Advertisement

Neural Processing Letters

, Volume 3, Issue 3, pp 139–149 | Cite as

Neural network for optimal steiner tree computation

  • Chotipat Pornavalai
  • Norio Shiratori
  • Goutam Chakraborty
Article
  • 26 Downloads

Abstract

Hopfield neural network model for finding the shortest path between two nodes in a graph was proposed recently in some literatures. In this paper, we present a modified version of Hopfield model to a more general problem of searching an optimal tree (least total cost tree) from a source node to a number of destination nodes in a graph. This problem is called Steiner tree in graph theory, where it is proved to be a NP-complete. Through computer simulations, it is shown that the proposed model could always find an optimal or near-optimal valid solution in various graphs.

Key words

Steiner tree neural networks Hopfield model optimization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Cavalieri, “Optimal path determination in a graph by hopfield neural network”, Neural Networks, Vol. 7, No. 2, pp. 397–404, 1994.Google Scholar
  2. 2.
    M. K. Mehmet and F. Kamoun, “Neural networks for shortest path computation and routing in computer networks”, IEEE Trans. on Neural Network, Vol. 4, No. 6, pp. 941–954, 1993.Google Scholar
  3. 3.
    L. Kou, G. Markowsky and L. Berman, “A fast algorithm for steiner trees”, Acta Informatica, 15: 141–145, 1981.Google Scholar
  4. 4.
    R. Widyono, “The design and evaluation of routing algorithms for real-time channels”, Technical Report TR-94-024, International Computer Science Institute, Berkeley, June 1994.Google Scholar
  5. 5.
    C. Pornavalai, G. Chakraborty and N. Shiratori, “Neural networks for solving constrained steiner tree problem”, in 1995 IEEE Int. Conf. on Neural Networks (ICNN'95), Perth Australia, November 1995.Google Scholar
  6. 6.
    D. W. Tank and J. Hopfield, “Simple neural optimization networks: an a/d converter, signal decision circuit, and a linear programming circuit” IEEE Trans on Circuits and Systems, Vol. 33, No. 5, pp. 533–541, 1986.Google Scholar
  7. 7.
    M. W. Dixon, G. R. Cole and M. I. Bellgard, “Using the hopfield neural network with mean field annealing to solve the shortest path problem in a communication network”, in 1995 IEEE Int. Conf. on Neural Networks (ICNN'95), Perth Australia, November 1995.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Chotipat Pornavalai
    • 1
  • Norio Shiratori
    • 1
  • Goutam Chakraborty
    • 2
  1. 1.Research Institute of Electrical CommunicationTohoku UniversitySendaiJapan
  2. 2.Software CenterThe University of AizuAizu-Wakamatsu cityJapan

Personalised recommendations