On the Average Running Time of Odd-Even Merge Sort

Trus paper is concerned with the average rUDDing time of Batcher's odd-even merge sort when implemented on a collection of processors. We consider the case where n, the size of the input, is an arbitrary multiple of the number p of processors used. We show that Batcher's odd-even merge (for two sorted lists of length n each) can be implemented to run in time O«nlp)(log(2 + p2 In))) on the average, and that odd-even merge sort can be implemented to run in time 0 « n I p )(log n + log p log( 2 + p2 In))) on the average. In the case of merging (sorting), theaverage is taken over all possible outcomes of the merging (all possible permutations of n elements). That means that odd-even merge and odd-even merge sort have an optimal average running time if n ~ p2. The constants involved are also quite small.