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When Can Cluster Deletion with Bounded Weights Be Solved Efficiently?

Authors Jaroslav Garvardt , Christian Komusiewicz , Nils Morawietz

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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
Nils Morawietz
  • Institute of Computer Science, Friedrich Schiller University Jena, Germany

Funding

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

Cite As Get BibTex

Jaroslav Garvardt, Christian Komusiewicz, and Nils Morawietz. When Can Cluster Deletion with Bounded Weights Be Solved Efficiently?. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.32

Abstract

In the NP-hard Weighted Cluster Deletion problem, the input is an undirected graph G = (V,E) and an edge-weight function ω: E → ℕ, and the task is to partition the vertex set V into cliques so that the total weight of edges in the cliques is maximized. Recently, it has been shown that Weighted Cluster Deletion is NP-hard on some graph classes where Cluster Deletion, the special case where every edge has unit weight, can be solved in polynomial time. We study the influence of the value t of the largest edge weight assigned by ω on the problem complexity for such graph classes. Our main results are that Weighted Cluster Deletion is fixed-parameter tractable with respect to t on graph classes whose graphs consist of well-separated clusters that are connected by a sparse periphery. Concrete examples for such classes are split graphs and graphs that are close to cluster graphs. We complement our results by strengthening previous hardness results for Weighted Cluster Deletion. For example, we show that Weighted Cluster Deletion is NP-hard on restricted subclasses of cographs even when every edge has weight 1 or 2.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Graph clustering
  • split graphs
  • cographs
  • parameterized complexity

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