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An Exact Exponential Time Algorithm for Power Dominating Set

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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 the exhaustive application of the following two rules. 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 design an algorithm solving this problem in time \(\mathcal{O}^{*}(1.7548^{n})\) on general graphs, using polynomial space only. To achieve this, we introduce so-called reference search trees that can be seen as a compact representation of usual search trees, providing non-local pointers in order to indicate pruned subtrees.

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  1. FB 4—Abteilung Informatik/Wirtschaftsinformatik, Universität Trier, Trier, Germany

    Daniel Binkele-Raible & Henning Fernau

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  1. Daniel Binkele-Raible
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  2. Henning Fernau
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Correspondence to Henning Fernau.

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Binkele-Raible, D., Fernau, H. An Exact Exponential Time Algorithm for Power Dominating Set . Algorithmica 63, 323–346 (2012). https://doi.org/10.1007/s00453-011-9533-2

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  • DOI: https://doi.org/10.1007/s00453-011-9533-2

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