Insertion Sort is O(n log n)

TL;DR

This paper demonstrates that by introducing gaps, Insertion Sort can be optimized to run in O(n log n) time with high probability, challenging the traditional O(n^2) complexity.

Contribution

It introduces Gapped Insertion Sort, showing it achieves O(log n) insertion time and overall O(n log n) complexity with high probability, a significant improvement over classical methods.

Findings

Gapped Insertion Sort reduces insertion time to O(log n)

Total running time becomes O(n log n) with high probability

Physical-world analogy inspires computational optimization

Abstract

Traditional Insertion Sort runs in O(n^2) time because each insertion takes O(n) time. When people run Insertion Sort in the physical world, they leave gaps between items to accelerate insertions. Gaps help in computers as well. This paper shows that Gapped Insertion Sort has insertion times of O(log n) with high probability, yielding a total running time of O(n log n) with high probability.