Competitive Strategies for Online Clique Clustering

  • Marek Chrobak
  • Christoph Dürr
  • Bengt J. Nilsson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9079)


A clique clustering of a graph is a partitioning of its vertices into disjoint cliques. The quality of a clique clustering is measured by the total number of edges in its cliques. We consider the online variant of the clique clustering problem, where the vertices of the input graph arrive one at a time. At each step, the newly arrived vertex forms a singleton clique, and the algorithm can merge any existing cliques in its partitioning into larger cliques, but splitting cliques is not allowed. We give an online strategy with competitive ratio \(15.645\) and we prove a lower bound of \(6\) on the competitive ratio, improving the previous respective bounds of \(31\) and \(2\).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56(1–3), 89–113 (2004)CrossRefMATHGoogle Scholar
  2. 2.
    Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering gene expression patterns. Journal of Computational Biology 6(3/4), 281–297 (1999)CrossRefGoogle Scholar
  3. 3.
    Borodin, A., El-Yaniv, R.: Online computation and competitive analysis. Cambridge University Press (1998)Google Scholar
  4. 4.
    Charikar, M., Chekuri, C., Feder, T., Motwani, R.: Incremental clustering and dynamic information retrieval. SIAM J. Comput. 33(6), 1417–1440 (2004)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Chaudhuri, K., Godfrey, B., Rao, S., Talwar, K.: Paths, trees, and minimum latency tours. In: 44th Symposium on Foundations of Computer Science (FOCS 2003), Proceedings, Cambridge, MA, USA, October 11–14, pp. 36–45 (2003)Google Scholar
  6. 6.
    Chrobak, M., Hurand, M.: Better bounds for incremental medians. Theor. Comput. Sci. 412(7), 594–601 (2011)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Chrobak, M., Kenyon, C., Noga, J., Young, N.E.: Incremental medians via online bidding. Algorithmica 50(4), 455–478 (2008)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Chrobak, M., Kenyon-Mathieu, C.: SIGACT news online algorithms column 10: competitiveness via doubling. SIGACT News 37(4), 115–126 (2006)CrossRefGoogle Scholar
  9. 9.
    Dessmark, A., Jansson, J., Lingas, A., Lundell, E.-M., Persson, M.: On the approximability of maximum and minimum edge clique partition problems. Int. J. Found. Comput. Sci. 18(2), 217–226 (2007)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Fabijan, A., Nilsson, B.J., Persson, M.: Competitive online clique clustering. In: Proc. 8th International Conference on Algorithms and Complexity (CIAC 2013), pp. 221–233 (2013)Google Scholar
  11. 11.
    Figueroa, A., Borneman, J., Jiang, T.: Clustering binary fingerprint vectors with missing values for DNA array data analysis. Journal of Computational Biology 11(5), 887–901 (2004)CrossRefGoogle Scholar
  12. 12.
    Lin, G., Nagarajan, C., Rajaraman, R., Williamson, D.P.: A general approach for incremental approximation and hierarchical clustering. SIAM J. Comput. 39(8), 3633–3669 (2010)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Mathieu, C., Sankur, O., Schudy, W.: Online correlation clustering. In: 27th International Symposium on Theoretical Aspects of Computer Science (STACS 2010), pp. 573–584 (2010)Google Scholar
  14. 14.
    Valinsky, L., Vedova, G.D., Scupham, R.J., Alvey, S., Figueroa, A., Yin, B., Jack Hartin, R., Chrobak, M., Crowley, D.E., Jiang, T., Borneman, J.: Analysis of bacterial community composition by oligonucleotide fingerprinting of rRNA genes. Applied and Environmental Microbiology 68, 2002 (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Christoph Dürr
    • 2
    • 3
  • Bengt J. Nilsson
    • 4
  1. 1.University of California at RiversideRiversideUSA
  2. 2.Sorbonne UniversitésUPMC Univ Paris 06, UMR 7606, LIP6ParisFrance
  3. 3.CNRSUMR 7606, LIP6ParisFrance
  4. 4.Department of Computer ScienceMalmö UniversityMalmöSweden

Personalised recommendations