Skip to main content
SpringerLink
Log in

Graphs Partitioning: An Optimal MIMD Queueless Routing for BPC-Permutations on Hypercubes

  • Conference paper
Parallel Processing and Applied Mathematics (PPAM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6067))

Abstract

Bit-Permute-Complement permutations (BPC) constitute the subclass of particular permutations which have gained the more attention in the search of optimal routing of permutations on hypercubes. The reason of this attention comes from the fact that they care permutations for general-purpose computing like matrix transposing, vector reversal, bit shuffling and perfect shuffling. In this paper we revisit the optimal routing of BPC problem on hypercubes under MIMD queueless communication model through a new paradigm which takes advantage of their topology: the so-called graphs partitioning. We prove that BPC are partitionable in any dimension of the hypercube and that the resulting permutations are also BPC. It follows that any BPC on n-dimensional hypercube is routable in at most n steps of data exchanges, each one realizing the partition of the hypercube.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Draper, J.T., Ghosh, J.: Multipath e-cube algorithms (MECA) for adaptive wormhole routing and broadcasting in k-ary n-cubes. In: Proceedings of International Parallel Processing Symposium, pp. 407–410 (1992)

    Google Scholar 

  2. Szymanski, T.: On the permutation capability of a circuit switched hypercube. In: Proceedings of the 1989 International Conference on Parallel Processing, pp. I-103–I-110 (1989)

    Google Scholar 

  3. Lubiw, A.: Counter example to a conjecture of Szymanski on hypercube routing. Informations Processing Letters 35, 57–61 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  4. Shen, X., Hu, Q., Liang, W.: Realization of arbitrary permutations on a hypercube. Informations Processing Letters 51(5), 237–243 (1994)

    Article  MathSciNet  Google Scholar 

  5. Zhang, L.: Optimal bounds for matching routing on trees. In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, pp. 445–453 (1997)

    Google Scholar 

  6. Hwang, F., Yao, Y., Grammatikakis, M.: A d-move local permutation routing for d-cube. Discrete Applied Mathematics 72, 199–207 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hwang, F., Yao, Y., Dasgupta, B.: Some permutation routing algorithms for low dimensional hypercubes. Theoretical Computer Science 270, 111–124 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Vöcking, B.: Almost optimal permutation routing on hypercubes. In: Proceedings of the 33rd Annual ACM- Symposium on Theory of Computing, pp. 530–539. ACM Press, New York (2001)

    Google Scholar 

  9. Ramras, M.: Routing permutations on a graph. Networks 23, 391–398 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  10. Gu, Q.-P., Tamaki, H.: Routing a permutation in the hypercube by two sets of edge disjoint paths. J.of Parallel and Distr. Computing 44, 147–152 (1997)

    Article  MATH  Google Scholar 

  11. Laing, A.K., Krumme, D.W.: Optimal Permutation Routing for Low-dimensional Hypercubes. EEECS Tufts University (July 11, 2003)

    Google Scholar 

  12. Nassimi, D., Sahni, S.: Optimal BPC permutations on a cube connected SIMD computer. IEEE Trans. Comput. C-31(4), 338–341 (1982)

    Article  Google Scholar 

  13. Johnsson, S.L., Ho, C.T.: Algorithms for matrix transposition for boolean n-cube configured ensemble architectures. SIAM J. Matrix Appl. 9(3), 419–454 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  14. Johnsson, S.L., Ho, C.T.: Optimal communication channel utilization for matrix transpose and related permutations on boolean cubes. Disc. Appl. Math. 53(1-3), 251–274 (1994)

    Article  MathSciNet  Google Scholar 

  15. Berge, C.: Graphes, 3ème édition, Dunod, Paris (1983)

    Google Scholar 

  16. Neiman, V.I.: Structures et commandes des réseau18 sans blocage, Annales des Télécom (1969)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dpt. d’Informatique, Université de Metz - UFR MIM, Ile du Saulcy BP 80794, 57012, Metz Cedex 01, France

    Jean-Pierre Jung & Ibrahima Sakho

Authors
  1. Jean-Pierre Jung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ibrahima Sakho
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computational and Information Sciences, Czestochowa University of Technology,  

    Roman Wyrzykowski

  2. Department of Electrical Engineering and Computer Science, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack Dongarra

  3. Institute of Computer and Information Science, Czestochowa University of Technology, Dabrowskiego 73, PL-42-200, Czestochowa, Poland

    Konrad Karczewski

  4. Department of Informatics and Mathematical Modeling, Technical University of Denmark, Richard Petersens Plads, Building 321, 2800, Kongens Lyngby, Denmark

    Jerzy Wasniewski

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jung, JP., Sakho, I. (2010). Graphs Partitioning: An Optimal MIMD Queueless Routing for BPC-Permutations on Hypercubes. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2009. Lecture Notes in Computer Science, vol 6067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14390-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14390-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14389-2

  • Online ISBN: 978-3-642-14390-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation