Optimal time-space trade-offs for sorting

We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space)for this problem. Beame has shown a lower bound of Omega(n(2)) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n(2) log n) due to Frederickson. Since then, no progress has been made towards tightening this gap. The main contribution of this paper is a comparison based sorting algorithm which closes the gap by meeting the lower bound of Beame. The time-space product O(n(2)) upper bound holds for the full range of space bounds between log n and n/log n. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame.