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Conference Papers Year : 2023

Algorithms and Hardness for Metric Dimension on Digraphs

Abstract

In the Metric Dimension problem, one asks for a minimumsize set R of vertices such that for any pair of vertices of the graph, there is a vertex from R whose two distances to the vertices of the pair are distinct. This problem has mainly been studied on undirected graphs and has gained a lot of attention in the recent years. We focus on directed graphs, and show how to solve the problem in linear-time on digraphs whose underlying undirected graph (ignoring multiple edges) is a tree. This (nontrivially) extends a previous algorithm for oriented trees. We then extend the method to unicyclic digraphs (understood as the digraphs whose underlying undirected multigraph has a unique cycle). We also give a fixed-parameter-tractable algorithm for digraphs when parameterized by the directed modular-width, extending a known result for undirected graphs. Finally, we show that Metric Dimension is NPhard even on planar triangle-free acyclic digraphs of maximum degree 6.
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hal-04216265 , version 1 (24-09-2023)
hal-04216265 , version 2 (13-10-2023)

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Antoine Dailly, Florent Foucaud, Anni Hakanen. Algorithms and Hardness for Metric Dimension on Digraphs. 49th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2023), Jun 2023, fribourg, Switzerland. pp.232-245, ⟨10.1007/978-3-031-43380-1_17⟩. ⟨hal-04216265v2⟩
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