Skip to main content
SpringerLink
Log in

A new neural network algorithm for planarization problems

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

To deal with the planarization problem widely used in many applications including routing very-large-scale integration (VLSI) circuits, this paper points out that only when its vertices are arranged in some specific order in a line can a planar graph be embedded on a line without any cross connections or cross edges. Energy function is proposed to meet the need of embedding a graph on a single line and route it correctly. A Hopfield network is designed according to the proposed energy function for such embedding and routing. The advantage of the proposed method is that it not only can detect if a graph is a planar one or not, but also can embed a planar graph or the maximal planar subgraph of a non-planar graph on a single line. In addition, simulated annealing is employed for helping the network to escape from local minima during the running of the Hopfield network. Experiments of the proposed method and its comparison with some existent conventional methods were performed and the results indicate that the proposed method is of great feasibility and effectiveness especially for the planarization problem of large graphs.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Jayakumar R, Thulasiraman K, Swamy M N S. O(n 2) algorithms for graph planarization. IEEE Trans Comp Aid Des Integr Circ Syst, 1989, 8(3): 257–267

    Article  Google Scholar 

  2. Garey M R, Johnson D S. Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979

    MATH  Google Scholar 

  3. Cai J, Hans X, Tarjan R E. An O(m log n)-time algorithm for the maximal planar subgraph problem. SIAM J Comp, 1993, 22(6): 1142–1162

    Article  MATH  Google Scholar 

  4. Takefuji Y, Lee K-C. A near-optimum parallel planarization algorithm. Science, 1989, 245(15): 1221–1223

    Article  Google Scholar 

  5. Gladkov L A, Kurejchik V M. A genetic algorithm for planarization of graphs (in Russian). Izv Akad Nauk, 2004, 5: 113–126

    Google Scholar 

  6. Wang R-L, Okazaki K. Solving the graph planarization problem using an improved genetic algorithm. IEICE Trans Fund Electr Commun Comput Sci, 2006, E89-A(5): 1507–1512

    Google Scholar 

  7. Dujmović V, Fellows M, Hallett M, et al. A fixed-parameter approach to two-layer planarization. In: Graph Drawing. 9th International Symposium, GD 2001. Revised Papers. Lect Notes in Comput Sci, Vol 2265. Berlin: Springer-Verlag, 2002. 1–4

    Google Scholar 

  8. Lu S X. Dynamic elimination method for solving TSP by Hopfield network (in Chinese). J Zhejiang Univ, 2005, 32(3): 278–291

    Google Scholar 

  9. Xu D X, Qian F C. Optimal control of discrete bilinear system based on the Hopfield neural network (in Chinese). Inf Contr, 2006, 35(1): 90–92

    MathSciNet  Google Scholar 

  10. Cimikowski A, Shope P. A neural-network algorithm for a graph layout problem. IEEE Trans Neural Netw, 1996, 7(2): 341–345

    Article  Google Scholar 

  11. Yiu K F C, Liu Y, Teo K L. A hybrid descent method for global optimization. J Global Optim, 2004, 28(2): 229–238

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, Xidian University, Xi’an, 710071, China

    JunYing Zhang & Qiang Qin

Authors
  1. JunYing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiang Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to JunYing Zhang.

Additional information

Supported by the Sino-Italy Joint Cooperation Project and the National Visiting Scholar fund of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, J., Qin, Q. A new neural network algorithm for planarization problems. Sci. China Ser. F-Inf. Sci. 51, 1947–1957 (2008). https://doi.org/10.1007/s11432-008-0134-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-008-0134-x

Keywords

Search

Navigation