Power Domination in $\mathcal{O}^*(1.7548^n)$ Using Reference Search Trees
Identifieur interne : 000045 ( LNCS/Analysis ); précédent : 000044; suivant : 000046Power 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
Affiliations:
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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></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Allemagne"><noRegion><name sortKey="Raible, Daniel" sort="Raible, Daniel" uniqKey="Raible D" first="Daniel" last="Raible">Daniel Raible</name></noRegion><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name><name sortKey="Fernau, Henning" sort="Fernau, Henning" uniqKey="Fernau H" first="Henning" last="Fernau">Henning Fernau</name><name sortKey="Raible, Daniel" sort="Raible, Daniel" uniqKey="Raible D" first="Daniel" last="Raible">Daniel Raible</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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