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Algorithmica

, Volume 64, Issue 1, pp 152–169 | Cite as

Cluster Editing: Kernelization Based on Edge Cuts

  • Yixin Cao
  • Jianer ChenEmail author
Article

Abstract

Kernelization algorithms for the cluster editing problem have been a popular topic in the recent research in parameterized computation. Most kernelization algorithms for the problem are based on the concept of critical cliques. In this paper, we present new observations and new techniques for the study of kernelization algorithms for the cluster editing problem. Our techniques are based on the study of the relationship between cluster editing and graph edge-cuts. As an application, we present a simple algorithm that constructs a 2k-vertex kernel for the integral-weighted version of the cluster editing problem. Our result matches the best kernel bound for the unweighted version of the cluster editing problem, and significantly improves the previous best kernel bound for the weighted version of the problem. For the more general real-weighted version of the problem, our techniques lead to a simple kernelization algorithm that constructs a kernel of at most 4k vertices.

Keywords

Cluster editing Parameterized computation Kernelization Edge-cut Bioinformatics 

Notes

Acknowledgements

Supported in part by the US National Science Foundation under the Grants CCF-0830455 and CCF-0917288.

References

  1. 1.
    Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM 55(5), 1–27 (2008). Article 23 MathSciNetCrossRefGoogle Scholar
  2. 2.
    Alon, N., Lokshtanov, D., Saurabh, S.: Fast FAST. In: ICALP 2009. LNCS, vol. 5555, pp. 49–58. Springer, Berlin (2009) Google Scholar
  3. 3.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1), 89–113 (2004) zbMATHCrossRefGoogle Scholar
  4. 4.
    Berkhin, P.: A survey of clustering data mining techniques. In: Grouping Multidimensional Data, pp. 25–71. Springer, Berlin (2006) CrossRefGoogle Scholar
  5. 5.
    Betzler, N., Guo, J., Komusiewicz, C., Niedermeier, R.: Average parameterization and partial kernelization for computing medians. J. Comput. Syst. Sci. 77(4), 774–789 (2011) MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Bessy, S., Fomin, F.V., Gaspers, S., Paul, C., Perez, A., Saurabh, S., Thomassé, S.: Kernels for feedback arc set in tournaments. J. Comput. Syst. Sci. (2010). doi: 10.1016/j.jcss.2010.10.001 Google Scholar
  7. 7.
    Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: parameterized algorithms for cluster editing. Theor. Comput. Sci. 410, 5467–5480 (2009) zbMATHCrossRefGoogle Scholar
  8. 8.
    Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. J. Comput. Syst. Sci. 71(3), 360–383 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Chen, J., Meng, J.: A 2k kernel for the cluster editing problem. J. Comput. Syst. Sci. (2011). doi: 10.1016/j.jcss.2011.04.001 Google Scholar
  10. 10.
    Cunningham, W.H., Edmonds, J.: A combinatorial decomposition theory. Can. J. Math. 32(3), 734–765 (1980) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dean, J., Henzinger, M.R.: Finding related pages in the World Wide Web. Comput. Netw. 31, 1467–1479 (1999) CrossRefGoogle Scholar
  12. 12.
    Feige, U.: Faster FAST. In: CoRR (2009). arXiv:0911.5094 Google Scholar
  13. 13.
    Fellows, M.R., Langston, M.A., Rosamond, F.A., Shaw, P.: Efficient parameterized preprocessing for cluster editing. In: FCT 2007. LNCS, vol. 4639, pp. 312–321. Springer, Berlin (2007) Google Scholar
  14. 14.
    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) MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410(8–10), 718–726 (2009) zbMATHCrossRefGoogle Scholar
  16. 16.
    Hearst, M.A., Pedersen, J.O.: Reexamining the cluster hypothesis: scatter/gather on retrieval results. In: Proceedings of SIGIR, pp. 76–84 (1996) Google Scholar
  17. 17.
    Karpinski, M., Schudy, W.: Faster algorithms for feedback arc set tournament, Kemeny rank aggregation and betweenness tournament. In: ISAAC 2010. LNCS, vol. 6506, pp. 3–14. Springer, Berlin (2010) Google Scholar
  18. 18.
    Komusiewicz, C.: Algorithmics for network analysis: Clustering & querying. PhD thesis, Technische Universität Berlin, Berlin, Germany (2011) Google Scholar
  19. 19.
    Krivánek, M., Morávek, J.: NP-hard problems in hierarchical-tree clustering. Acta Inform. 23(3), 311–323 (1986) MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    de Montgolfier, F.: Décomposition modulaire des graphes. Théorie, extensions et algorithmes. Thése de doctorat, Université Montpellier II (2003) Google Scholar
  21. 21.
    Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Appl. Math. 144(1–2), 173–182 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    van Zuylen, A., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. Math. Oper. Res. 34(3), 594–620 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    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 Bioinform. 8(1), 396 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringTexas A&M UniversityCollege StationUSA

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