Bazgan, Cristina

Brankovic, Ljiljana

Casel, Katrin

Fernau, Henning

Jansen, Klaus

Klein, Kim-Manuel

Lampis, Michael

Liedloff, Mathieu

Monnot, Jérôme

Paschos, Vangelis Th

2016

<p>We consider Upper Domination, the problem of finding a maximum cardinality minimal dominating set in a graph. We show that this problem does not admit an n1-ϵ approximation for any ϵ>0, making it significantly harder than Dominating Set, while it remains hard even on severely restricted special cases, such as cubic graphs (APX-hard), and planar subcubic graphs (NP-hard). We complement our negative results by showing that the problem admits an O(Δ) approximation on graphs of maximum degree Δ, as well as an EPTAS on planar graphs. Along the way, we also derive essentially tight n1-1d upper and lower bounds on the approximability of the related problem Maximum Minimal Hitting Set on d-uniform hypergraphs, generalising known results for Maximum Minimal Vertex Cover.</p>

Combinatorial Algorithms: Proceedings of the 27th International Workshop on Combinatorial Algorithms, p. 241-252

9783319445434

9783319445427

331944543X

https://hdl.handle.net/1959.11/54504

Springer

Lecture Notes in Computer Science

Upper Domination: Complexity and Approximation

Conference Publication

Publication