Efficient stable sorting with minimal extra space

• Authors: Edward C. Horvath
• Venue: STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
• Year: 1974

In his chapter on sorting, Knuth [1]@@@@ describes the open problem of stable sorting with no more than 0(log2N) bits of extra space and less than 0(N2) computation time. In this paper we define the concept of a contiguent and show that a contiguent forming algorithm may be used as the basis for a stable sort. A class of such contiguent forming algorithm may be used as the basis for a stable sort. A class of such contiguent forming algorithms is described, the most naive of which requires 0(log N) bits of extra space and 0(N log2N) computation time. We also describe a stable merging algorithm which requires 0(N) time and 0(log N) bits of extra space, but which is not applicable to all cases. It is shown, however, that this merge may be combined with a contiguent compilation algorithm to yield a generally applicable stable sorting algorithm. One such combination provides the basis for a stable sorting algorithm which requires 0(N.logN.G(N)) time and 0(log N) bits of extra space. Another such combination provides the basis for a stable sorting algorithm which requires 0(N log N) time and 0(log2N) bits of extra space.