Skip to main content

A 2k Kernel for the Cluster Editing Problem

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6196))

Abstract

The cluster editing problem for a given graph G and a given parameter k asks if one can apply at most k edge insertion/deletion operations on G so that the resulting graph is a union of disjoint cliques. The problem has attracted much attention because of its applications in bioinformatics. In this paper, we present a polynomial time kernelization algorithm for the problem that produces a kernel of size bounded by 2k, improving the previously best kernel of size 4k for the problem.

This work was supported in part by the USA National Science Foundation under the Grants CCF-0830455 and CCF-0917288.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben-dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. Journal of Computational Biology 6(3/4), 281–297 (1999)

    Article  Google Scholar 

  2. Charikar, M., Guruswami, V., Wirth, A.: Clustering with qualitative information. Journal of Computer and System Sciences 71(3), 360–383 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen, Z.-Z., Jiang, T., Lin, G.: Computing phylogenetic roots with bounded degrees and errors. SIAM Journal on Computing 32(4), 864–879 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Dehne, F., Langston, M., 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)

    Chapter  Google Scholar 

  5. Dom, M., Guo, J., Huffner, F., Niedermeier, R.: Extending the tractability border for closest leaf powers. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, pp. 397–408. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Fellows, M.: The lost continent of polynomial time: preprocessing and kernelization. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 276–277. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Fellows, M., Langston, M., Rosamond, F., 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)

    Chapter  Google Scholar 

  8. Gramm, J., Guo, J., Huffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39(4), 321–347 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gramm, J., Guo, J., Huffner, F., Niedermeier, R.: Graph-modeled data clustering: exact algorithms for clique generation. Theory of Computing Systems 38(4), 373–392 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Guo, J.: A more effective linear kernelization for cluster edting. Theoretical Computer Science 410(8-10), 718–726 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  11. Hsu, W., Ma, T.: 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 

  12. Huffner, F., Komusiewicz, C., Moser, H., Niedermeier, R.: Fixed-parameter algorithms for cluster vertex deletion. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 711–722. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Jain, A., Dubes, R.: Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  14. Lin, G., Kearney, P.E., Jiang, T.: Phylogenetic k-root and steiner k-root. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 539–551. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Shamir, R., Sharan, R.: Algorithmic approaches to clustering gene expression data. In: Jiang, T., Xu, Y., Zhang, M. (eds.) Current Topics in Computational Molecular Biology, pp. 269–299. MIT press, Cambridge (2002)

    Google Scholar 

  16. Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 379–390. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. Discrete Applied Mathematics 144, 173–182 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Zuylen, A., Williamson, D.: 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, J., Meng, J. (2010). A 2k Kernel for the Cluster Editing Problem. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14031-0_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14030-3

  • Online ISBN: 978-3-642-14031-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics