Skip to main content
SpringerLink
Log in

Graph-Modeled Data Clustering: Fixed-Parameter Algorithms for Clique Generation

  • Conference paper
  • First Online:
Algorithms and Complexity (CIAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2653))

Included in the following conference series:

Abstract

We present efficient fixed-parameter algorithms for the NP-complete edge modification problems Cluster Editing and Cluster Deletion. Here, the goal is to make the fewest changes to the edge set of an input graph such that the new graph is a vertex-disjoint union of cliques. Allowing up to k edge additions and deletions (Cluster Editing), we solve this problem in O(2.27k + |V|3) time; allowing only up to k edge deletions (Cluster Deletion), we solve this problem in O(1.77k + |V|3) time. The key ingredients of our algorithms are two easy to implement bounded search tree algorithms and a reduction to a problem kernel of size O(k 3). This improves and complements previous work.

Supported by the Deutsche Forschungsgemeinschaft (DFG), research project “OPAL” (optimal solutions for hard problems in computational biology), NI 369/2.

Partially supported by the Deutsche Forschungsgemeinschaft (DFG), junior research group “PIAF” (fixed-parameter algorithms), NI 369/4.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Alber, J. Gramm, and R. Niedermeier. Faster exact solutions for hard problems: a parameterized point of view. Discrete Mathematics, 229:3–27, 2001.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  3. Leizhen Cai. Fixed-parameter tractability of graph modification problems for hereditary properties. Information Processing Letters, 58:171–176, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Chen, I. Kanj, and W. Jia Vertex cover: further observations and further improvements. Journal of Algorithms, 41:280–301, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  5. R. G. Downey and M. R. Fellows. Parameterized Complexity. Springer. 1999.

    Google Scholar 

  6. M. R. Fellows. Parameterized complexity: the main ideas and connections to practical computing. In Experimental Algorithmics, number 2547 in LNCS, pages 51–77, 2002. Springer.

    Chapter  Google Scholar 

  7. J. Gramm, J. Guo, F. Hüffner, and R. Niedermeier. Automated generation of search tree algorithms for graph modification problems. Manuscript in preparation, March 2003.

    Google Scholar 

  8. P. Hansen and B. Jaumard. Cluster analysis and mathematical programming. Mathematical Programming, 79:191–215, 1997.

    MathSciNet  Google Scholar 

  9. A. K. Jain and R. C. Dubes. Algorithms for clustering data. Prentice Hall, 1988.

    Google Scholar 

  10. H. Kaplan, R. Shamir, and R. E. Tarjan. Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM Journal on Computing, 28(5):1906–1922, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Khot and V. Raman. Parameterized complexity of finding subgraphs with hereditary properties. Theoretical Computer Science, 289:997–1008, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  12. O. Kullmann. New methods for 3-SAT decision and worst-case analysis. Theoretical Computer Science, 223(1–2):1–72, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  13. M. Mahajan and V. Raman. Parameterizing above guaranteed values: MaxSat and MaxCut. Journal of Algorithms, 31:335–354, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  14. A. Natanzon, R. Shamir, and R. Sharan. Complexity classification of some edge modification problems. Discrete Applied Mathematics, 113:109–128, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Niedermeier and P. Rossmanith. A general method to speed up fixed parameter-tractable algorithms. Information Processing Letters, 73:125–129, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  16. R. Niedermeier and P. Rossmanith. On efficient fixed-parameter algorithms for Weighted Vertex Cover. Journal of Algorithms, to appear, 2003.

    Google Scholar 

  17. R. Shamir, R. Sharan, and D. Tsur. Cluster graph modification problems. In Proc. of 28th WG, number 2573 in LNCS, pages 379–390, 2002, Springer.

    Google Scholar 

  18. R. Sharan and R. Shamir. CLICK: A clustering algorithm with applications to gene expression analysis. In Proc. of 8th ISMB, pp. 307–316, 2000. AAAI Press.

    Google Scholar 

  19. R. Sharan and R. Shamir. Algorithmic approaches to clustering gene expression data. In T. Jiang et al. (eds): Current Topics in Computational Molecular Biology, pages 269–300, The MIT Press. 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, D-72076, Tübingen, Germany

    Jens Gramm, Jiong Guo, Falk Hüffner & Rolf Niedermeier

Authors
  1. Jens Gramm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiong Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Falk Hüffner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rolf Niedermeier
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Infornatica, Università di Roma “La Sapienza”, Via Salaria 113, 00198, Rome, Italy

    Rossella Petreschi  & Riccardo Silvestri  & 

  2. Dipartimento di Infornatica ed Applicazioni “R.M. Capocelli”, Università di Salerno, Via S. Allende 2, 84081, Baronissi, SA, Italy

    Giuseppe Persiano

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gramm, J., Guo, J., Hüffner, F., Niedermeier, R. (2003). Graph-Modeled Data Clustering: Fixed-Parameter Algorithms for Clique Generation. In: Petreschi, R., Persiano, G., Silvestri, R. (eds) Algorithms and Complexity. CIAC 2003. Lecture Notes in Computer Science, vol 2653. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44849-7_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-44849-7_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40176-6

  • Online ISBN: 978-3-540-44849-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation