# Upper Domination: Complexity and Approximation

Abstract : 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 $n^{1-\epsilon}$ approximation for any $\epsilon>0$, 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 $O(\Delta)$ approximation on graphs of maximum degree $\Delta$, as well as an EPTAS on planar graphs. Along the way, we also derive essentially tight \$n^{1-1/d} 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.
Type de document :
Communication dans un congrès
27th International Workshop on Combinatorial Algorithms (IWOCA), Aug 2016, Helsinki, Finland. 9843, pp.241-252, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-44543-4_19〉

https://hal.archives-ouvertes.fr/hal-01367856
Contributeur : Mathieu Liedloff <>
Soumis le : vendredi 16 septembre 2016 - 19:02:26
Dernière modification le : jeudi 11 janvier 2018 - 06:17:30

### Citation

Cristina Bazgan, Ljiljana Brankovic, Katrin Casel, Henning Fernau, Klaus Jansen, et al.. Upper Domination: Complexity and Approximation. 27th International Workshop on Combinatorial Algorithms (IWOCA), Aug 2016, Helsinki, Finland. 9843, pp.241-252, 2016, Lecture Notes in Computer Science. 〈10.1007/978-3-319-44543-4_19〉. 〈hal-01367856〉

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