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Programming by Optimisation Meets Parameterised Algorithmics: A Case Study for Cluster Editing

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Learning and Intelligent Optimization (LION 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8994))

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Abstract

Inspired by methods and theoretical results from parameterised algorithmics, we improve the state of the art in solving Cluster Editing, a prominent NP-hard clustering problem with applications in computational biology and beyond. In particular, we demonstrate that an extension of a certain preprocessing algorithm, called the \((k+1)\)-data reduction rule in parameterised algorithmics, embedded in a sophisticated branch-&-bound algorithm, improves over the performance of existing algorithms based on Integer Linear Programming (ILP) and branch-&-bound. Furthermore, our version of the \((k+1)\)-rule outperforms the theoretically most effective preprocessing algorithm, which yields a 2k-vertex kernel. Notably, this 2k-vertex kernel is analysed empirically for the first time here. Our new algorithm was developed by integrating Programming by Optimisation into the classical algorithm engineering cycle – an approach which we expect to be successful in many other contexts.

Sepp Hartung—Major parts of this work were done during a research visit of SH at the University of British Columbia in Vancouver (Canada), supported by a “DFG Forschungsstipendium” (HA 7296/1-1).

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Notes

  1. 1.

    Notably, our implementation is still able to solve \(M\)-Tree Clustering. However, here our focus is on improving over state-of-the-art exact solvers for Cluster Editing.

  2. 2.

    http://www.mi.fu-berlin.de/w/LiSA/YoshikoCharles.

  3. 3.

    We removed the largest instance with 8836 vertices from the dataset. It is more than two times larger than the second largest instance and could not be solved.

  4. 4.

    http://fpt.akt.tu-berlin.de/cluEdit/.

  5. 5.

    PAR-10 is the average with timeouts counted as 10 times the cut-off time.

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Acknowledgement

We thank Tomasz Przedmojski who provided, as part of his bachelor thesis, an accelerated implementation of the \(\mathcal {O}(M\cdot k)\) kernel [20].

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Authors and Affiliations

  1. Institut Für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany

    Sepp Hartung

  2. Department of Computer Science, University of British Columbia, Vancouver, Canada

    Holger H. Hoos

Authors
  1. Sepp Hartung
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  2. Holger H. Hoos
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Correspondence to Sepp Hartung .

Editor information

Editors and Affiliations

  1. Lille University, Villeneuve d'Ascq, France

    Clarisse Dhaenens

  2. Lille University, Villeneuve d'Ascq, France

    Laetitia Jourdan

  3. Lille University, Villeneuve d'Ascq, France

    Marie-Eléonore Marmion

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Hartung, S., Hoos, H.H. (2015). Programming by Optimisation Meets Parameterised Algorithmics: A Case Study for Cluster Editing. In: Dhaenens, C., Jourdan, L., Marmion, ME. (eds) Learning and Intelligent Optimization. LION 2015. Lecture Notes in Computer Science(), vol 8994. Springer, Cham. https://doi.org/10.1007/978-3-319-19084-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-19084-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19083-9

  • Online ISBN: 978-3-319-19084-6

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