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Linear-time 3-approximation algorithm for the r-star covering problem

Lingas, Andrzej LU ; Wasylewicz, Agnieszka and Zylinski, Pawel (2012) In International Journal of Computational Geometry and Applications 22(2). p.103-141
Abstract
The complexity status of the minimum r-star cover problem for orthogonal polygons had been open for many years, until 2004 when Ch. Worman and J. M. Keil proved it to be polynomially tractable (Polygon decomposition and the orthogonal art gallery problem, IJCGA 17(2) (2007), 105-138). However, since their algorithm has (O) over tilde (n(17))-time complexity, where (O) over tilde (.) hides a polylogarithmic factor, and thus it is not practical, in this paper we present a linear-time 3-approximation algorithm. Our approach is based upon the novel partition of an orthogonal polygon into so-called o-star-shaped orthogonal polygons.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Approximation algorithms, r-star cover, orthogonal polygon
in
International Journal of Computational Geometry and Applications
volume
22
issue
2
pages
103 - 141
publisher
World Scientific
external identifiers
  • wos:000308706700001
  • scopus:84866403378
ISSN
0218-1959
DOI
10.1142/S021819591250001X
language
English
LU publication?
yes
id
a4c9b8eb-ff52-41ec-a822-9c229d167634 (old id 3135836)
date added to LUP
2012-11-26 15:08:48
date last changed
2017-02-12 03:57:59
@article{a4c9b8eb-ff52-41ec-a822-9c229d167634,
  abstract     = {The complexity status of the minimum r-star cover problem for orthogonal polygons had been open for many years, until 2004 when Ch. Worman and J. M. Keil proved it to be polynomially tractable (Polygon decomposition and the orthogonal art gallery problem, IJCGA 17(2) (2007), 105-138). However, since their algorithm has (O) over tilde (n(17))-time complexity, where (O) over tilde (.) hides a polylogarithmic factor, and thus it is not practical, in this paper we present a linear-time 3-approximation algorithm. Our approach is based upon the novel partition of an orthogonal polygon into so-called o-star-shaped orthogonal polygons.},
  author       = {Lingas, Andrzej and Wasylewicz, Agnieszka and Zylinski, Pawel},
  issn         = {0218-1959},
  keyword      = {Approximation algorithms,r-star cover,orthogonal polygon},
  language     = {eng},
  number       = {2},
  pages        = {103--141},
  publisher    = {World Scientific},
  series       = {International Journal of Computational Geometry and Applications},
  title        = {Linear-time 3-approximation algorithm for the r-star covering problem},
  url          = {http://dx.doi.org/10.1142/S021819591250001X},
  volume       = {22},
  year         = {2012},
}