On efficient embeddings of grids into grids in PARIX

  • Thomas Römke
  • Markus Röttger
  • Ulf-Peter Schroeder
  • Jens Simon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 966)


A hardware independent method of programming a massively parallel machine (MPP) can best be supported by a well-designed run-time environment. An important problem in this design is the ability of efficiently simulating networks different from the hardware topology. We will describe the mapping kernel of the virtual processors library for the commercial run-time system PARIX3. This kernel contains description classes for several topologies (so-called virtual topologies) and implementations of respective embeddings which map given instances of virtual topologies onto others or onto the hardware. Using these functions, PARIX is able to establish concrete virtual topologies with corresponding communication channels. The implemented functions were selected with respect to the well-known criteria for graph embeddings: equal load and small dilation. Additionally, we focus on fast distributed computation and universal applicability. As an example, we will show new methods for efficiently embedding an arbitrary 2-dimensional grid as a guest graph into any 2-dimensional grid as a host graph.

Key words

parallel run-time system PARIX virtual processors embedding grids 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Thomas Römke
    • 1
  • Markus Röttger
    • 2
  • Ulf-Peter Schroeder
    • 2
  • Jens Simon
    • 1
  1. 1.Paderborn Center for Parallel Computing (PC2)University of PaderbornPaderbornGermany
  2. 2.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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