TY - GEN

T1 - Bipartizing (Pseudo-)Disk Graphs

T2 - 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

AU - Xue, Jie

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© Daniel Lokshtanov, Fahad Panolan, Saket Saurabh, Jie Xue, and Meirav Zehavi.

PY - 2024/9/1

Y1 - 2024/9/1

N2 - 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.

AB - 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.

KW - approximation algorithms

KW - bipartization

KW - geometric intersection graphs

UR - http://www.scopus.com/inward/record.url?scp=85204483711&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.APPROX/RANDOM.2024.6

DO - 10.4230/LIPIcs.APPROX/RANDOM.2024.6

M3 - Conference contribution

AN - SCOPUS:85204483711

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024

A2 - Kumar, Amit

A2 - Ron-Zewi, Noga

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Y2 - 28 August 2024 through 30 August 2024

ER -