Algorithms and Hardness for Metric Dimension on Digraphs

In the Metric Dimension problem, one asks for a minimum-size set R of vertices such that any pair graph, there is vertex from whose two distances to are distinct. This problem has mainly been studied on undirected graphs and gained lot attention in recent years. We focus directed graphs, show how solve linear-time digraphs underlying graph (ignoring multiple edges) tree. (nontrivially) extends previous algorithm oriented trees. then extend method unicyclic (understood as multigraph unique cycle). also give fixed-parameter-tractable when parameterized by modular-width, extending known result graphs. Finally, we NP-hard even planar triangle-free acyclic maximum degree 6.