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Insertion Sort is O(n log n)

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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.

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Authors and Affiliations

  1. Department of Computer Science, SUNY Stony Brook, Stony Brook, NY 11794-4400, USA

    Michael A. Bender

  2. Department of Computer Science, Rutgers University, Piscataway, NJ 08854, USA

    Martin Farach-Colton & Miguel A. Mosteiro

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  1. Michael A. Bender
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  2. Martin Farach-Colton
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  3. Miguel A. Mosteiro
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Correspondence to Michael A. Bender, Martin Farach-Colton or Miguel A. Mosteiro.

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Bender, M., Farach-Colton, M. & Mosteiro, M. Insertion Sort is O(n log n). Theory Comput Syst 39, 391–397 (2006). https://doi.org/10.1007/s00224-005-1237-z

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  • DOI: https://doi.org/10.1007/s00224-005-1237-z

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