eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
45:1
45:15
10.4230/LIPIcs.MFCS.2023.45
article
Finding a Highly Connected Steiner Subgraph and its Applications
Eiben, Eduard
1
https://orcid.org/0000-0003-2628-3435
Majumdar, Diptapriyo
2
https://orcid.org/0000-0003-2677-4648
Ramanujan, M. S.
3
https://orcid.org/0000-0002-2116-6048
Royal Holloway, University of London, Egham, UK
Indraprastha Institute of Information Technology Delhi, New Delhi, India
University of Warwick, Coventry, UK
Given a (connected) undirected graph G, a set X ⊆ V(G) and integers k and p, the Steiner Subgraph Extension problem asks whether there exists a set S ⊇ X of at most k vertices such that G[S] is a p-edge-connected subgraph. This problem is a natural generalization of the well-studied Steiner Tree problem (set p = 1 and X to be the terminals). In this paper, we initiate the study of Steiner Subgraph Extension from the perspective of parameterized complexity and give a fixed-parameter algorithm (i.e., FPT algorithm) parameterized by k and p on graphs of bounded degeneracy (removing the assumption of bounded degeneracy results in W-hardness).
Besides being an independent advance on the parameterized complexity of network design problems, our result has natural applications. In particular, we use our result to obtain new single-exponential FPT algorithms for several vertex-deletion problems studied in the literature, where the goal is to delete a smallest set of vertices such that: (i) the resulting graph belongs to a specified hereditary graph class, and (ii) the deleted set of vertices induces a p-edge-connected subgraph of the input graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.45/LIPIcs.MFCS.2023.45.pdf
Parameterized Complexity
Steiner Subgraph Extension
p-edge-connected graphs
Matroids
Representative Families