Finding secluded places of special interest in graphs. (English) Zbl 1398.68408

van Bevern, René; Fluschnik, Till; Mertzios, George B.; Molter, Hendrik; Sorge, Manuel; Suchý, Ondřej

Guo, Jiong (ed.) et al., 11th international symposium on parameterized and exact computation (IPEC 2016), Aarhus, Denmark, August 24–26, 2016. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-95977-023-1). LIPIcs – Leibniz International Proceedings in Informatics 63, Article 5, 16 p. (2017).

Summary: Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topics in algorithmic graph theory. The focus herein is often on minimizing or maximizing the size of the solution, that is, the size of the desired vertex set. In several applications, however, we also want to limit the “exposure” of the solution to the rest of the graph. This is the case, for example, when the solution represents persons that ought to deal with sensitive information or a segregated community. In this work, we thus explore the (parameterized) complexity of finding such secluded vertex subsets for a wide variety of properties that they shall fulfill. More precisely, we study the constraint that the (open or closed) neighborhood of the solution shall be bounded by a parameter and the influence of this constraint on the complexity of minimizing separators, feedback vertex sets, \(\mathcal{F}\)-free vertex deletion sets, dominating sets, and the maximization of independent sets.
For the entire collection see [Zbl 1360.68013].

MSC:

68R10	Graph theory (including graph drawing) in computer science
68Q25	Analysis of algorithms and problem complexity

Keywords:

neighborhood; feedback vertex set; vertex deletion; separator; dominating set