Liar's Domination in Unit Disk Graphs
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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 11/2-factor approximation algorithm <cit.> 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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