On embedding 2-dimensional toroidal grids into de Bruijn graphs with clocked congestion one

  • Thomas Andreae
  • Michael Nölle
  • Christof Rempel
  • Gerald Schreiber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1120)


For integers m, d, D with m≥3, d≥2, and D≥2, let T(m) be a 2-dimensional quadratic toroidal grid with side length m and let B(d,D) be the base d, dimension D de Bruijn graph; assume that ¦T(m)¦=¦B(d, D)¦. The starting point for our investigations is the observation that, for m, D even, embeddings f:T(m)B(d, D) with load 1, expansion 1, and dilation D/2 can easily be found (and have previously been described in the literature). In the present paper, we pose the question whether or not there exist embeddings f:T(m)B(d, D) with these properties and with clocked congestion 1. We prove results implying a positive answer to this question when d is greater than two. For d=2, we do not have a complete answer, but present partial results.

Key words

de Bruijn graphs toroidal grids graph embeddings clocked congestion dilation interconnection networks parallel computers 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Thomas Andreae
    • 1
  • Michael Nölle
    • 2
  • Christof Rempel
    • 1
  • Gerald Schreiber
    • 2
  1. 1.Mathematisches SeminarUniversität HamburgHamburgGermany
  2. 2.Technische Informatik ITechnische Universität Hamburg-HarburgHamburgGermany

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