Efficiently approximating max-clique in a Hopfield-style network

The author approximates max-clique in a special case of the Hopfield network whose stable states are maximal cliques. Several energy-descent optimizing dynamics, both discrete and continuous, are presented. One of these emulates, as a special case, two well known greedy algorithms for approximating MAX-CLIQUE. Detailed empirical comparisons of random graphs are reported. Mean-field annealing, an efficient approximation to simulated annealing, is judged to be the most effective.<<ETX>>

[1]  László Lovász,et al.  Approximating clique is almost NP-complete , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  Jack Minker,et al.  An Analysis of Some Graph Theoretical Cluster Techniques , 1970, JACM.

[4]  Wesley E. Snyder,et al.  Optimization by Mean Field Annealing , 1988, NIPS.

[5]  Carsten Peterson,et al.  A New Method for Mapping Optimization Problems Onto Neural Networks , 1989, Int. J. Neural Syst..

[6]  Arun Jagota.  Applying a Hopfield-style network to degraded text recognition , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[7]  Yoshiyasu Takefuji,et al.  Parallel algorithms for finding a near-maximum independent set of a circle graph , 1990, IEEE Trans. Neural Networks.

[8]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Egon Balas,et al.  Finding a Maximum Clique in an Arbitrary Graph , 1986, SIAM J. Comput..

[10]  G. Grimmett,et al.  On colouring random graphs , 1975 .

[11]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12]  Pierluigi Crescenzi,et al.  A Note on the Approximation of the MAX CLIQUE Problem , 1991, Inf. Process. Lett..

[13]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.