# Upper Domination: Complexity and Approximation

@inproceedings{Bazgan2016UpperDC, title={Upper Domination: Complexity and Approximation}, author={Cristina Bazgan and Ljiljana Brankovic and Katrin Casel and Henning Fernau and Klaus Jansen and Kim-Manuel Klein and Michael Lampis and Mathieu Liedloff and J{\'e}r{\^o}me Monnot and Vangelis Th. Paschos}, booktitle={IWOCA}, year={2016} }

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(\varDelta…

## 11 Citations

### Upper Domination: Towards a Dichotomy Through Boundary Properties

- MathematicsAlgorithmica
- 2017

This work discovers the first boundary class for this problem and proves the dichotomy for monogenic classes in finitely defined classes of graphs.

### Domination chain: Characterisation, classical complexity, parameterised complexity and approximability

- MathematicsDiscret. Appl. Math.
- 2020

### Weighted upper domination number

- Mathematics, Computer ScienceElectron. Notes Discret. Math.
- 2017

### Minimal Zero Forcing Sets

- Mathematics
- 2022

In this paper, we study minimal (with respect to inclusion) zero forcing sets. We ﬁrst investigate when a graph can have polynomially or exponentially many distinct minimal zero forcing sets. We also…

### An E↵ective Dynamic Programming Algorithm for the Minimum-Cost Maximal Knapsack Packing

- Computer Science
- 2017

KP is NP-hard, but it is well-known that fairly large instances can be solved to and (I, p, w,C) as a knapsack instance.

### Parameterized Complexity of Upper Edge Domination

- MathematicsArXiv
- 2022

. In this paper we study a maximization version of the classical Edge Dominating Set (EDS) problem, namely, the Upper EDS problem, in the realm of Parameterized Complexity. In this problem, given an…

### An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem

- Computer Science, BusinessEur. J. Oper. Res.
- 2017

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