Power Domination in $\mathcal{O}^*(1.7548^n)$ Using Reference Search Trees
Identifieur interne : 001937 ( Istex/Curation ); précédent : 001936; suivant : 001938Power Domination in $\mathcal{O}^*(1.7548^n)$ Using Reference Search Trees
Auteurs : Daniel Raible [Allemagne] ; Henning Fernau [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2008.
Abstract
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.
Url:
DOI: 10.1007/978-3-540-92182-0_15
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<front><div type="abstract" xml:lang="en">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.</div>
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