License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2017.45
URN: urn:nbn:de:0030-drops-82460
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8246/
 Go to the corresponding LIPIcs Volume Portal

### On Directed Covering and Domination Problems

 pdf-format:

### Abstract

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.

### BibTeX - Entry

@InProceedings{hanaka_et_al:LIPIcs:2017:8246,
author =	{Tesshu Hanaka and Naomi Nishimura and Hirotaka Ono},
title =	{{On  Directed Covering and Domination Problems}},
booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages =	{45:1--45:12},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-054-5},
ISSN =	{1868-8969},
year =	{2017},
volume =	{92},
editor =	{Yoshio Okamoto and Takeshi Tokuyama},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8246},
URN =		{urn:nbn:de:0030-drops-82460},
doi =		{10.4230/LIPIcs.ISAAC.2017.45},
annote =	{Keywords: directed graph, vertex cover, dominating set, edge dominating set, fixed-parameter algorithms}
}

 Keywords: directed graph, vertex cover, dominating set, edge dominating set, fixed-parameter algorithms Collection: 28th International Symposium on Algorithms and Computation (ISAAC 2017) Issue Date: 2017 Date of publication: 07.12.2017

DROPS-Home | Fulltext Search | Imprint | Privacy