Advertisement

A better upper bound on the bisection width of de Bruijn networks

Extended abstract
  • Rainer Feldmann
  • Burkhard Monien
  • Peter Mysliwietz
  • Stefan Tschöke
Algorithms III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)

Abstract

We approach the problem of bisectioning the de Bruijn network into two parts of equal size and minimal number of edges connecting the two parts (cross-edges). We introduce a general method that is based on required substrings. A partition is defined by taking as one part all the nodes containing a certain string and as the other part all the other nodes. This leads to good bisections for a large class of dimensions. The analysis of this method for a special kind of substrings enables us to compute for an infinite class of de Bruijn networks a bisection, that has asymptotically only 2·ln(2) · 2n/n cross-edges. This improves previously known bisections with 4 · 2n/n cross-edges.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [BP89]
    J.C. Bermond and C. Peyrat. De Bruijn and Kautz networks: a Competitor for the Hypercube? In Proceedings of the 1st European Workshop on Hypercubes and Distributed Computers, pages 279–293. North-Holland, 1989.Google Scholar
  2. [DMP95]
    R. Diekmann, B. Monien and R. Preis. Using Helpful Sets to Improve Graph Bisections. In DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Am. Math. Society, 1995.Google Scholar
  3. [FMMT96]
    R. Feldmann, B. Monien, P. Mysliwietz and S. Tschöke. A Better Upper Bound on the Bisection Width of de Bruijn Networks Technical report, University of Paderborn, 1996, to appear.Google Scholar
  4. [HM91]
    J. Hromkovic and B. Monien. The Bisection Problem for Graphs of Degree 4 (configuring Transputer Systems). In Proceedings of the 16th Math. Foundations of Computer Science (MFCS'91), Springer LNCS 520, pp 211–220, 1991.Google Scholar
  5. [Lei92]
    F.T. Leighton. Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes. Morgan Kaufmann Publishers, 1992.Google Scholar
  6. [Len94]
    T. Lengauer. Combinatorial Algorithms for Integrated Circuit Layout. Teubner, 1994.Google Scholar
  7. [Mil60]
    E.P. Miles. Generalized Fibonacci Numbers and Associated Matrices. Am. Math. Month., pages 745–752, 1960.Google Scholar
  8. [Per95]
    S. Perennes. Personal communication. 1995.Google Scholar
  9. [SP89]
    M.R. Samatham and D.K. Pradhan. The de Bruijn Multiprocessor Network: A Versatile Parallel Processing and Sorting Network for VLSI. IEEE Transactions on Computers, 38(4):567–581, 1989.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rainer Feldmann
    • 1
  • Burkhard Monien
    • 1
  • Peter Mysliwietz
    • 1
  • Stefan Tschöke
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornGermany

Personalised recommendations