In this article, we study a variant of the minimum dominating set problem known as the minimum liar's dominating set (MLDS) problem. We prove that the MLDS problem is NP-hard in unit disk graphs. Next, we show that the recent sub-quadratic time 211-factor approximation algorithm \cite{bhore} for the MLDS problem is erroneous and propose a simple O(n+m) time 7.31-factor approximation algorithm, where n and m are the number of vertices and edges in the input unit disk graph, respectively. Finally, we prove that the MLDS problem admits a polynomial-time approximation scheme.
@article{arxiv.2005.13913,
title = {Liar's Domination in Unit Disk Graphs},
author = {Ramesh K. Jallu and Sangram K. Jena and Gautam K. Das},
journal= {arXiv preprint arXiv:2005.13913},
year = {2020}
}