Sequences of Discrete Hopfield’s Networks for the Maximum Clique Problem

  • G. Grossi
Conference paper
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)


We propose here a neural approximation technique for the Maximum Clique problem. The core of the method consists of a sequence of Hopfield’s networks that, in polynomial time, converge to a state representing a clique for a given graph. Some experiments made on the DIMACS benchmark show that the approximated solutions found are promising. Finally, the possibility to extend this technique to other NP-hard problems and to implement it onto neural hardware are discussed.


Maximum Clique problem constrained optimization Hopfield’s networks 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. A. Alberti, A. Bertoni, P. Campadelli, G. Grossi, and R. Posenato. A Neural Circuit for the Maximum 2-Satisfiability Problem. In Mateo Valero and Antonio Gonzalez, editors, Euromicro Workshop on Parallel and Distributed Processing, pages 319–323, Los Alamitos, CA, January, 25–27 1995. EUROMICRO, IEEE Computer Society Press.CrossRefGoogle Scholar
  2. 2.
    M. Bellare, O. Goldreich, and M. Sudan. Free bits, peps and non-approximability — towards tight results. In Technical Report TR95-024, Electronic Colluquium on Computational Complexity, 1996.Google Scholar
  3. 3.
    U. Feige, S. Goldwasser, S. Safra L. Lovasz, and M. Szegedy. Approximating clique is almost np-complete. In Proceedings of the 32nd Annual IEEE Symposium on the Foundations of Computer Science, pages 2–12, 1991.Google Scholar
  4. 4.
    J.J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. In Proceedings of the National Academy of Sciences, pages 2554–2558, 1982.Google Scholar
  5. 5.
    D.S. Johnson and M. Trick. Dimacs series in discrete mathematics and theoretical computer science. In Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challange. in press.Google Scholar
  6. 6.
    R.M. Karp. Reducibility among Combinatorial Problems, pages 85–103. Complexity of Computer Computations. Plenum Press, New York, 1972.Google Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • G. Grossi
    • 1
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly

Personalised recommendations