A Hopfield network learning method for bipartite subgraph problem

IEEE Transactions on Neural Networks

Volumn 15, Issue 6, 2004, Pages 1458-1465

  Wang, Rong Long ^a   Tang, Zheng ^b   Cao, Qi Ping ^c  

^a UNIVERSITY OF FUKUI   (Japan)

^b UNIVERSITY OF TOYAMA   (Japan)

^c Tateyama Systems Institute   (Japan)

Author keywords

Bipartite subgraph problem; Gradient ascent learning; Hopfield neural network; NP complete problem; Total coloring problem

Indexed keywords

COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GRAPH THEORY; LEARNING ALGORITHMS; OPTIMIZATION; PARALLEL ALGORITHMS; PROBLEM SOLVING;

BIPARTITE SUBGRAPH PROBLEM; GRADIENT ASCENT LEARNING; HOPFIELD NEURAL NETWORK; TOTAL COLORING PROBLEM;

NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; COMPARATIVE STUDY; COMPUTER SIMULATION; DECISION SUPPORT SYSTEM; EVALUATION; FEEDBACK SYSTEM; METHODOLOGY; STATISTICAL MODEL;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; DECISION SUPPORT TECHNIQUES; FEEDBACK; LOGISTIC MODELS; NEURAL NETWORKS (COMPUTER); PATTERN RECOGNITION, AUTOMATED;

EID: 9244243659     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2004.836234     Document Type: Article

References (19)

1. R. Garey and S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1991.
2. M. R. Garey, D. S. Johnson, and L. J. Stockmeyer, "Some simplified NP-complete graph problem," Theor. Comput. Sci., vol. 1, pp. 237-267, 1976.
3. R. M. Karp, "Reducibility among combinatorial problems," in Complexity of Computer Computations. New York: Plenum, 1972, pp. 85-104.
4. S. Even and Y. Shiloach, "NP-completeness of several arrangement problems," Dept. Computer Science, Technion, Haifa, Israel, Tech. Rep. 43, 1975.
5. J. A. Bondy and S. C. Locke, "Largest bipartite subgraph in triangle-free graphs with maximum degree three," J. Graph Theory vol. 10, pp. 477-504, 1986.
6. M. Grotschel and W. R. Pulleyblank, "Weakly bipartite graphs and the max-cut problem," Oper. Res. Lett., vol. 1, pp. 23-27, 1981.
7. F. Barahona, "On some weakly bipartite graph," Oper Res. Lett., vol. 2, no. 5, pp. 239-242, 1983.
8. J. J. Hopfield and D. W. Tank, "Neural computation of decisions in optimization problems," Biol. Cybern., no. 52, pp. 141-152, 1985.
9. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Nat. Acad. Sci., vol. 81, pp. 3088-3092, 1984.
10. K. C. Lee, N. Funabiki, and Y. Takefuji, "A parallel improvement algorithm for the bipartite subgraph problem," IEEE Trans. Neural Networks, vol. 3, pp. 139-145, Jan. 1992.
11. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science, vol. 220, pp. 671-680, 1983.
12. K. Smith, M. Palaniswami, and M. Krishnamoorthy, "Neural techniques for combinatorial optimization with applications," IEEE Trans. Neural Networks, vol. 9, pp. 1301-1318, Nov. 1998.
13. D. E. Van der Bout and T. K. Miller, "Graph partitioning using annealed neural networks," IEEE Tran. Neural Networks, vol. 1, pp. 192-203, Mar. 1990.
14. P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications. Norwell, MA: Kluwer, 1988.
15. A. H. Gee, "Problem solving with optimization networks," Ph.D. dissertation, Queen's College, Cambridge, U.K., 1993.
16. D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon, "Optimization by simulated annealing: An experimental evaluation; Part 1: Graph partitioning," Oper. Res., vol. 37, no. 6, pp. 865-892, 1989.
17. A. Sanchez-Arroyo, "Determining the total coloring number is NP-hard," Discr. Math., vol. 78, pp. 315-319, 1989.
18. M. Behzad, "Graphs and their chromatic numbers," Ph.D. dissertation, Michigan State Univ., East Lansing, MI, 1965.
19. C. McDiarmid and B. Reed, "On total colorings of graphs," J. Combin. Theory Ser. B, vol. 57, pp. 122-130, 1993.