eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-09-16
6:1
6:14
10.4230/LIPIcs.APPROX/RANDOM.2024.6
article
Bipartizing (Pseudo-)Disk Graphs: Approximation with a Ratio Better than 3
Lokshtanov, Daniel
1
https://orcid.org/0000-0002-3166-9212
Panolan, Fahad
2
https://orcid.org/0000-0001-6213-8687
Saurabh, Saket
3
https://orcid.org/0000-0001-7847-6402
Xue, Jie
4
https://orcid.org/0000-0001-7015-1988
Zehavi, Meirav
5
https://orcid.org/0000-0002-3636-5322
University of California, Santa Barbara, USA
University of Leeds, UK
Institute of Mathematical Sciences, India
New York University Shanghai, China
Ben-Gurion University, Israel
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol317-approx-random2024/LIPIcs.APPROX-RANDOM.2024.6/LIPIcs.APPROX-RANDOM.2024.6.pdf
bipartization
geometric intersection graphs
approximation algorithms