Skip to main content

A distributed algorithm for finding all maximal cliques in a network graph

  • Conference paper
  • First Online:
LATIN '92 (LATIN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 583))

Included in the following conference series:

Abstract

A time efficient distributed algorithm for computing all maximal cliques in an arbitrary network is presented that is time efficient for every class of networks with a polynomial number of maximal cliques. The algorithm makes use of the algebraic properties of bipartite cliques which form a lattice structure. Assuming that it takes unit time to transmit the message of length \(\mathcal{O}\)(log n) bits, the algorithm has a time complexity of \(\mathcal{O}\)(M n log n) where M is the number of maximal cliques, and n is the number of processors in the network. The communication complexity is \(\mathcal{O}\)(M2 n2 log n) assuming message length is \(\mathcal{O}\)(log n) bits.

This article was processed using the LATEX macro package with LMAMULT style

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Awerbuch, Complexity of network synchronization, J. Assoc. Comput. Mach. 32(1985): pp. 804–823.

    Google Scholar 

  2. N. Chiba and T. Nishizeki, Aboricity and Subgraph Listing Algorithms, SIAM J. of Comput. 14(1985), pp. 210–223.

    Google Scholar 

  3. I. Cidon and I. S. Gopal, Dynamic Detection of Subgraphs in Computer Networks, Algorithmica 5(1990), pp. 277–294.

    Google Scholar 

  4. E. Dahlhaus and M. Karpinski, A Fast Parallel Algorithm for Computing All Maximal Cliques in a Graph and the Related Problems (Extended Abstract), Proceeding of the First Scandinavian Workshop on Algorithm Theory (1988), pp. 139–144.

    Google Scholar 

  5. M. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, 1979.

    Google Scholar 

  6. I. S. Gopal, Personal communication.

    Google Scholar 

  7. E. Jennings, A. Lingas, L. Motyčková, Dynamic Detection of Forest of Tree-Connected Meshes, Proceedings of the 1991 International Conference on Parallel Processing, Vol. 3, Algorithms and Applications, pp. 300–301.

    Google Scholar 

  8. S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirakawa, A New Algorithm for Generating all the Maximal Independent Sets, SIAM J. Comput. 6(1977), pp. 505–517.

    Google Scholar 

  9. R. Wille, Subdirect Decomposition of Concept Lattices, Algebra Universalis 17(1983), pp.275–287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Imre Simon

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jennings, E., Motyčková, L. (1992). A distributed algorithm for finding all maximal cliques in a network graph. In: Simon, I. (eds) LATIN '92. LATIN 1992. Lecture Notes in Computer Science, vol 583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023836

Download citation

  • DOI: https://doi.org/10.1007/BFb0023836

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55284-0

  • Online ISBN: 978-3-540-47012-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics