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Subexponential-time algorithms for maximum independent set and related problems on box graphs

Lingas, Andrzej LU and Wahlén, Martin LU (2003) 9th Annual International Conference, COCOON 2003 In Computing and combinatorics / Lecture notes in computer science 2697. p.50-56
Abstract
A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time... (More)
A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time 2(O(d2dbn1-1/dlogn)) on, such box graphs in d-dimensions. We do this by applying a separator theorem by Smith and Wormald [7]. Finally, we show that in general graph case substantially subexponential algorithms for maximum independent set and the maximum induced subgraph with polynomial-time testable hereditary property Pi problems can yield non-trivial upper bounds on approximation factors achievable in polynomial time. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Computing and combinatorics / Lecture notes in computer science
volume
2697
pages
50 - 56
publisher
Springer
conference name
9th Annual International Conference, COCOON 2003
external identifiers
  • wos:000185044800007
  • scopus:35248826866
ISSN
1611-3349
0302-9743
ISBN
978-3-540-40534-4
DOI
10.1007/3-540-45071-8_7
language
English
LU publication?
yes
id
f1e5aac0-776c-4304-80b9-74d41fe2a44e (old id 302300)
date added to LUP
2007-09-17 10:52:02
date last changed
2018-05-29 11:01:29
@inproceedings{f1e5aac0-776c-4304-80b9-74d41fe2a44e,
  abstract     = {A box graph is the intersection graph of orthogonal rectangles in the plane. We consider such basic combinatorial problems on box graphs as maximum independent set, minimum vertex cover and maximum induced subgraph with polynomial-time testable hereditary property Pi. We show that they can be exactly solved in subexponential time, more precisely, in time 2(O(rootnlog n)), by applying Miller's simple cycle planar separator theorem [6] (in spite of the fact that the input box graph might be strongly non-planar). Furthermore we extend our idea to include the intersection graphs of orthogonal d-cubes of bounded aspect ratio and dimension. We present an algorithm that solves maximum independent set and the other aforementioned problems in time 2(O(d2dbn1-1/dlogn)) on, such box graphs in d-dimensions. We do this by applying a separator theorem by Smith and Wormald [7]. Finally, we show that in general graph case substantially subexponential algorithms for maximum independent set and the maximum induced subgraph with polynomial-time testable hereditary property Pi problems can yield non-trivial upper bounds on approximation factors achievable in polynomial time.},
  author       = {Lingas, Andrzej and Wahlén, Martin},
  booktitle    = {Computing and combinatorics / Lecture notes in computer science},
  isbn         = {978-3-540-40534-4},
  issn         = {1611-3349},
  language     = {eng},
  pages        = {50--56},
  publisher    = {Springer},
  title        = {Subexponential-time algorithms for maximum independent set and related problems on box graphs},
  url          = {http://dx.doi.org/10.1007/3-540-45071-8_7},
  volume       = {2697},
  year         = {2003},
}