Computational Model

Random-Access Machine (RAM)

  • Unit cost for

    • any instruction on O(log(n))-bit words

    • Read/write a single memory location from an infinite memory

  • The cost measure: time complexity

variant: Parallel RAM (PRAM) model

Fork-Join Model

  • is the main model of parallel execution in the OpenMP framework

  • In addition to RAM instructions, you can also use in parallel and parallel for instructions.

mergesort(A, lo, hi):
  if lo < hi:
    mid = ⌊lo + (hi - lo) / 2
    fork mergesort(A, lo, mid) // process (potentially) in parallel with main task
      mergesort(A, mid, hi)    // main task handles second recursion
    join
      merge(A, lo, mid, hi)

Work-Span Model

  • For all computations, draw a DAG

    • A->B means that B can be performed only when A has been finished

  • Work: the total number of operations

  • Span (depth): the longest length of chain

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