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Approximation algorithms for guarding 1.5 dimensional terrains King, James Alexander
Abstract
The 1.5-dimensional terrain guarding problem gives an x-monotone chain (the terrain) and asks for the minimum set of vertices of the terrain (guards) such that every vertex of the terrain is seen by at least one guard. This terrain guarding problem is a restriction of the SET COVER problem, which is known to be both NP-complete and inapproximable within a sub-logarithmic factor [19]. Fortunately, it is known that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [5, 11], though no attempt has been made to minimize the approximation factor. We give a 4-approximation algorithm for the general 1.5D terrain guarding problem, as well as a 2-approximation algorithm for the case with upwardlooking guards, i.e. when guards cannot see vertices that are below themselves.
Item Metadata
Title |
Approximation algorithms for guarding 1.5 dimensional terrains
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2005
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Description |
The 1.5-dimensional terrain guarding problem gives an x-monotone chain (the
terrain) and asks for the minimum set of vertices of the terrain (guards) such
that every vertex of the terrain is seen by at least one guard. This terrain
guarding problem is a restriction of the SET COVER problem, which is known to
be both NP-complete and inapproximable within a sub-logarithmic factor [19].
Fortunately, it is known that the 1.5-dimensional terrain guarding problem is
approximable to within a constant factor [5, 11], though no attempt has been
made to minimize the approximation factor.
We give a 4-approximation algorithm for the general 1.5D terrain guarding
problem, as well as a 2-approximation algorithm for the case with upwardlooking
guards, i.e. when guards cannot see vertices that are below themselves.
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Genre | |
Type | |
Language |
eng
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Date Available |
2009-12-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0051328
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2005-11
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.