Neural network-based heuristic algorithms for hypergraph coloring problems with applications

Journal of Parallel and Distributed Computing

Volumn 63, Issue 9, 2003, Pages 786-800

  Kaznachey, Dmitri ^a   Jagota, Arun ^b   Das, Sajal ^c  

^a Portfolio Analytics and Research   (United States)

^b University of California Santa Cruz   (United States)

^c The University of Texas at Arlington   (United States)

Author keywords

Combinatorial optimization; Hopfield network; Hypergraph coloring

Indexed keywords

EID: 0242371116     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0743-7315(03)00064-9     Document Type: Article

References (20)

1. C. Berge, Graphs and Hypergraphs, North-Holland, New York, 1973.
2. P. Bofill, Optimizing neural networks for the generation of block designs, Ph.D. Thesis, Department of Computer Science, University of Catalunya, Barcelona, Spain.
3. S. Das, F. Sarkar, M.C. Pinotti, Conflict-free access of trees in parallel memory systems and its generalization, TR CRPDC-94-21, Department of Computer Science, University of North Texas, Denton, TX, 1994.
4. S. Das, F. Sarkar, Conflict-free data access of arrays and trees in parallel memory systems, Proceedings of the Sixth IEEE Symposium on Parallel and Distributed Systems, October, 1994.
5. T. Grossman, A neural computation approach to the set covering problem, Proceedings of the Neural Information Processing Systems Conference, 1995.
6. T. Grossman, A. Wool, Computational experience with approximation algorithms for the set covering problem, unpublished report, 1995.
7. K. Hertz, A. Krogh, R. Palmer, Introduction to the Theory of Neural Computation, Addison-Wesley, Reading, MA, 1991.
8. J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. 79 (1982) 2554-2558.
9. A. Jagota, Optimization by reduction to maximum clique, Proceedings of the International Conference on Neural Networks, New York, March 1993, pp. 1526-1531.
10. A. Jagota, Optimization by a Hopfield-style network, in: D.S. Levine, W. Elsberry (Eds.), Optimality in Artificial and Biological Networks, Lawrence Erlbaum, London, 1994.
11. A. Jagota, An adaptive, multiple restarts neural network algorithm for graph coloring, European J. Oper. Res. 93 (1996) 257-270.
12. A. Jagota, M. Garzon, On the mappings of optimization problems to neural networks, Proceedings of the World Congress on Neural Networks, IEEE, New York, June 1994, pp. 391-398.
13. D. Kaznachey, A. Jagota, An improved neural net algorithm for the hypergraph vertex cover problem, Proceedings of the International Conference on Neural Information Processing, Hong Kong, September 1996.
14. D. Kaznachey, A. Jagota, Approximating minimum set cover in a Hopfield-style network, Inform. Sci. 98 (1-4) (1997) 203-216.
15. D. Kaznachey, Neural network algorithms for hypergraph optimization problems, Ph.D. Thesis, Department of Mathematical Sciences, University of Memphis, 1998.
16. D. Kaznachey, A. Jagota, Neural net algorithms for the hypergraph uniform k-coloring problem, in: C. Dagli, M. Akay, O. Ersoy (Eds.), Intelligent Engineering Systems Through Artificial Neural Networks: Smart Engineering Systems: Neural Networks, Fuzzy Logic, Data Mining and Evolutionary Programming, Vol. 7, ASME Press, New York, 1997, pp. 917-923.
17. D. Kaznachey, A. Jagota, S. Das, Primal-target neural net heuristics for the hypergraph k-coloring problem, Proceedings of the International Conference on Neural Networks, Houston, 1997, pp. 1251-1255.
18. J.H.M. Korst, E.H.L. Aarts, Combinatorial optimization on a Boltzmann machine, J. Parallel Distrib. Comput. 6 (1989) 331-357.
19. C.H. Papadimitriou, K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Englewood Cliffs, NJ, 1982.
20. M. Trick, A. Mehrotra, A column generation approach to graph coloring, GSIA Technical Report Series, 1994, C program available in http://mat.gsia.cmu.edu/color/solvers/trick.c.