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Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time

Authors Hjalmar Schulz, André Nichterlein , Rolf Niedermeier , Christopher Weyand

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Author Details

Hjalmar Schulz
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
André Nichterlein
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Rolf Niedermeier
  • Algorithmics and Computational Complexity, Technische Universität Berlin, Germany
Christopher Weyand
  • Karlsruhe Institute of Technology, Germany

Acknowledgements

In memory of Rolf Niedermeier, our colleague, friend, and mentor, who sadly passed away before this paper was published.

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Hjalmar Schulz, André Nichterlein, Rolf Niedermeier, and Christopher Weyand. Applying a Cut-Based Data Reduction Rule for Weighted Cluster Editing in Polynomial Time. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 25:1-25:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.IPEC.2022.25

Abstract

Given an undirected graph, the task in Cluster Editing is to insert and delete a minimum number of edges to obtain a cluster graph, that is, a disjoint union of cliques. In the weighted variant each vertex pair comes with a weight and the edge modifications have to be of minimum overall weight. In this work, we provide the first polynomial-time algorithm to apply the following data reduction rule of Böcker et al. [Algorithmica, 2011] for Weighted Cluster Editing: For a graph G = (V,E), merge a vertex set S ⊆ V into a single vertex if the minimum cut of G[S] is at least the combined cost of inserting all missing edges within G[S] plus the cost of cutting all edges from S to the rest of the graph. Complementing our theoretical findings, we experimentally demonstrate the effectiveness of the data reduction rule, shrinking real-world test instances from the PACE Challenge 2021 by around 24% while previous heuristic implementations of the data reduction rule only achieve 8%.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Correlation Clustering
  • Minimum Cut
  • Maximum s-t-Flow

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Supplementary Materials

References

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