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Modularity Clustering Parameterized by Max Leaf Number

Authors Jaroslav Garvardt , Christian Komusiewicz

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Author Details

Jaroslav Garvardt
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany
Christian Komusiewicz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany

Funding

  • Garvardt, Jaroslav: Supported by the Carl Zeiss Foundation, Germany, within the project ‘‘Interactive Inference’’.

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Jaroslav Garvardt and Christian Komusiewicz. Modularity Clustering Parameterized by Max Leaf Number. In 19th International Symposium on Parameterized and Exact Computation (IPEC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 321, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.IPEC.2024.16

Abstract

The modularity score is one of the most important measures for assessing the quality of clusterings of undirected graphs. In the notoriously difficult Modularity problem, one is given an undirected graph G and the task is to find a clustering with maximum modularity. We show that Modularity is fixed-parameter tractable with respect to the max leaf number of G. This improves on a previous result by Meeks and Skerman [Algorithmica '20] who showed an XP-algorithm for this parameter. In addition, we strengthen previous hardness results for Modularity by showing W[1]-hardness for the parameter vertex deletion distance to disjoint union of stars.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • Graph clustering
  • parameterized complexity

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