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Optimum simulation of meshes by small hypercubes

  • Bin Cong
  • Zevi Miller
  • I. H. Sudborough
Part II Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 464)

Abstract

We consider optimum simulations of large mesh networks by hypercubes. For any arbitrary mesh M, let "M's optimum hypercube" be the smallest hypercube that has at least as many processors as M and, for any k>0, let Q(M/2k) be "M's 1/2k-size hypercube", which has 1/2k as many processors as M's optimum hypercube. The ratio MI/Q(M/2k) is called M's 1/2 k - density. We show that (a) for every 2-D mesh M, if M's 1/2-density≤1.828, then M can be embedded into its 1/2-size hypercube with dilation 1 and load factor 2, (b) for every 2-D mesh M, if M's 1/4-density≤3.809, then M can be embedded into its 1/4-size hypercube with dilation 1 and load factor 4, and if M's 1/4-density≤2.8125, then M can be embedded into its 1/4-size hypercube with dilation 1 and load factor 3, (c) If every 2-D mesh M with 1/2k1-density≤a can be embedded into its 1/2k1-size hypercube with dilation 1 and load factor l1, and every 2-D mesh M with 1/2k2-density ≤b can be embedded into its 1/2k2-size hypercube with dilation 1 and load factor l2, then we can obtain the densities for load factor l1+l2 and load factor l1×l2 based on a, b.

Keywords

Load Factor Cycle Length Product Theorem Optimum Embedding Arbitrary Mesh 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Bin Cong
    • 1
  • Zevi Miller
    • 2
  • I. H. Sudborough
    • 1
  1. 1.Computer Science ProgramUniversity of Texas at DallasRichardson
  2. 2.Department of MathematicsMiami UniversityOxford

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