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 greater than equivalent to n, the time complexity of this problem is THETA (log n/log (1 plus p/n) are presented. This complements left bracket AKS-83 right bracket in settling the problem since the AKS sorting network established that for p greater than equivalent to n the time complexity is THETA (n log n/p). To prove the lower bounds we show that to achieve k greater than equivalent to log n parallel time, we need OMEGA (n**1** plus **1**/**k) processors.