Skip to main content

Fast Winner-Takes-All Networks for the Maximum Clique Problem

  • Conference paper
  • First Online:
KI 2002: Advances in Artificial Intelligence (KI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2479))

Included in the following conference series:

Abstract

We present an in-depth mathematical analysis of a winner-takes-all Network tailored to the maximum clique problem, a well-known intractable combinatorial optimization problem which has practical applications in several real world domains. The analysis yields tight bounds for the parameter settings to ensure energy descent to feasible solutions. To verify the theoretical results we employ a fast annealing schedule to the WTA algorithm and show the effectiveness of the proposed approach for large scaled problems in extensive computer simulations.

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

Access this chapter

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. E. Balas and C.S. Yu. Finding a maximum clique in an arbitrary graph. SIAM Journal of Computing, 15(4):1054–1068, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  2. I.M. Bomze, M. Budinich, P.M. Pardalos, and M. Pelillo. The maximum clique problem. In D.-Z. Du and P.M. Pardalos, editors, Handbook of Combinatorial Optimization, volume 4, pages 1–74. Kluwer Academic Publishers, Boston, MA, 1999.

    Google Scholar 

  3. U. Feige, S. Goldwasser, L. Lovasz, S. Safra, and M. Szegedy. Approximating clique is almost np-complete. In Proc. 32nd Ann. IEEE Symp. Found. Comput. Sci., pages 2–12, 1991.

    Google Scholar 

  4. N. Funabiki and S. Nishikawa. Comparisons of energy-descent optimization algorithms for maximum clique. IEICE Trans. Fundamentals, E79-A(4):452–460, 1996.

    Google Scholar 

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

    MATH  Google Scholar 

  6. L. Gerhards and W. Lindenberg. Clique detection for nondirected graphs: two new algorithms. Computing, 21:295–322, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  7. S. Homer and M. Peinado. On the performance of polynomial-time clique approximation algorithms. In D.S. Johnson and M. Trick, editors, Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, 1996.

    Google Scholar 

  8. J.J. Hopfield and D.W. Tank. Neural computation of decisions in optimization problems. Biological Cybernetics, 52:141–152, 1985.

    MATH  MathSciNet  Google Scholar 

  9. R. Horaud and T. Skordas. Stereo correspondence through feature grouping and maximal cliques. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(11):1168–1180, 1989.

    Article  Google Scholar 

  10. A. Jagota. Approximating maximum clique with a Hopfield network. IEEE Trans. Neural Networks, 6:724–735, 1995.

    Article  Google Scholar 

  11. B.J. Jain and F. Wysotzki. Distance-based classification of structures within a connectionist framework. In R. Klinkenberg et al., editor, Proceedings Fachgrup pentreffen Maschinelles Lernen, 2001.

    Google Scholar 

  12. J.E. Lecky, O.J. Murphy, and R.G. Absher. Graph theoretic algorithms for the pla folding problem. IEEE Transactions on Computer Aided Design, 8(9):1014–1021, 1989.

    Article  Google Scholar 

  13. H. Ogawa. Labeled point pattern matching by delauney triangulation and maximal cliques. Pattern Recognition, 19(1):35–40, 1986.

    Article  Google Scholar 

  14. M. Pelillo, K. Siddiqi, and S.W. Zucker. Matching hierarchical structures using association graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(11):1105–1120, 1999.

    Article  Google Scholar 

  15. K. Schädler and F. Wysotzki. Application of a neural net in classification and knowledge discovery. In M. Verleysen, editor, Proc. ESANN’98, pages 117–122. D-Facto, Brussels, 1998.

    Google Scholar 

  16. K. Schädler and F. Wysotzki. Comparing structures using a Hopfield-style neural network. Applied Intelligence, 11:15–30, 1999.

    Article  Google Scholar 

  17. K.A. Smith. Neural networks for combinatorial optimisation: A review of more than a decade of research. INFORMS Journal on Computing, 11(1):15–34, 1999.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jain, B.J., Wysotzki, F. (2002). Fast Winner-Takes-All Networks for the Maximum Clique Problem. In: Jarke, M., Lakemeyer, G., Koehler, J. (eds) KI 2002: Advances in Artificial Intelligence. KI 2002. Lecture Notes in Computer Science(), vol 2479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45751-8_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-45751-8_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44185-4

  • Online ISBN: 978-3-540-45751-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics