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Liar's domination in unit disk graphs
Theoretical Computer Science ( IF 0.9 ) Pub Date : 2020-09-02 , DOI: 10.1016/j.tcs.2020.08.029
Ramesh K. Jallu , Sangram K. Jena , Gautam K. Das

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. We point out that the approximation guarantee of 112 for the approximation algorithm for unit disk graphs proposed by Banerjee and Bhore [S. Banerjee, S. Bhore, Algorithm and hardness results on liars dominating set and k-tuple dominating set, in: International Workshop on Combinatorial Algorithms, Springer, 2019, pp. 48–60] is not correct and we propose a simple O(n+m) time 7.31-factor approximation algorithm, where n and m are the number of vertices and edges, respectively, in the given unit disk graph. Finally, we prove that the MLDS problem admits a polynomial-time approximation scheme.



中文翻译:

骗子在单位盘图中的统治

在本文中,我们研究了最小控制集问题的变体,称为最小骗子控制集(MLDS)问题。我们证明了MLDS问题在单位磁盘图中是NP-hard的。我们指出112Banerjee和Bhore提出的单位圆图的近似算法[S. Banerjee,S. Bhore,关于骗子支配集和k元组支配集的算法和硬度结果,在:国际组合算法研讨会,施普林格,2019年,第48–60页]中,这是不正确的,我们提出了一个简单的方法Øñ+时间7.31因子近似算法,其中nm分别是给定单位圆图中的顶点和边数。最后,我们证明MLDS问题采用了多项式时间近似方案。

更新日期:2020-09-02
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