Competitive Online Clique Clustering

  • Aleksander Fabijan
  • Bengt J. Nilsson
  • Mia Persson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7878)


Clique clustering is the problem of partitioning a graph into cliques so that some objective function is optimized. In online clustering, the input graph is given one vertex at a time, and any vertices that have previously been clustered together are not allowed to be separated. The objective here is to maintain a clustering the never deviates too far in the objective function compared to the optimal solution. We give a constant competitive upper bound for online clique clustering, where the objective function is to maximize the number of edges inside the clusters. We also give almost matching upper and lower bounds on the competitive ratio for online clique clustering, where we want to minimize the number of edges between clusters. In addition, we prove that the greedy method only gives linear competitive ratio for these problems.


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  1. 1.
    Alvey, S., Borneman, J., Chrobak, M., Crowley, D., Figueroa, A., Hartin, R., Jiang, G., Scupham, A.T., Valinsky, L., Vedova, D., Yin, B.: Analysis of bacterial community composition by oligonucleotide fingerprinting of rRNA genes. Applied and Environmental Microbiology 68, 3243–3250 (2002)CrossRefGoogle Scholar
  2. 2.
    Bansal, N., Blum, A., Chawla, S.: Correlation Clustering. Machine Learning 56(1-3), 89–113 (2004)zbMATHCrossRefGoogle Scholar
  3. 3.
    Ben-Dor, A., Shamir, R., Yakhini, Z.: Clustering Gene Expression Patterns. Journal of Computational Biology 6(3/4), 281–297 (1999)CrossRefGoogle 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)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Charikar, M., Guruswami, V., Wirth, A.: Clustering with Qualitative Information. In: Proc. 44th Annual Symposium on Foundations of Computer Science, FOCS 2003, pp. 524–533 (2003)Google Scholar
  6. 6.
    Demaine, E.D., Immorlica, N.: Correlation Clustering with Partial Information. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 1–13. Springer, Heidelberg (2003)Google Scholar
  7. 7.
    Dessmark, A., Jansson, J., Lingas, A., Lundell, E., Persson, M.: On the Approximability of Maximum and Minimum Edge Clique Partition Problems. Int. J. Found. Comput. Sci. 18(2), 217–226 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Figueroa, A., Goldstein, A., Jiang, T., Kurowski, M., Lingas, A., Persson, M.: Approximate clustering of incomplete fingerprints. J. Discrete Algorithms 6(1), 103–108 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Mathieu, C., Sankur, O., Schudy, W.: Online Correlation Clustering. In: Proc. 7th International Symposium on Theoretical Aspects of Computer Science (STACS 2010), pp. 573–584 (2010)Google Scholar
  11. 11.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aleksander Fabijan
    • 1
  • Bengt J. Nilsson
    • 2
  • Mia Persson
    • 2
  1. 1.Faculty of Computer and Information ScienceUniversity of LjubljanaSlovenia
  2. 2.Department of Computer ScienceMalmö UniversitySweden

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