Subexponential-time algorithms for maximum independent set and related problems on box graphs
(2003) 9th Annual International Conference, COCOON 2003 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/302300
- author
- Lingas, Andrzej LU and Wahlén, Martin LU
- organization
- publishing date
- 2003
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Computing and combinatorics / Lecture notes in computer science
- volume
- 2697
- pages
- 50 - 56
- publisher
- Springer
- conference name
- 9th Annual International Conference, COCOON 2003
- conference location
- Big Sky, MT, United States
- conference dates
- 2003-07-25 - 2003-07-28
- 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
- 2016-04-01 11:58:31
- date last changed
- 2024-01-08 03:30:34
@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}},
doi = {{10.1007/3-540-45071-8_7}},
volume = {{2697}},
year = {{2003}},
}