Exact and parameterized algorithms for the independent cutset problem

The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. This problem is ▪-complete even when the input graph is planar and has maximum degree five. We first present a O⁎(1.4423n)-time algorithm to compute a minimum independent cu...

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Veröffentlicht in:Journal of computer and system sciences Jg. 148; S. 103598
Hauptverfasser: Rauch, Johannes, Rautenbach, Dieter, Souza, Uéverton S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.03.2025
Schlagworte:
Exact algorithms
Independent cutset
Parameterized algorithms
Independent cutset
Parameterized algorithms
Exact algorithms
ISSN:0022-0000
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Zusammenfassung:The Independent Cutset problem asks whether there is a set of vertices in a given graph that is both independent and a cutset. This problem is ▪-complete even when the input graph is planar and has maximum degree five. We first present a O⁎(1.4423n)-time algorithm to compute a minimum independent cutset (if any). Since the property of having an independent cutset is MSO1-expressible, our main results are concerned with structural parameterizations for the problem considering parameters incomparable with clique-width. We present ▪-time algorithms under the following parameters: the dual of the maximum degree, the dual of the solution size, the size of a dominating set (where a dominating set is given as an additional input), the size of an odd cycle transversal, the distance to chordal graphs, and the distance to P5-free graphs. We close by introducing the notion of α-domination, which generalizes key ideas of this article.
ISSN:0022-0000
DOI:10.1016/j.jcss.2024.103598