Optimization by a Hopfield-Style Network

Optimality in Biological and Artificial Networks?

Volumn , Issue , 2013, Pages 203-226

  Jagota, Arun ^a,b  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b University of California Santa Cruz   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 49949103183     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203773833-19     Document Type: Chapter

References (44)

1. Aarts, E., and Korst, J. (1989). Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. New York: Wiley.
2. Adorf, H., and Johnston, M. D. (1990, June). A discrete stochastic neural network for constraint satisfaction problems. International Joint Conference on Neural Networks (Vol. 3, pp. 917-924). San Diego: IEEE.
3. Akiyama, Y., Yamashita, A., Kajiura, M.. and Aiso, H. (1989). Combinatorial optimization with gaussian machines. In International Joint Conference on Neural Networks (Vol. 1, pp. 533-540). Piscataway, NJ: IEEE.
4. Arora, S., Lund, C, Motwani, R., Sudan, M., and Szegedy, M. (1992). Proof verification and hardness of approximation problems. Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science (pp. 14-23). IEEE Computer Science Society Press.
5. Ballard, D. H., Gardner, P. C, and Srinivas, M. A. (1987). Graph problems and connectionist architectures (Tech. Rep. No. 167) Department of Computer Science, University of Rochester.
6. Baram, Y., and Dechter, R. (1991). Processing constraints by neural networks. Department of Computer and Information Science, University of California, Irvine, June, unpublished.
7. Barrow, H., and Burstall, R. (1976). Subgraph isomorphism, matching relational structures and maximal cliques. Information Processing Letters, 4, 83-84.
8. Bollobas, B., and Erdos, P. (1976). Cliques in random graphs. Proceedings of the Cambridge Philosophical Society, 80, 419-427.
9. Bourret, P., and Gaspin, C. (1992). A neural based approach of constraints satisfaction problem. In International Joint Conference on Neural Networks, Baltimore, June, 1992 (Vol. 4, pp. 588-593). Piscataway, NJ: IEEE.
10. Caspi, Y. (1992). The performance of an artificial neural network for graph coloring. In C. H. Dagli, L. I. Burke, and Y. C. Shin (Eds.), Intelligent Engineering Systems Through Artificial Neural Networks (Vol. 2, pp. 319-324). New York: ASME Press.
11. Chen, W., and Hsieh, K. (1989). A neural network for 3-satisfiability problems. In International Joint Conference on Neural Networks, Washington, DC, June, 1989 (Vol. 2, p. 587). Piscataway, NJ: IEEE. Abstract in Proceedings.
12. Crescenzi, P., Fiorini, C, and Silvestri, R. (1991). A note on the approximation of the maxclique problem. Information Processing Letters, 40, 1-5.
13. Dahl, E. D. (1987). Neural networks algorithms for an np-complete problem: map and graph coloring. In IEEE First International Conference on Neural Networks (Vol. 3, pp. 113-120). San Diego: IEEE/ICNN.
14. Freige, U., Goldwasser, S., Lovasz, L., Safra, S., and Szegedy, M. (1991). Approximating clique is almost NP-complete. In Symposium on Foundations of Computer Science (pp. 2-12). IEEE Computer Science Society Press.
15. Garey, M. R., and Johnson, D. S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: Freeman.
16. Godbeer, G. H., Lipscomb, J., and Luby, M. (1988). On the computational complexity of finding stable stale vectors in connectionisl models (Hopfield nets) (Tech. Rep. No. 208/88). Department of Computer Science, University of Toronto.
17. Griggs, J. R. (1983). Lower bounds on the independence number in terms of the degrees. Journal of Combinatorial Theory, Series B, 34, 22-39.
18. Grossman, T., and Jagota, A. (1992). On the equivalence of two {Hopfield}-type networks. In IEEE International Conference on Neural Networks (pp. 1063-1068). Piscataway, NJ: IEEE.
19. Hertz, J., Krogh, A., and Palmer, R. G. (1991). Introduction to the Theory of Neural Computation. Reading, MA: Addison-Wesley.
20. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, USA, 79, 2554-2558.
