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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8246/
Hanaka, Tesshu ;
Nishimura, Naomi ;
Ono, Hirotaka
On Directed Covering and Domination Problems
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: |
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directed graph, vertex cover, dominating set, edge dominating set, fixed-parameter algorithms |
Collection: |
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28th International Symposium on Algorithms and Computation (ISAAC 2017) |
Issue Date: |
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2017 |
Date of publication: |
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07.12.2017 |