Optimal Time-Space Trade-Offs for Sorting

Jakob Pagter
Theis Rauhe

May 1998


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 tex2html_wrap_inline20 for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of tex2html_wrap_inline22 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 this gap by meeting the lower bound of Beame. The time-space product tex2html_wrap_inline24 upper bound holds for the full range of space bounds between tex2html_wrap_inline26 and tex2html_wrap_inline28. Hence in this range our algorithm is optimal for comparison based models as well as for the very powerful general models considered by Beame

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