Wavefront diffusion and LMSR: Algorithms for dynamic repartitioning of adaptive meshes

  • Schloegel K
  • Karypis G
  • Kumar V
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Abstract

Current multilevel repartitioning schemes tend to perform well on
certain types of problems while obtaining worse results for other types
of problems. We present two new multilevel algorithms for repartitioning
adaptive meshes that improve the performance of multilevel schemes for
the types of problems that current schemes perform poorly while
maintaining similar or better results for those problems that current
schemes perform well. Specifically, we present a new scratch-remap
scheme called Locally-matched Multilevel Scratch-remap (or simply LMSR)
for repartitioning of adaptive meshes. LMSR tries to compute a
high-quality partitioning that has a large amount of overlap with the
original partitioning. We show that LMSR generally decreases the data
redistribution costs required to balance the load compared to current
scratch-remap schemes. We present a new diffusion-based scheme that we
refer to as Wavefront Diffusion. In Wavefront Diffusion, the flow of
vertices moves in a wavefront from overweight to underweight subdomains.
We show that Wavefront Diffusion obtains significantly lower data
redistribution costs while maintaining similar or better edge-cut
results compared to existing diffusion algorithms. We also compare
Wavefront Diffusion with LMSR and show that these provide a trade-off
between edge-cut and data redistribution costs for a wide range of
problems. Our experimental results on a Gray T3E, an IBM SP2, and a
cluster of Pentium Pro workstations show that both schemes are fast and
scalable. For example, both are capable of repartitioning a seven
million vertex graph in under three seconds on 128 processors of a Gray
T3E. Our schemes obtained relative speedups of between nine and 12 when
the number of processors was increased by a factor of 16 on a Gray T3E

Author-supplied keywords

  • Adaptive mesh computations
  • Dynamic graph partitioning
  • LMSR
  • Multilevel diffusion
  • Scratch-remap
  • Wavefront diffusion

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Authors

  • Kirk Schloegel

  • George Karypis

  • Vipin Kumar

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