TY - GEN
T1 - On directed covering and domination problems
AU - Hanaka, Tesshu
AU - Nishimura, Naomi
AU - Ono, Hirotaka
N1 - Funding Information:
∗ This work is supported by the Natural Sciences and Engineering Research Council of Canada. † This work is partially supported by KAKENHI, no. 26241031, 26540005, 17H01698 and 17K19960.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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 NPcomplete even if r = 1.
AB - 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 NPcomplete even if r = 1.
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U2 - 10.4230/LIPIcs.ISAAC.2017.45
DO - 10.4230/LIPIcs.ISAAC.2017.45
M3 - Conference contribution
AN - SCOPUS:85038598677
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017
A2 - Tokuyama, Takeshi
A2 - Okamoto, Yoshio
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 28th International Symposium on Algorithms and Computation, ISAAC 2017
Y2 - 9 December 2017 through 22 December 2017
ER -