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Adaptive sorting: an information theoretic perspective

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Abstract

We present two algorithms that are near optimal with respect to the number of inversions present in the input. One of the algorithms is a variation of insertion sort, and the other is a variation of merge sort. The number of comparisons performed by our algorithms, on an input sequence of length n that has I inversions, is at most \(n\,{\rm log}_{2} (\frac{I}{n} + 1) + O(n)\) . Moreover, both algorithms have implementations that run in time \(O(n\,{\rm log}_{2} (\frac{I}{n} + 1)\,+\,n)\) . All previously published algorithms require at least \(cn\,{\rm log}_{2} (\frac{I}{n} + 1)\) comparisons for some c > 1.

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Authors and Affiliations

  1. Department of Computer Engineering and Systems, Alexandria University, Alexandria, Egypt

    Amr Elmasry

  2. Department of Computer Science, Rutgers University, New Brunswick, NJ, 08903, USA

    Michael L. Fredman

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  1. Amr Elmasry
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  2. Michael L. Fredman
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Correspondence to Michael L. Fredman.

Additional information

M. L. Fredman was supported in part by NSF grant CCR-9732689.

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Elmasry, A., Fredman, M.L. Adaptive sorting: an information theoretic perspective. Acta Informatica 45, 33–42 (2008). https://doi.org/10.1007/s00236-007-0061-0

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  • DOI: https://doi.org/10.1007/s00236-007-0061-0

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