# On dominating set of some subclasses of string graphs

## Article Type

Research Article

## Publication Title

Computational Geometry: Theory and Applications

## 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.

## DOI

10.1016/j.comgeo.2022.101884

## Publication Date

12-1-2022

## Recommended Citation

Chakraborty, Dibyayan; Das, Sandip; and Mukherjee, Joydeep, "On dominating set of some subclasses of string graphs" (2022). *Journal Articles*. 2873.

https://digitalcommons.isical.ac.in/journal-articles/2873

## Comments

Open Access, Bronze, Green