Chakraborty, D. orcid.org/0000-0003-0534-6417, Das, S. and Mukherjee, J. (Cover date: December 2022) On dominating set of some subclasses of string graphs. Computational Geometry, 107. 101884. ISSN 0925-7721
Abstract
We provide constant factor approximation algorithms for the Minimum Dominating Set (MDS) problem on several subclasses of string graphs i.e. intersection graphs of simple curves on the plane. For k ≥ 0, unit Bk-VPG graphs are intersection graphs of simple rectilinear curves having at most k cusps (bends) and each segment of the curve being unit length. We give an 18-approximation algorithm for the MDS problem on unit B0-VPG graphs. This partially addresses a question of Katz et al. (2005) [24]. We also give an O(k4)- approximation algorithm for the MDS problem on unit Bk-VPG graphs. We show that there is an 8-approximation algorithm for the MDS problem on vertically-stabbed L-graphs. We also give a 656-approximation algorithm for the MDS problem on stabbed rectangle overlap graphs. This is the first constant-factor approximation algorithm for the MDS problem on stabbed rectangle overlap graphs and extends a result of Bandyapadhyay et al. (2019) [31]. We prove some hardness results to complement the above results.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2023, Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/. This is an author produced version of an article published in Computational Geometry. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Dominating set; Approximation algorithm; Geometric intersection graph; String graph |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Oct 2023 14:57 |
Last Modified: | 05 Oct 2023 15:00 |
Published Version: | https://www.sciencedirect.com/science/article/pii/... |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.comgeo.2022.101884 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202890 |
Download
Filename: On_dominating_set_of_some_subclasses_of_string_graphs.pdf
Licence: CC-BY-NC-ND 4.0