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 $\frac{11}{2}$ 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.

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$\frac{11}{2}$Banerjee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$Ø（ñ+米）$时间7.31因子近似算法，其中n和m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。