Harman Patil (Editor)

HBJ model

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In Computer Science Helman-Bader-JaJa model is a concise message passing model of parallel computation defined with the following parameters:

  • p is number of processors.
  • n is the problem size.
  • m is number of machine words in a packet sent over the network.
  • τ is the latency, or time at which a processor takes to initiate a communication on a network.
  • σ is the bandwidth, or time per machine word at which a processor can inject or receive m machine words from the network.
  • T c o m p is the largest computation time expended on a processor.
  • T c o m m is the time spent in communication on the network.
  • This model assumes that for any subset of q processors, a block permutation among the q processors takes ( τ + σ m ) time, where m is the size of the largest block.

    Analysis of common parallel algorithms

    Complexities of common parallel algorithms contained in the MPI libraries:

  • Point to point communication: O ( τ + σ m )
  • Reduction : O ( l o g ( p ) ( τ + σ m ) )
  • Broadcast: O ( l o g ( p ) ( τ + σ m ) )
  • Parallel prefix: O ( l o g ( p ) n p ( τ + σ m ) )
  • All to all: O ( p ( τ + σ m ) ) )
  • References

    HBJ model Wikipedia