Correlating Theory and Practice in Finding Clubs and Plexes

Authors Aleksander Figiel, Tomohiro Koana, André Nichterlein, Niklas Wünsche

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Author Details

Aleksander Figiel
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Tomohiro Koana
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
André Nichterlein
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Niklas Wünsche
  • Unaffiliated Researcher, Berlin, Germany

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Aleksander Figiel, Tomohiro Koana, André Nichterlein, and Niklas Wünsche. Correlating Theory and Practice in Finding Clubs and Plexes. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 47:1-47:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


For solving NP-hard problems there is often a huge gap between theoretical guarantees and observed running times on real-world instances. As a first step towards tackling this issue, we propose an approach to quantify the correlation between theoretical and observed running times. We use two NP-hard problems related to finding large "cliquish" subgraphs in a given graph as demonstration of this measure. More precisely, we focus on finding maximum s-clubs and s-plexes, i. e., graphs of diameter s and graphs where each vertex is adjacent to all but s vertices. Preprocessing based on Turing kernelization is a standard tool to tackle these problems, especially on sparse graphs. We provide a parameterized analysis for the Turing kernelization and demonstrate their usefulness in practice. Moreover, we demonstrate that our measure indeed captures the correlation between these new theoretical and the observed running times.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
  • Preprocessing
  • Turing kernelization
  • Pearson correlation coefficient


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