Insertion Sort is O(n log n)

Authors:
Michael A. Bender;Martin Farach-Colton;Miguel A. Mosteiro
Affiliations:
Department of Computer Science, SUNY Stony Brook, Stony Brook, NY 11794-4400, USA;Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA;Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA
Venue:
Theory of Computing Systems
Year:
2006

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Abstract

Traditional Insertion Sort runs in O(n2) 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.