License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2018.37
URN: urn:nbn:de:0030-drops-96198
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9619/
Bandyapadhyay, Sayan ;
Maheshwari, Anil ;
Mehrabi, Saeed ;
Suri, Subhash
Approximating Dominating Set on Intersection Graphs of Rectangles and L-frames
Abstract
We consider the Minimum Dominating Set (MDS) problem on the intersection graphs of geometric objects. Even for simple and widely-used geometric objects such as rectangles, no sub-logarithmic approximation is known for the problem and (perhaps surprisingly) the problem is NP-hard even when all the rectangles are "anchored" at a diagonal line with slope -1 (Pandit, CCCG 2017). In this paper, we first show that for any epsilon>0, there exists a (2+epsilon)-approximation algorithm for the MDS problem on "diagonal-anchored" rectangles, providing the first O(1)-approximation for the problem on a non-trivial subclass of rectangles. It is not hard to see that the MDS problem on "diagonal-anchored" rectangles is the same as the MDS problem on "diagonal-anchored" L-frames: the union of a vertical and a horizontal line segment that share an endpoint. As such, we also obtain a (2+epsilon)-approximation for the problem with "diagonal-anchored" L-frames. On the other hand, we show that the problem is APX-hard in case the input L-frames intersect the diagonal, or the horizontal segments of the L-frames intersect a vertical line. However, as we show, the problem is linear-time solvable in case the L-frames intersect a vertical as well as a horizontal line. Finally, we consider the MDS problem in the so-called "edge intersection model" and obtain a number of results, answering two questions posed by Mehrabi (WAOA 2017).
BibTeX - Entry
@InProceedings{bandyapadhyay_et_al:LIPIcs:2018:9619,
author = {Sayan Bandyapadhyay and Anil Maheshwari and Saeed Mehrabi and Subhash Suri},
title = {{Approximating Dominating Set on Intersection Graphs of Rectangles and L-frames}},
booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
pages = {37:1--37:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-086-6},
ISSN = {1868-8969},
year = {2018},
volume = {117},
editor = {Igor Potapov and Paul Spirakis and James Worrell},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9619},
URN = {urn:nbn:de:0030-drops-96198},
doi = {10.4230/LIPIcs.MFCS.2018.37},
annote = {Keywords: Minimum dominating set, Rectangles and L-frames, Approximation schemes, Local search, APX-hardness}
}
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Keywords: |
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Minimum dominating set, Rectangles and L-frames, Approximation schemes, Local search, APX-hardness |
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Collection: |
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43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) |
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Issue Date: |
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2018 |
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Date of publication: |
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27.08.2018 |
