Practical In-Place Mergesort

Two in-place variants of the classical mergesort algorithm are analysed in detail. The first, straightforward variant performs at most N log2 N + O(N) comparisons and 3N log2 N + O(N) moves to sort N elements. The second, more advanced variant requires at most N log2 N + O(N) comparisons and eN log2 N moves, for any fixed e > 0 and any N > N(e). In theory, the second one is superior to advanced versions of heapsort. In practice, due to the overhead in the index manipulation, our fastest in-place mergesort behaves still about 50 per cent slower than the bottom-up heapsort. However, our implementations are practical compared to mergesort algorithms based on in-place merging.

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