21. Hopfield, J. J. (1984). Neurons with graded responses have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences, USA, 81, 3088-3092.
22. Jagota, A. (1990a). A HopfieId-style network as a maximal clique graph machine (Tech. Rep. No. 90-25). Department of Computer Science, SUNY at Buffalo.
23. Jagota, A. (1990b). A new Hopfield-slyle network for content-addressable memories (Tech. Rep. No. 90-02). Department of Computer Science, SUNY at Buffalo.
24. Jagota, A. (1991). Backtracking dynamics in a Hopfield-style network. In International Joint Conference on Neural Networks, Seattle, July, 1991. Piscataway, NJ: IEEE. Abstract in Proceedings.
25. Jagota, A. (1992a). Efficiently approximating Max-Clique in a Hopfield-style network. In International Joint Conference on Neural Networks (Vol. 2, pp. 248-253). Piscataway, NJ: IEEE.
26. Jagota, A. (1992b). On the computational complexity of analyzing the Hopfie Id-clique network Unpublished manuscript, Department of Computer Science, SUNY at Buffalo.
27. Jagota, A. (1994). A Hopfield-style network with a graph-theoretic characterization. Journal of Artificial Neural Networks, 1, 145-166.
28. Jagota, A., and Regan, K. W. (1992). Performance of max-clique heuristics under description-length weighted distributions (Tech. Rep. No. 92-24). Department of Computer Science, SUNY at Buffalo.
29. Kajiura, M., Akiyama, Y., and Anzai, Y. (1989). Neural networks vs. tree search in puzzle solving. In International Joint Conference on Neural Networks, Washington, DC, June, 1989 (Vol. 2, p. 588). Piscataway, NJ: IEEE. Abstract in Proceedings.
30. Karp, R. M. (1972). Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher (Eds.), Complexity of Computer Computations (pp. 85-103). New York: Plenum Press.
31. Karp, R. M. (1976). The probabilistic analysis of some combinatorial search algorithms. In J. F. Traub (Ed.), Algorithms and Complexity: New Directions and Recent Results (pp. 1-19). New York: Academic Press.
32. Korst, J. H. M., and Aarts, E. H. L. (1989). Combinatorial optimization on a Boltzmann machine. Journal of Parallel and Distributed Computing, 6, 331-357.
33. Koutsoupias, E., and Papadimitriou, C. H. (1992). On the greedy algorithm for satisfiability. Information Processing Letters, 43, 53-55.
34. Mackworth, A. K. (1992). Constraint satisfaction. In S. C. Shapiro (Ed.), Encyclopedia of Artificial Intelligence (2nd ed., pp. 285-290). New York: Wiley.
35. Motwani, R. (1992). Lecture notes on approximation algorithms (Tech. Rep.) Department of Computer Science, Stanford University.
36. Nadel, B. A. (1989). Representation selection for constraint satisfaction: A case study using fl-queens. IEEE Expert, 2, 16-23.
37. Palmer, E. M. (1985). Graphical Evolution. New York: Wiley. (Matula’s theorem is on page 76).
38. Pinkas, G. (1991). Symmetric neural nets and propositional logic satisfiability. Neural Compulation, 3, 282-291.
39. Ramanujam, J., and Sadayappan, P. (1988). Optimization by neural networks. In IEEE International Conference on Neural Networks, San Diego, June, 1988 (Vol. 2, pp. 325-332). Piscataway, NJ: IEEE.
40. Shrivastava, Y., Dasgupta, S., and Reddy, S. M. (1990). Neural network solutions to a graph theoretic problem. In Proceedings of IEEE International Symposium on Circuits and Systems (pp. 2528-2531). New York: IEEE.
41. Spencer, J. (1987). Random graphs ii. In J. Spencer (Ed.), Ten Lectures on the Probabilistic Method (pp. 51-56). Philadelphia: Society for Industrial and Applied Mathematics.
42. Tagliarini, G. A., and Page, E. (1987). Solving constraint satisfaction problems with neural networks. In IEEE First International Conference on Neural Networks (Vol. 3, pp. 741-747). San Diego: IEEE/ICNN.
43. Takefuji, Y. (1992). Neural network models and /V-queen problems. In Y. Takefuji (Ed.), Neural Network Parallel Computing (pp. 1-26). Boston: Kluwer.
44. Turner, J. S. (1988). Almost all k-colorable graphs are easy to color. Journal of Algorithms, 9, 63-82.