Batcher's odd–even mergesort is a generic construction devised by Ken Batcher
Ken Batcher
Ken Batcher is an emeritus professor of Computer Science at Kent State University. He also worked as a computer architect at Goodyear Aerospace in Akron, Ohio for 28 years. In 1964, Batcher received his Ph.D. in electrical engineering from the University of Illinois...
A sorting network is an abstract mathematical model of a network of wires and comparator modules that is used to sort a sequence of numbers. Each comparator connects two wires and sorts the values by outputting the smaller value to one wire, and the larger to the other...
s 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
Donald Knuth
Donald Ervin Knuth is a computer scientist and Professor Emeritus at Stanford University.He is the author of the seminal multi-volume work The Art of Computer Programming. Knuth has been called the "father" of the analysis of algorithms...
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!"
It is popularized by the second GPU Gems book, 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
Python (programming language)
Python is a general-purpose, high-level programming language whose design philosophy emphasizes code readability. Python claims to "[combine] remarkable power with very clear syntax", and its standard library is large and comprehensive...
. The input is a list x of length a power of 2. The output is a list sorted in ascending order.
def compare_and_swap(x, a, b):
if x[a] > x[b]:
x[a], x[b] = x[b], x[a]
def oddeven_merge(x, lo, hi, r):
step = r * 2
if step < hi - lo:
oddeven_merge(x, lo, hi, step)
oddeven_merge(x, lo + r, hi, step)
for i in range(lo + r, hi - r, step):
compare_and_swap(x, i, i + r)
else:
compare_and_swap(x, lo, lo + r)
def oddeven_merge_sort_range(x, 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)
oddeven_merge_sort_range(x, lo, mid)
oddeven_merge_sort_range(x, mid + 1, hi)
oddeven_merge(x, lo, hi, 1)
