Sorting with minimum data movement (preliminary draft)

Abstract

In this paper, we ask whether one can sort a list of n elements using constant extra space and O(n lg n) comparisons, but only a linear number of data movements. We develop an in-place algorithm that sorts n distinct elements using linear data movements and making O(n lg n) comparisons on the average. We also improve on the existing worst case algorithms that make linear data movements. We present a family of in-place sorting algorithms, that lie between selection sort and heapsort, culminating in one that makes, in the worst case, linear data movements and O(n ^1+ε) comparisons for any fixed constant ε satisfying 0<ε<1. When O(n ^∈) extra space for pointers is available, we give an algorithm that sorts n elements using linear data movements and O(n lg n) comparisons in the worst case.

Research supported by Natural Sciences and Engineering Research Council of Canada grant No.A-8237 and the Information Technology Research Centre of Ontario