parallel prefix computation


Definition: Calculate an associative function, f, on all prefixes of an n-element array, that is, s[0], f(s[0], s[1]), f(s[0], f(s[1], s[2])), …, f(s[0], f(s[1], … f(s[n-2], s[n-1])…)), using Θ(n) processors in Θ(log n) time. The algorithm is

 for j := 0 to lg(n)-1 do 
for i := 2j to n-1 parallel-do
s[i] := f(s[i-2j], s[i])
where lg is the logarithm base 2, and parallel-do does the innermost computations in parallel.

Note: In particular, this calculates any associative function, such as sum, maximum, or concatenate, over a list of values in logarithmic time. Note the write-after-read hazards in the parallel-do loop: old values of s[2j] to s[n-1-2j] must be read before being overwritten. Since this algorithm overwrites the initial values, the n processors can copy input values to a result array in parallel in one additional step.
From Yair Tuaff (, 29 December 1999.

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 25 January 2010.
HTML page formatted Wed Mar 13 12:42:46 2019.

Cite this as:
Paul E. Black, "parallel prefix computation", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed. 25 January 2010. (accessed TODAY) Available from: