (gallery) P is an m-polyomino, a polyform whose cells are m unit squares. We study the combinatorics of guarding polyominoes in terms of the parameter m, in contrast with the traditional parameter n, the number of vertices of P; in particular, we show that floor((m+1)/3) point guards are always sufficient and sometimes necessary to cover an m-polyomino. When m d 3n/4 - 4, the point guard sufficiency condition yields a strictly lower guard number than floor(n/4), given by the art gallery theorem for orthogonal polygons. When pixels behave themselves like guards (pixel guards), we prove that floor(3m/11) + 1 guards are sufficient and sometimes necessary to cover an m-polyomino. We also study the algorithmic complexity of computing optimal guard sets for polyominoes. We prove that determining the guard number of a given m-polyomino is NP-hard. We provide polynomial-time algorithms to solve exactly some special cases in which the polyomino is "thin".
Starting Page	387
Ending Page	396
Page Count	10
File Format	PDF
ISBN	9781450306829
DOI	10.1145/1998196.1998261
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-06-13
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Computational geometry Art gallery problem Np-hardness Visibility problem Polyomino
Content Type	Text
Resource Type	Article

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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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