Skip to main content
SpringerLink
Log in

An Algorithm Based on Hopfield Network Learning for Minimum Vertex Cover Problem

  • Conference paper
Advances in Neural Networks – ISNN 2004 (ISNN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3173))

Included in the following conference series:

Abstract

An efficient algorithm for the minimum vertex cover problem based on Hopfield neural network leaning is presented. The learning algorithm has two phases, the Hopfield network phase and the learning phase. When network gets stuck in local minimum, the learning phase is performed in an attempt to fill up the local minimum valley by modifying parameter in a gradient ascent direction of the energy function. The proposed algorithm is tested on benchmark graphs. The simulation results show that the proposed algorithm is an effective algorithm for the minimum vertex cover problem in terms of the computation time and solution quality.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Khuri, S., Back, T.: An Evolutionary Heuristic for the Minimum Vertex Cover Problem. In: KI-1994 Workshops, Bonn, pp. 83–84 (1994) (extended abstracts)

    Google Scholar 

  2. Karp, R.M.: Reducibility Among Combinatorial Problems. Complexity of Computer Computation, pp. 85–103. Plenum Press, New York (1972)

    Google Scholar 

  3. Dehne, F., et al.: Solving Large FPT Problems on Coarse Grained Parallel Machines. Available: http://www.scs.carleton.ca/~fpt/papers/index.htm

  4. Sanchis, L.A.: Generating Hard and Diverse Test Sets for NP-hard Graph Problems. Discrete Applied Mathematics 58, 35–66 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hopfield, J.J., Tank, D.W.: Neural Computation of Decisions in Optimization Problems. Bio. Cybern. 52, 141–152 (1985)

    MATH  MathSciNet  Google Scholar 

  6. Downey, R.G., Fellows, M.R.: Fixed Parameter Tractability and Completeness II: Completeness for W [1]. Theoretical Computer Science 141, 109–131 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Sanchis, L.A.: Test Case Construction for the Vertex Cover Problem. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 15, 315–326 (1994)

    Google Scholar 

  8. Cao, Q.P., Tang, Z., Wang, R.L.: A Gradient Ascent Learning Algorithm in Weight Domain for Hopfield Neural Network. IEEJ Trans. EIS 122(4), 677–683 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, Toyama University, 930-8555, Toyama, Japan

    Xiaoming Chen, Zheng Tang, Xinshun Xu, Guangpu Xia & Jiahai Wang

  2. Faculty of Information, ShenYang University of Technology, 110023, Shenyang, China

    Xiaoming Chen

  3. Faculty of Engineering, Toyama Prefectural University, 939-0398, Toyama, Japan

    Songsong Li

Authors
  1. Xiaoming Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinshun Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Songsong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Guangpu Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jiahai Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Electronic and Information Engineering, Dalian University of Technology, 116023, Dalian, China

    Fu-Liang Yin

  2. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China

    Jun Wang

  3. School of Electronic and Information Engineering, Dalian University of Technology, 116023, Dalian, Liaoning, China

    Chengan Guo

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, X., Tang, Z., Xu, X., Li, S., Xia, G., Wang, J. (2004). An Algorithm Based on Hopfield Network Learning for Minimum Vertex Cover Problem. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_72

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-28647-9_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22841-7

  • Online ISBN: 978-3-540-28647-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation