Early History

Abstract

The Bitonic Merge Sorting and the Odd–Even Merge Sorting algorithms are two parallel sorting algorithms. Both sort N keys in no more than log² N steps with no more than N/2 comparators in each step. To sort N keys using Bitonic Merge Sorting, firstly create two N/2 ordered lists: one in monotonic non-decreasing order and the other in monotonic non-increasing order. Then, apply bitonic merging to create two bitonic lists: H and L where H contains the largest N/2 keys and L contains the least N/2 keys. This would be repeated, recursively, until an N-key sorted list is generated. Odd–Even Merge Sorting of N-keys proceeds by merging two N/2 sorted lists A and B into the sorted list C. To do so, all the keys with odd indices in A and B are merged into one ordered list, D. Similarly, all the keys with even indices in A and B are merged into one ordered list, E. The first key in the output list C (i.e. c ₁) would be the first key in D. Then, each two consecutive keys in C would be obtained by comparing the i + 1th key in D with the ith key in E.