Going Weighted: Parameterized Algorithms for Cluster Editing

  • Sebastian Böcker
  • Sebastian Briesemeister
  • Quang B. A. Bui
  • Anke Truss
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5165)


The goal of the Cluster Editing problem is to make the fewest changes to the edge set of an input graph such that the resulting graph is a disjoint union of cliques. This problem is NP-complete but recently, several parameterized algorithms have been proposed. In this paper we present a surprisingly simple branching strategy for Cluster Editing. We generalize the problem assuming that edge insertion and deletion costs are positive integers. We show that the resulting search tree has size O(1.82 k ) for edit cost k, resulting in the currently fastest parameterized algorithm for this problem. We have implemented and evaluated our approach, and find that it outperforms other parametrized algorithms for the problem.


Search Tree Weighted Graph Input Graph Vertex Pair Transitive 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Böcker, S., Briesemeister, S., Bui, Q.B.A., Truß, A.: A fixed-parameter approach for weighted cluster editing. In: Proc. of Asia-Pacific Bioinformatics Conference (APBC 2008). Series on Advances in Bioinformatics and Computational Biology, vol. 5, pp. 211–220. Imperial College Press (2008)Google Scholar
  2. 2.
    Böcker, S., Briesemeister, S., Klau, G.W.: Exact algorithms for cluster editing: Evaluation and experiments. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 289–302. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Bodlaender, H.L., Cai, L., Chen, J., Fellows, M.R., Telle, J.A., Marx, D.: Open problems in parameterized and exact computation — IWPEC 2006. Technical Report UU-CS-2006-052, Department of Information and Computing Sciences, Utrecht University (2006)Google Scholar
  4. 4.
    Dehne, F., Langston, M.A., Luo, X., Pitre, S., Shaw, P., Zhang, Y.: The cluster editing problem: Implementations and experiments. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 13–24. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixed-parameter algorithms for clique generation. Theor. Comput. Syst. 38(4), 373–392 (2005)zbMATHCrossRefGoogle Scholar
  7. 7.
    Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45, 52–96 (1989)CrossRefGoogle Scholar
  8. 8.
    Guo, J.: A more effective linear kernelization for Cluster Editing. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 36–47. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Hsu, W.-L., Ma, T.-H.: Substitution decomposition on chordal graphs and applications. In: Hsu, W.-L., Lee, R.C.T. (eds.) ISA 1991. LNCS, vol. 557, pp. 52–60. Springer, Heidelberg (1991)Google Scholar
  10. 10.
    Křivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta Inform. 23(3), 311–323 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)zbMATHGoogle Scholar
  12. 12.
    Niedermeier, R., Rossmanith, P.: A general method to speed up fixed-parameter-tractable algorithms. Inform. Process. Lett. 73, 125–129 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144(1–2), 173–182 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Sharan, R., Maron-Katz, A., Shamir, R.: CLICK and EXPANDER: a system for clustering and visualizing gene expression data. Bioinformatics 19(14), 1787–1799 (2003)CrossRefGoogle Scholar
  15. 15.
    van Zuylen, A., Williamson, D.P.: Deterministic algorithms for rank aggregation and other ranking and clustering problems. In: Proc. of Workshop on Approximation and Online Algorithms (WAOA 2007). LNCS, vol. 4927, pp. 260–273. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Wittkop, T., Baumbach, J., Lobo, F., Rahmann, S.: Large scale clustering of protein sequences with FORCE – a layout based heuristic for weighted cluster editing. BMC Bioinformatics 8(1), 396 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sebastian Böcker
    • 1
  • Sebastian Briesemeister
    • 2
  • Quang B. A. Bui
    • 1
  • Anke Truss
    • 1
  1. 1.Lehrstuhl für BioinformatikFriedrich-Schiller-Universität JenaJenaGermany
  2. 2.Div. for Simulation of Biological Systems, ZBIT/WSIEberhard Karls Universität TübingenGermany

Personalised recommendations