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On Directed Covering and Domination Problems Hanaka, Tesshu Nishimura, Naomi Ono, Hirotaka directed graph vertex cover dominating set edge dominating set fixed-parameter algorithms In this paper, we study covering and domination problems on directed graphs. Although undirected Vertex Cover and Edge Dominating Set are well-studied classical graph problems, the directed versions have not been studied much due to the lack of clear definitions. We give natural definitions for Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set as directed generations of Vertex Cover and Edge Dominating Set. For these problems, we show that (1) Directed r-In (Out) Vertex Cover and Directed (p,q)-Edge Dominating Set are NP-complete on planar directed acyclic graphs except when r=1 or (p,q)=(0,0), (2) if r>=2, Directed r-In (Out) Vertex Cover is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs, (3) if either p or q is greater than 1, Directed (p,q)-Edge Dominating Set is W[2]-hard and (c*ln k)-inapproximable on directed acyclic graphs, (4) all problems can be solved in polynomial time on trees, and (5) Directed (0,1),(1,0),(1,1)-Edge Dominating Set are fixed-parameter tractable in general graphs. The first result implies that (directed) r-Dominating Set on directed line graphs is NP-complete even if r=1. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tesshu Hanaka and Naomi Nishimura and Hirotaka Ono 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.45 urn:nbn:de:0030-drops-82460 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.45 eng https://creativecommons.org/licenses/by/3.0/legalcode