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Engineering Exact Quasi-Threshold Editing

Authors Lars Gottesbüren , Michael Hamann , Philipp Schoch, Ben Strasser , Dorothea Wagner , Sven Zühlsdorf

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Author Details

Lars Gottesbüren
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany
Michael Hamann
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany
Philipp Schoch
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany
Ben Strasser
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany
Dorothea Wagner
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany
Sven Zühlsdorf
  • Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Germany

Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grants WA654/19-2 and WA654/22-2. The authors acknowledge support by the state of Baden-Württemberg through bwHPC.

Acknowledgements

We thank James Nastos and Mark Ortmann for helpful discussions.

Cite AsGet BibTex

Lars Gottesbüren, Michael Hamann, Philipp Schoch, Ben Strasser, Dorothea Wagner, and Sven Zühlsdorf. Engineering Exact Quasi-Threshold Editing. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.SEA.2020.10

Abstract

Quasi-threshold graphs are {C₄, P₄}-free graphs, i.e., they do not contain any cycle or path of four nodes as an induced subgraph. We study the {C₄, P₄}-free editing problem, which is the problem of finding a minimum number of edge insertions or deletions to transform an input graph into a quasi-threshold graph. This problem is NP-hard but fixed-parameter tractable (FPT) in the number of edits by using a branch-and-bound algorithm and admits a simple integer linear programming formulation (ILP). Both methods are also applicable to the general ℱ-free editing problem for any finite set of graphs ℱ. For the FPT algorithm, we introduce a fast heuristic for computing high-quality lower bounds and an improved branching strategy. For the ILP, we engineer several variants of row generation. We evaluate both methods for quasi-threshold editing on a large set of protein similarity graphs. For most instances, our optimizations speed up the FPT algorithm by one to three orders of magnitude. The running time of the ILP, that we solve using Gurobi, becomes only slightly faster. With all optimizations, the FPT algorithm is slightly faster than the ILP, even when listing all solutions. Additionally, we show that for almost all graphs, solutions of the previously proposed quasi-threshold editing heuristic QTM are close to optimal.

Subject Classification

ACM Subject Classification
  • Information systems → Clustering
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Fixed parameter tractability
  • Theory of computation → Branch-and-bound
Keywords
  • Edge Editing
  • Integer Linear Programming
  • FPT algorithm
  • Quasi-Threshold Editing

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References

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