Enumerating Isolated Cliques in Synthetic and Financial Networks

  • Falk Hüffner
  • Christian Komusiewicz
  • Hannes Moser
  • Rolf Niedermeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5165)

Abstract

We do computational studies concerning the enumeration of maximal isolated cliques in graphs. Isolation, as recently introduced, measures the degree of connectedness of the cliques to the rest of the graph. Isolation helps both in getting faster algorithms than for the enumeration of maximal general cliques and in filtering out cliques with special semantics. We perform experiments with synthetic graphs (in the G n,m,p  model) and financial networks, proposing the enumeration of isolated cliques as a useful instrument in analyzing financial networks.

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References

  1. 1.
    Abu-Khzam, F.N., Collins, R.L., Fellows, M.R., Langston, M.A., Suters, W.H., Symons, C.T.: Kernelization algorithms for the vertex cover problem: Theory and experiments. In: Proc. 6th ALENEX, pp. 62–69. SIAM, Philadelphia (2004)Google Scholar
  2. 2.
    Behrisch, M., Taraz, A.: Efficiently covering complex networks with cliques of similar vertices. Theoret. Comput. Sci. 355(1), 37–47 (2006)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Boginski, V., Butenko, S., Pardalos, P.M.: Statistical analysis of financial networks. Comput. Statist. Data Anal. 48(2), 431–443 (2005)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Boginski, V., Butenko, S., Pardalos, P.M.: Mining market data: A network approach. Comput. Oper. Res. 33(11), 3171–3184 (2006)MATHCrossRefGoogle Scholar
  5. 5.
    Butenko, S., Wilhelm, W.E.: Clique-detection models in computational biochemistry and genomics. European J. Oper. Res. 173(1), 1–17 (2006)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chesler, E.J., Lu, L., Shou, S., Qu, Y., Gu, J., Wang, J., Hsu, H.C., Mountz, J.D., Baldwin, N.E., Langston, M.A., Threadgill, D.W., Manly, K.F., Williams, R.W.: Complex trait analysis of gene expression uncovers polygenic and pleiotropic networks that modulate nervous system function. Nat. Genet. 37(3), 233–242 (2005)CrossRefGoogle Scholar
  7. 7.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)Google Scholar
  8. 8.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, New York (1979)MATHGoogle Scholar
  9. 9.
    Håstad, J.: Clique is hard to approximate within n 1 − ε. Acta Math. 182(1), 105–142 (1999)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Ito, H., Iwama, K., Osumi, T.: Linear-time enumeration of isolated cliques. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 119–130. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Koch, I.: Enumerating all connected maximal common subgraphs in two graphs. Theoret. Comput. Sci. 250(1–2), 1–30 (2001)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Komusiewicz, C., Hüffner, F., Moser, H., Niedermeier, R.: Isolation concepts for enumerating dense subgraphs. In: Lin, G. (ed.) COCOON. LNCS, vol. 4598, pp. 140–150. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Mantegna, R.N., Stanley, H.E.: Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  14. 14.
    Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theoret. Comput. Sci. 363(1), 28–42 (2006)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Falk Hüffner
    • 1
  • Christian Komusiewicz
    • 1
  • Hannes Moser
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für InformatikFriedrich-Schiller-Universität JenaJenaGermany

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