Skip to main content
SpringerLink
Log in

Exact Algorithms for Cluster Editing: Evaluation and Experiments

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

The Cluster Editing problem is defined as follows: Given an undirected, loopless graph, we want to find a set of edge modifications (insertions and deletions) of minimum cardinality, such that the modified graph consists of disjoint cliques.

We present empirical results for this problem using exact methods from fixed-parameter algorithmics and linear programming. We investigate parameter-independent data reduction methods and find that effective preprocessing is possible if the number of edge modifications k is smaller than some multiple of  \(\lvert V\rvert\) , where V is the vertex set of the input graph. In particular, combining parameter-dependent data reduction with lower and upper bounds we can effectively reduce graphs satisfying \(k\leq25\lvert V\rvert\) .

In addition to the fastest known fixed-parameter branching strategy for the problem, we investigate an integer linear program (ILP) formulation of the problem using a cutting plane approach. Our results indicate that both approaches are capable of solving large graphs with 1000 vertices and several thousand edge modifications. For the first time, complex and very large graphs such as biological instances allow for an exact solution, using a combination of the above techniques. (A preliminary version of this paper appeared under the title “Exact algorithms for cluster editing: Evaluation and experiments” in the Proceedings of the 7th Workshop on Experimental Algorithms, WEA 2008, in: LNCS, vol. 5038, Springer, pp. 289–302.)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. J. Comput. Biol. 6(3–4), 281–297 (1999)

    Article  Google Scholar 

  2. 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, London (2008)

    Chapter  Google Scholar 

  3. Böcker, S., Briesemeister, S., Bui, Q.B.A., Truß, A.: Going weighted: Parameterized algorithms for cluster editing. In: Proc. of Conference on Combinatorial Optimization and Applications (COCOA 2008). Lect. Notes Comput. Sc., vol. 5165, pp. 1–12. Springer, Berlin (2008)

    Chapter  Google Scholar 

  4. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71(3), 360–383 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dehne, F., Langston, M.A., Luo, X., Pitre, S., Shaw, P., Zhang, Y.: The cluster editing problem: Implementations and experiments. In: Proc. of International Workshop on Parameterized and Exact Computation (IWPEC 2006). Lect. Notes Comput. Sc., vol. 4169, pp. 13–24. Springer, Berlin (2006)

    Chapter  Google Scholar 

  6. 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)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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)

    Article  MATH  Google Scholar 

  8. Grötschel, M., Wakabayashi, Y.: A cutting plane algorithm for a clustering problem. Math. Program. 45, 52–96 (1989)

    Article  Google Scholar 

  9. Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410(8–10), 718–726 (2009)

    Article  MATH  Google Scholar 

  10. Kochenberger, G.A., Glover, F., Alidaee, B., Wang, H.: Clustering of microarray data via clique partitioning. J. Comb. Optim. 10(1), 77–92 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Křivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta Inform. 23(3), 311–323 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  12. Müller, R.: On the partial order polytope of a digraph. Math. Program. 73, 31–49 (1996)

    Article  MATH  Google Scholar 

  13. Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, London (2006)

    Book  MATH  Google Scholar 

  14. Rahmann, S., Wittkop, T., Baumbach, J., Martin, M., Truß, A., Böcker, S.: Exact and heuristic algorithms for weighted cluster editing. In: Proc. of Computational Systems Bioinformatics (CSB 2007), vol. 6, pp. 391–401 (2007)

  15. Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144(1–2), 173–182 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Stoer, M., Wagner, F.: A simple min-cut algorithm. J. ACM 4, 585–591 (1997)

    Article  MathSciNet  Google Scholar 

  18. Tatusov, R.L., Fedorova, N.D., Jackson, J.D., Jacobs, A.R., Kiryutin, B., Koonin, E.V., Krylov, D.M., Mazumder, R., Mekhedov, S.L., Nikolskaya, A.N., Rao, B.S., Smirnov, S., Sverdlov, A.V., Vasudevan, S., Wolf, Y.I., Yin, J.J., Natale, D.A.: The COG database: an updated version includes eukaryotes. BMC Bioinformatics 4, 41 (2003)

    Article  Google Scholar 

  19. 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). Lect. Notes Comput. Sc., vol. 4927, pp. 260–273. Springer, Berlin (2008)

    Chapter  Google Scholar 

  20. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany

    Sebastian Böcker

  2. Jena Centre for Bioinformatics, Jena, Germany

    Sebastian Böcker

  3. Div. for Simulation of Biological Systems, ZBIT/WSI, Eberhard Karls Universität Tübingen, Tübingen, Germany

    Sebastian Briesemeister

  4. CWI, P.O. Box 94079, 1090 GB, Amsterdam, Netherlands

    Gunnar W. Klau

Authors
  1. Sebastian Böcker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Briesemeister
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gunnar W. Klau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Böcker.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Böcker, S., Briesemeister, S. & Klau, G.W. Exact Algorithms for Cluster Editing: Evaluation and Experiments. Algorithmica 60, 316–334 (2011). https://doi.org/10.1007/s00453-009-9339-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-009-9339-7

Keywords

Search

Navigation