A Tighter Upper Bound on the Worst Case Behavior of Conway's Parallel Sorting Algorithm

Abstract We analyze the worst case behavior of a parallel sorting algorithm, attributed to Conway, that uses a linear array of n − 1 finite state machines to sort n keys. Warshauer (J. Algorithms7 (1986), 270–276) shows that the algorithm requires at most 2n − 3 iterations of the outer loop to sort all keys, and he exhibits a class of inputs for which [ 4n 3 ] − 1 iterations are required. We improve the upper bound to 4n 3 + O(1) for all inputs and any n matching Warshauer's lower bound to within an additive constant.