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An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width

Authors Luisa Gargano, Adele A. Rescigno

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Author Details

Luisa Gargano
  • Department of Computer Science, University of Salerno, Italy
Adele A. Rescigno
  • Department of Computer Science, University of Salerno, Italy

Funding

This work was partially supported by project SERICS (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU.

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Luisa Gargano and Adele A. Rescigno. An FPT Algorithm for Spanning Trees with Few Branch Vertices Parameterized by Modular-Width. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.50

Abstract

The minimum branch vertices spanning tree problem consists in finding a spanning tree T of an input graph G having the minimum number of branch vertices, that is, vertices of degree at least three in T. This NP-hard problem has been widely studied in the literature and has many important applications in network design and optimization. Algorithmic and combinatorial aspects of the problem have been extensively studied and its fixed parameter tractability has been recently considered. In this paper we focus on modular-width and show that the problem of finding a spanning tree with the minimum number of branch vertices is FPT with respect to this parameter.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Mathematics of computing → Graph theory
Keywords
  • Spanning Trees
  • Branch vertices
  • Fixed-parameter tractable algorithms
  • Modular-width

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