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Finding a Highly Connected Steiner Subgraph and its Applications

Authors Eduard Eiben , Diptapriyo Majumdar , M. S. Ramanujan

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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Dynamic programming
Keywords
  • Parameterized Complexity
  • Steiner Subgraph Extension
  • p-edge-connected graphs
  • Matroids
  • Representative Families

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Abstract

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.

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Eduard Eiben, Diptapriyo Majumdar, and M. S. Ramanujan. Finding a Highly Connected Steiner Subgraph and its Applications. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.45

Author Details

Eduard Eiben
  • Royal Holloway, University of London, Egham, UK
Diptapriyo Majumdar
  • Indraprastha Institute of Information Technology Delhi, New Delhi, India
M. S. Ramanujan
  • University of Warwick, Coventry, UK

Funding

  • Ramanujan, M. S.: Supported by Engineering and Physical Sciences Research Council (EPSRC) grants EP/V007793/1 and EP/V044621/1.

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