The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph $G$. Here, a set $S \subseteq V(G)$ is resolving if no two distinct vertices of $G$ have the same distance vector to $S$. The complexity of Metric Dimension in graphs of bounded treewidth remained elusive in the past years. Recently, Bonnet and Purohit [IPEC 2019] showed that the problem is W[1]-hard under treewidth parameterization. In this work, we strengthen their lower bound to show that Metric Dimension is NP-hard in graphs of treewidth 24.

翻译：矩阵尺寸问题要求在给定的( 未加权、 未定向) 图形中设定一个最小大小的解决方案 $G 。 在这里, 一套 $S \ subseteq V (G) $S 正在解决, 如果没有两个不同的 G$ 的脊椎具有与 $S 相同的距离矢量。 在过去的几年里, 捆绑的树枝图中的计量尺寸的复杂性仍然难以捉摸。 最近, Bonnet 和 Purohit [IPEC 2019] 显示, 问题在于树宽参数化下的 W[1] 硬度。 在这项工作中, 我们强化了它们的下限, 以显示Metric 尺寸在树宽 24 的图表中是硬的。