Optimal Parallel Merging by Counting

We present a new optimal deterministic parallel algorithm for merging two sorted arrays A = (a
₀
, a
₁
, ... , a
_n1
- 1) and B = (b
₀
, b
₁
, ... , b
_n2
- 1) of integers. The elements of two sorted arrays are drawn from a domain of integers [0, n - 1], where n = Max(n
₁
, n
₂
). The algorithm takes O(log n) time and O(n) space using n/log n processors on EREW PRAM. Also, the algorithm is stable