Abstract
The Power Dominating Set problem is an extension of the well-known domination problem on graphs in a way that we enrich it by a second propagation rule: Given a graph G(V,E) a set P ⊆ V is a power dominating set if every vertex is observed after we have applied the next two rules exhaustively. First, a vertex is observed if v ∈ P or it has a neighbor in P. Secondly, if an observed vertex has exactly one unobserved neighbor u, then also u will be observed as well. We show that Power Dominating Set remains \(\mathcal{NP}\)-hard on cubic graphs. We designed an algorithm solving this problem in time \(\mathcal{O}^*(1.7548^n)\) on general graphs. To achieve this we have used a new notion of search trees called reference search trees providing non-local pointers.
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Raible, D., Fernau, H. (2008). Power Domination in \(\mathcal{O}^*(1.7548^n)\) Using Reference Search Trees. In: Hong, SH., Nagamochi, H., Fukunaga, T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92182-0_15
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DOI: https://doi.org/10.1007/978-3-540-92182-0_15
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