SDSU CS 662 Theory of Parallel Algorithms
Odd-Even Sort

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San Diego State University -- This page last updated February 20, 1996, 1996
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References


Akl, The Design and Analysis of Parallel Algorithms, section 4.3
Rescheduling Principle

A parallel machine model satisfies the rescheduling principle (or slow down principle) if given an algorithm with time complexity T on P processors and given any s, 1 <= s <= p the algorithm can be run in s*T time using at most processors.

Models with uniform cost per access of shared memory satisfy the rescheduling principle.

proof: Draw picture and wave hands
Odd-Even Transposition Sort


Assume each processor PJ contains one element xJ, for J = 1, 2, ..., N


Odd-Even Transposition Sort
for K = 1 to do
for I = 1, 3, 5, ..., do in parallel
if xI> xI+1 then swap(xI,xI+1)
end for
for I = 2, 4, 6, ..., do in parallel
if xI> xI+1 then swap(xI,xI+1)
end for
end for

A Better Odd-Even Transposition Sort


Assume we have P processors and N items to sort

Each processor has items

Pad the last processor with to insure it has items

Let SJ be the items in processor PJ

Odd-Even Transposition Sort
	for K = 1 to P do in parallel
		QuickSort(SK)
	end for
	for K = 1 to  do
		for I = 1, 3, 5, ...,  do in parallel
			(s1, s2, s3, ..., ) = sequential merge(SI, SI+1)
			SI = (s1, s2, s3, ..., )
			SI+1 = ( ,  ..., )
		end for

		for I = 2, 4, 6, ...,  do in parallel
			(s1, s2, s3, ..., ) = sequential merge(SI, SI+1)
			SI = (s1, s2, s3, ..., )
			SI+1 = ( ,  ..., )
		end for
end for

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