Batcher odd–even mergesort

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Batcher odd–even mergesort
Visualization of the odd–even mergesort network with eight inputs
Visualization of the odd–even mergesort network with eight inputs
ClassSorting algorithm
Data structureArray
Worst-case performance parallel time
Best-case performance parallel time
Average performance parallel time
Worst-case space complexity non-parallel time

Batcher's odd–even mergesort is a generic construction devised by Ken Batcher for sorting networks of size O(n (log n)2) and depth O((log n)2), where n is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in 1998, with respect to the AKS network that "Batcher's method is much better, unless n exceeds the total memory capacity of all computers on earth!"[1]

It is popularized by the second GPU Gems book,[2] as an easy way of doing reasonably efficient sorts on graphics-processing hardware.

Pseudocode[edit]

Various recursive and iterative schemes are possible to calculate the indices of the elements to be compared and sorted. This is one iterative technique to generate the indices for sorting n elements:

# note: the input sequence is indexed from 0 to (n-1)
for p = 1, 2, 4, 8, ... # as long as p < n
  for k = p, p/2, p/4, p/8, ... # as long as k >= 1
    for j = mod(k,p) to (n-1-k) with a step size of 2k
      for i = 0 to k-1 with a step size of 1
        if floor((i+j) / (p*2)) == floor((i+j+k) / (p*2))
          compare and sort elements (i+j) and (i+j+k)

Non-recursive calculation of the partner node index is also possible.[3]

See also[edit]

References[edit]

  1. ^ D.E. Knuth. The Art of Computer Programming, Volume 3: Sorting and Searching, Second Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219–247.
  2. ^ https://developer.nvidia.com/gpugems/GPUGems2/gpugems2_chapter46.html
  3. ^ "Sorting network from Batcher's Odd-Even merge: partner calculation". Renat Bekbolatov. Retrieved 7 May 2015.

External links[edit]