Liar's Domination in Unit Disk Graphs

Ramesh K. Jallu; Sangram K. Jena; Gautam K. Das

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arXiv · 2005.13913

Liar's Domination in Unit Disk Graphs

Ramesh K. Jallu·Sangram K. Jena·Gautam K. Das

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Abstract

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 $\frac{11}{2}$-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.

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BibTeX RIS

Ramesh K. Jallu, Sangram K. Jena, Gautam K. Das. 2020-05-28. Liar's Domination in Unit Disk Graphs. https://arxiv.org/abs/2005.13913

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