Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
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.
R.M. Karp. Reducibility among Combinatorial Problems, pages 85–103. Complexity of Computer Computations. Plenum Press, New York, 1972.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag London Limited
About this paper
Cite this paper
Grossi, G. (1998). Sequences of Discrete Hopfield’s Networks for the Maximum Clique Problem. In: Marinaro, M., Tagliaferri, R. (eds) Neural Nets WIRN VIETRI-97. Perspectives in Neural Computing. Springer, London. https://doi.org/10.1007/978-1-4471-1520-5_8
Download citation
DOI: https://doi.org/10.1007/978-1-4471-1520-5_8
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1522-9
Online ISBN: 978-1-4471-1520-5
eBook Packages: Springer Book Archive