Lokshtanov, D., Panolan, F. orcid.org/0000-0001-6213-8687, Saurabh, S. et al. (2 more authors) (2024) Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3. In: In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). APPROX/RANDOM 2024, 28-30 Aug 2024, London. Leibniz International Proceedings in Informatics (LIPIcs), 317 . LIPIcs , Wadern, Germany , 6:1-6:14. ISBN 978-3-95977-348-5
Abstract
In a disk graph, every vertex corresponds to a disk in R² and two vertices are connected by an edge whenever the two corresponding disks intersect. Disk graphs form an important class of geometric intersection graphs, which generalizes both planar graphs and unit-disk graphs. We study a fundamental optimization problem in algorithmic graph theory, Bipartization (also known as Odd Cycle Transversal), on the class of disk graphs. The goal of Bipartization is to delete a minimum number of vertices from the input graph such that the resulting graph is bipartite. A folklore (polynomial-time) 3-approximation algorithm for Bipartization on disk graphs follows from the classical framework of Goemans and Williamson [Combinatorica’98] for cycle-hitting problems. For over two decades, this result has remained the best known approximation for the problem (in fact, even for Bipartization on unit-disk graphs). In this paper, we achieve the first improvement upon this result, by giving a (3 − α)-approximation algorithm for Bipartization on disk graphs, for some constant α > 0. Our algorithm directly generalizes to the broader class of pseudo-disk graphs. Furthermore, our algorithm is robust in the sense that it does not require a geometric realization of the input graph to be given.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi; licensed under Creative Commons License CC-BY 4.0. |
Keywords: | bipartization, geometric intersection graphs, approximation algorithms |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Algorithms & Complexity |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Aug 2024 11:58 |
Last Modified: | 23 Sep 2024 16:23 |
Published Version: | https://drops.dagstuhl.de/entities/document/10.423... |
Status: | Published |
Publisher: | LIPIcs |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Identification Number: | 10.4230/LIPIcs.APPROX/RANDOM.2024.6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:216249 |