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Undid revision by The Anome – "near each point locally"? That's a tautology (rhetoric)
 
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{{Infobox Algorithm
|class=[[Sorting algorithm]]
|image=[[File:Batcher Odd-Even Mergesort for eight inputs.svg|Visualization of the odd–even mergesort network with eight inputs]]
|caption=Visualization of the odd–even mergesort network with eight inputs
|data=[[Array data structure|Array]]
|best-time= <math>O(\log^2(n))</math> parallel time
|average-time= <math>O(\log^2(n))</math> parallel time
|time=<math>O(\log^2(n))</math> parallel time
|space=<math>O(n\log^2(n))</math> comparators
|optimal=No
}}


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'''Batcher's odd–even mergesort''' is a generic construction devised by [[Ken Batcher]] for [[sorting network]]s of size O(''n''&nbsp;(log&nbsp;''n'')<sup>2</sup>) and depth O((log&nbsp;''n'')<sup>2</sup>), where ''n'' is the number of items to be sorted. Although it is not asymptotically optimal, [[Donald Knuth|Knuth]] concluded in 1998, with respect to the [[Sorting_network#Optimal_sorting|AKS network]] that "Batcher's method is much better, unless ''n'' exceeds the total memory capacity of all computers on earth!"<ref>[[Donald Knuth|D.E. Knuth]]. ''[[The Art of Computer Programming]]'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219&ndash;247.</ref>


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It is popularized by the second ''[[GPU Gems]]'' book,<ref>http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter46.html</ref> as an easy way of doing reasonably efficient sorts on graphics-processing hardware.


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== Example code ==
 
The following is an implementation of odd–even mergesort algorithm in [[Python (programming language)|Python]]. The input is a list ''x'' of length a power of 2. The output is a list sorted in ascending order.
<source lang="python">
def oddeven_merge(lo, hi, r):
    step = r * 2
    if step < hi - lo:
        yield from oddeven_merge(lo, hi, step)
        yield from oddeven_merge(lo + r, hi, step)
        yield from [(i, i + r) for i in range(lo + r, hi - r, step)]
    else:
        yield (lo, lo + r)
 
def oddeven_merge_sort_range(lo, hi):
    """ sort the part of x with indices between lo and hi.
 
    Note: endpoints (lo and hi) are included.
    """
    if (hi - lo) >= 1:
        # if there is more than one element, split the input
        # down the middle and first sort the first and second
        # half, followed by merging them.
        mid = lo + ((hi - lo) // 2)
        yield from oddeven_merge_sort_range(lo, mid)
        yield from oddeven_merge_sort_range(mid + 1, hi)
        yield from oddeven_merge(lo, hi, 1)
 
def oddeven_merge_sort(length):
    """ "length" is the length of the list to be sorted.
    Returns a list of pairs of indices starting with 0 """
    yield from oddeven_merge_sort_range(0, length - 1)
 
def compare_and_swap(x, a, b):
    if x[a] > x[b]:
        x[a], x[b] = x[b], x[a]
</source>
<source lang="pycon">
>>> data = [2, 4, 3, 5, 6, 1, 7, 8]
>>> pairs_to_compare = list(oddeven_merge_sort(len(data)))
>>> pairs_to_compare
[(0, 1), (2, 3), (0, 2), (1, 3), (1, 2), (4, 5), (6, 7), (4, 6), (5, 7), (5, 6), (0, 4), (2, 6), (2, 4), (1, 5), (3, 7), (3, 5), (1, 2), (3, 4), (5, 6)]
>>> for i in pairs_to_compare: compare_and_swap(data, *i)
>>> data
[1, 2, 3, 4, 5, 6, 7, 8]
</source>
 
==See also==
* [[Bitonic sorter]]
 
== References ==
{{reflist}}
 
==External links==
*[http://www.iti.fh-flensburg.de/lang/algorithmen/sortieren/networks/oemen.htm Odd–even mergesort] at fh-flensburg.de
 
{{sorting}}
 
{{DEFAULTSORT:Batcher odd-even mergesort}}
[[Category:Sorting algorithms]]
 
 
{{algorithm-stub}}

Revision as of 13:26, 3 January 2014

Template:Infobox Algorithm

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.

Example code

The following is an implementation of odd–even mergesort algorithm in Python. The input is a list x of length a power of 2. The output is a list sorted in ascending order. 

def oddeven_merge(lo, hi, r):
    step = r * 2
    if step < hi - lo:
        yield from oddeven_merge(lo, hi, step)
        yield from oddeven_merge(lo + r, hi, step)
        yield from [(i, i + r) for i in range(lo + r, hi - r, step)]
    else:
        yield (lo, lo + r)

def oddeven_merge_sort_range(lo, hi):
    """ sort the part of x with indices between lo and hi.

    Note: endpoints (lo and hi) are included.
    """
    if (hi - lo) >= 1:
        # if there is more than one element, split the input
        # down the middle and first sort the first and second
        # half, followed by merging them.
        mid = lo + ((hi - lo) // 2)
        yield from oddeven_merge_sort_range(lo, mid)
        yield from oddeven_merge_sort_range(mid + 1, hi)
        yield from oddeven_merge(lo, hi, 1)

def oddeven_merge_sort(length):
    """ "length" is the length of the list to be sorted.
    Returns a list of pairs of indices starting with 0 """
    yield from oddeven_merge_sort_range(0, length - 1)

def compare_and_swap(x, a, b):
    if x[a] > x[b]:
        x[a], x[b] = x[b], x[a]

>>> data = [2, 4, 3, 5, 6, 1, 7, 8]
>>> pairs_to_compare = list(oddeven_merge_sort(len(data)))
>>> pairs_to_compare
[(0, 1), (2, 3), (0, 2), (1, 3), (1, 2), (4, 5), (6, 7), (4, 6), (5, 7), (5, 6), (0, 4), (2, 6), (2, 4), (1, 5), (3, 7), (3, 5), (1, 2), (3, 4), (5, 6)]
>>> for i in pairs_to_compare: compare_and_swap(data, *i)
>>> data
[1, 2, 3, 4, 5, 6, 7, 8]

See also

References

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External links

Template:Sorting


Template:Algorithm-stub

  1. ↑ D.E. Knuth. The Art of Computer Programming, Volume 3: Sorting and Searching, Third Edition. Addison-Wesley, 1998. ISBN 0-201-89685-0. Section 5.3.4: Networks for Sorting, pp. 219–247.
  2. ↑ http://http.developer.nvidia.com/GPUGems2/gpugems2_chapter46.html
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