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Cluster Editing: Kernelization Based on Edge Cuts

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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.

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References

  1. Ailon, N., Charikar, M., Newman, A.: Aggregating inconsistent information: ranking and clustering. J. ACM 55(5), 1–27 (2008). Article 23

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Lokshtanov, D., Saurabh, S.: Fast FAST. In: ICALP 2009. LNCS, vol. 5555, pp. 49–58. Springer, Berlin (2009)

    Google Scholar 

  3. Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Mach. Learn. 56(1), 89–113 (2004)

    Article  MATH  Google Scholar 

  4. Berkhin, P.: A survey of clustering data mining techniques. In: Grouping Multidimensional Data, pp. 25–71. Springer, Berlin (2006)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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. Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: parameterized algorithms for cluster editing. Theor. Comput. Sci. 410, 5467–5480 (2009)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  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. Cunningham, W.H., Edmonds, J.: A combinatorial decomposition theory. Can. J. Math. 32(3), 734–765 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dean, J., Henzinger, M.R.: Finding related pages in the World Wide Web. Comput. Netw. 31, 1467–1479 (1999)

    Article  Google Scholar 

  12. Feige, U.: Faster FAST. In: CoRR (2009). arXiv:0911.5094

    Google Scholar 

  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. 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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  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. 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. Komusiewicz, C.: Algorithmics for network analysis: Clustering & querying. PhD thesis, Technische Universität Berlin, Berlin, Germany (2011)

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

    Article  MathSciNet  MATH  Google Scholar 

  20. de Montgolfier, F.: Décomposition modulaire des graphes. Théorie, extensions et algorithmes. Thése de doctorat, Université Montpellier II (2003)

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

    Article  MathSciNet  MATH  Google Scholar 

  22. van Zuylen, A., Williamson, D.P.: Deterministic pivoting algorithms for constrained ranking and clustering problems. Math. Oper. Res. 34(3), 594–620 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

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Acknowledgements

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

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  1. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, 77843, USA

    Yixin Cao & Jianer Chen

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  1. Yixin Cao
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  2. Jianer Chen
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Correspondence to Jianer Chen.

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Cao, Y., Chen, J. Cluster Editing: Kernelization Based on Edge Cuts. Algorithmica 64, 152–169 (2012). https://doi.org/10.1007/s00453-011-9595-1

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