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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Finding Highly Connected Subgraphs
verfasst von : Falk Hüffner, Christian Komusiewicz, Manuel Sorge
Erschienen in: SOFSEM 2015: Theory and Practice of Computer Science
Verlag: Springer Berlin Heidelberg
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A popular way of formalizing clusters in networks are
highly connected
subgraphs, that is, subgraphs of
k
vertices that have edge connectivity larger than
k
/2 (equivalently, minimum degree larger than
k
/2). We examine the computational complexity of finding highly connected subgraphs. We first observe that this problem is NP-hard. Thus, we explore possible parameterizations, such as the solution size, number of vertices in the input, the size of a vertex cover in the input, and the number of edges outgoing from the solution (edge isolation), and expose their influence on the complexity of this problem. For some parameters, we find strong intractability results; among the parameters yielding tractability, the edge isolation seems to provide the best trade-off between running time bounds and a small parameter value in relevant instances.