Skip to main content

Edge-Disjoint Hamiltonian Cycles of WK-Recursive Networks

  • Conference paper
Applied Parallel Computing. State of the Art in Scientific Computing (PARA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3732))

Included in the following conference series:

Abstract

In this paper, we show that there exist n edge-disjoint Hamiltonian cycles in the WK-Recursive networks with amplitude 2n +1. By the aid of these edge-disjoint Hamiltonian cycles, nearly optimal all-to-all broadcasting communication on all-port WK-Recursive networks can be derived.

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

Access this chapter

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. Vecchia, G.D., Sanges, C.: A recursively scalable network VLSI implementation. Future Generat. Comput. Syst. 4, 235–243 (1988)

    Article  Google Scholar 

  2. Vecchia, G.D., Sanges, C.: An optimal broadcasting technique forWK-Recursive topologies. Future Generat. Comput. Syst. 5, 353–357 (1989/1990)

    Google Scholar 

  3. Leighton, F.T.: Introduction to Parallel Algorithms and Architectures: Arrays,Trees, Hypercubes. Mogran Kaufmann, California (1992)

    MATH  Google Scholar 

  4. Fernandes, R.: Recursive interconnection networks for multicomputer networks. In: Proceed. Int. Conf. Parallel Process., vol. 1, pp. 76–79 (1992)

    Google Scholar 

  5. Fernandes, R., Kanevsky, A.: Substructure allocation in recursive interconnection networks. In: Proceed. Int. Conf. Parallel Process., vol. 1, pp. 315–318 (1993)

    Google Scholar 

  6. Mahdaly, A.I., Mouftah, H.T., Hanna, N.N.: Topological properties of WK-recursive networks. In: Proceed. Second IEEE Workshop on Future Trends of Distributed Computing Systems, pp. 374–380 (1990)

    Google Scholar 

  7. Vecchia, G.D., Sanges, C.: Recursively scalable network for message passing architecture. In: Proceed. Int. Conf. Parallel Processing and Applications, May 1987, vol. 1, pp. 33–40 (1987)

    Google Scholar 

  8. Johnsson, S.L., Ho, C.T.: Optimum broadcasting and personalized communication in hypercubes. IEEE Transaction on Computers 38, 1249–1268 (1989)

    Article  MathSciNet  Google Scholar 

  9. Chartrand, G., Oellermann, O.R.: Applied and Algorithmic Graph Theory. McGraw-Hill, New York (1993)

    Google Scholar 

  10. Barth, D., Raspaud, A.: Two edge-disjoint Hamiltonian cycles in the butterfly graph. Inform. Process. Lett. 51, 175–179 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bermond, J.C., Favaron, O., Maheo, M.: Hamiltonian decomposition of Cayley graphs of degree four. J. Combin. Theory 46, 142–153 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fang, J.F., Lai, G.J., Liu, Y.C., Fang, S.T.: Anovel broadcasting scheme forWK-Recursive networks. In: Proceed. IEEE Pacific RIM Conference on Communications, Computers, and Signal Processing, pp. 1028–1031 (2003)

    Google Scholar 

  13. Fu, J.S.: Hamiltonian-connectedness of the WK-recursive network. In: Proceed. Int. Conf. Symposium on Parallel Architectures, Algorithms and Networks, pp. 569–574 (2004)

    Google Scholar 

  14. Wu, F., Hsu, C.C.: A generalized processor allocation scheme for recursively decomposable interconnection networks. IEICE Transactions on Information and Systems E85-D, 694–713 (2002)

    Google Scholar 

  15. d’Acierno, A., Del Balio, R., De Pietro, G., Vaccaro, R.: A parallel simulation of fully connected neural networks on a WK-recursive topology. In: Proceed. IEEE International Joint Conference on Neural Networks, pp. 1850–1854 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Huang, CH., Fang, JF., Yang, CY. (2006). Edge-Disjoint Hamiltonian Cycles of WK-Recursive Networks. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_132

Download citation

  • DOI: https://doi.org/10.1007/11558958_132

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29067-4

  • Online ISBN: 978-3-540-33498-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics