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

  • Sepp HartungEmail author
  • Holger H. Hoos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8994)


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.


Search Tree Synthetic Dataset Tree Cluster Training Instance Cluster Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


  1. 1.
    Gurobi 5.62. Software (2014)Google Scholar
  2. 2.
    Agarwala, R., Bafna, V., Farach, M., Narayanan, B., Paterson, M., Thorup, M.: On the approximability of numerical taxonomy (fitting distances by tree matrices). SIAM J. Comput. 28(3), 1073–1085 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Ailon, N., Charikar, M.: Fitting tree metrics: hierarchical clustering and phylogeny. In: Proceedings of the 46th FOCS, pp. 73–82 (2005)Google Scholar
  4. 4.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1–3), 89–113 (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Böcker, S.: A golden ratio parameterized algorithm for cluster editing. J. Discrete Algorithms 16, 79–89 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Böcker, S., Baumbach, J.: Cluster editing. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 33–44. Springer, Heidelberg (2013) Google Scholar
  7. 7.
    Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: evaluation and experiments. Algorithmica 60(2), 316–334 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Bonchi, F., Gionis, A., Gullo, F., Ukkonen, A.: Chromatic correlation clustering. In: Proceedings of 18th ACM SIGKDD (KDD 2012), pp. 1321–1329. ACM Press (2012)Google Scholar
  9. 9.
    Cao, Y., Chen, J.: On parameterized and kernelization algorithms for the hierarchical clustering problem. In: Chan, T.-H., Lau, L., Trevisan, L. (eds.) TAMC 2013. LNCS, vol. 7876, pp. 319–330. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  10. 10.
    Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71(3), 360–383 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Chen, J., Meng, J.: A \(2k\) kernel for the cluster editing problem. J. Comput. Syst. Sci. 78(1), 211–220 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Chierichetti, F., Dalvi, N., Kumar, R.: Correlation clustering in MapReduce. In: Proceedings of 20th ACM SIGKDD (KDD 2014), pp. 641–650. ACM Press (2014)Google Scholar
  13. 13.
    de Oca, M.A.M., Aydin, D., Stützle, T.: An incremental particle swarm for large-scale continuous optimization problems: an example of tuning-in-the-loop (re)design of optimization algorithms. Soft Comput. 15(11), 2233–2255 (2011)CrossRefGoogle Scholar
  14. 14.
    Downey, R.G., Fellows, M.R.: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, London (2013) CrossRefzbMATHGoogle Scholar
  15. 15.
    Fawcett, C., Hoos, H.H.: Analysing differences between algorithm configurations through ablation. In: Proceedings of 10th MIC, pp. 123–132 (2013)Google Scholar
  16. 16.
    Fellows, M.R., Langston, M.A., Rosamond, F.A., Shaw, P.: Efficient parameterized preprocessing for cluster editing. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 312–321. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  17. 17.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: exact algorithms for clique generation. Theory Comput. Syst. 38(4), 373–392 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45(1–3), 59–96 (1989)CrossRefzbMATHGoogle Scholar
  19. 19.
    Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410(8–10), 718–726 (2009)CrossRefzbMATHGoogle Scholar
  20. 20.
    Guo, J., Hartung, S., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Exact algorithms and experiments for hierarchical tree clustering. In Proceedings of 24th AAAI. AAAI Press (2010)Google Scholar
  21. 21.
    Hoos, H.H.: Programming by optimization. Commun. ACM 55(2), 70–80 (2012)CrossRefGoogle Scholar
  22. 22.
    Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 5 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  23. 23.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006) CrossRefzbMATHGoogle Scholar
  24. 24.
    Sanders, P., Wagner, D.: Algorithm engineering. It - Inf. Technol. 53(6), 263–265 (2011)CrossRefGoogle Scholar
  25. 25.
    van Zuylen, A., Williamson, D.P.: Deterministic algorithms for rank aggregation and other ranking and clustering problems. In: Kaklamanis, C., Skutella, M. (eds.) WAOA 2007. LNCS, vol. 4927, pp. 260–273. Springer, Heidelberg (2008) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut Für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

Personalised recommendations