Tight Comparison Bounds on the Complexity of Parallel Sorting

The problem of sorting n elements using p processors in a parallel comparison model is considered. Lower and upper bounds which imply that for p ≥ n, the time complexity of this problem is Θ( log( 1 + p / n) logn _ __________ ) are presented. This complements [AKS-83] in settling the problem since the AKS sorting network established that for p≤n the time complexity is Θ( p nlogn _ _____ ). To prove the lower bounds we show that to achieve k ≤ logn parallel time, we need Ω(n 1 + 1/ k ) processors.