Abstract
We present a neural approach for approximating the automorphism partitioning problem of a given graph. This approach combines the energy minimization process of neural networks for combinatorial optimization problems with simple group-theoretic properties. Neural networks are applied to rapidly find relevant automorphisms while group-theoretic information guides the search for these automorphisms.
Similar content being viewed by others
References
Ambler, A. P., Barrow, H. G., Brown, C. M., Burstall, R. M. and Popplestone, R. J.: A versatile computer-controlled assembly system. In: International Joint Conference on Artificial Intelligence, pp. 298–307. Stanford University, California, 1973.
Babel, L., Chuvaeva, I. V., Klin, M. and Pasechnik, D. V.: Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. II. Program Implementation of the Weisfeiler-Leman Algorithm. Technical Report TUM-M9701, Technical University Munich, 1997.
Bomze, I. M., Budinich, M., Pardalos, P. M. and Pelillo, M.: The maximum clique problem. In: D.-Z. Du and P. M. Pardalos, (eds.), Handbook of Combinatorial Optimization, 4, pp. 1–74. Kluwer Academic Publishers, Boston, MA, 1999.
Brualdi, R. A.: Introductory Combinatorics. Englewood Cliffs, N.J., 1992, Prentice Hall.
Jagota, A.: Approximating maximum clique with a Hopfield network, IEEE Trans. Neural Networks, 6 (1995), 724–735.
Jain, B. J. and Wysotzki, F.: Fast winner-takes-all networks for the maximum clique problem. In: 25th German Conference on Artificial Intelligence, pp. 163–173, 2002, Springer.
Pelillo, M.: Replicator equations, maximal cliques, and graph isomorphism, Neural Computation, 11(8) (1999), 1933–1955.
Pelillo, M., Siddiqi, K. and Zucker, S. W.: Matching hierarchical structures using association graphs, IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(11) (1999), 1105–1120.
Ponomarenko, I. N.: Graph algebras and the graph isomorphism problem, Appl. Algebra Engrg. Comm. Comput., 5 (1994), 277–286.
Smith, K. A.: Smith Neural networks for combinatorial optimization: A review of more than a decade of research, INFORMS Journal on Computing, 11(1) (1999), 15–34.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jain, B.J., Wysotzki, F. Automorphism Partitioning with Neural Networks. Neural Processing Letters 17, 205–215 (2003). https://doi.org/10.1023/A:1023657727387
Issue Date:
DOI: https://doi.org/10.1023/A:1023657727387