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Asked: 2026-05-14T23:25:31+00:00

Swanepoel’s comment here lead me to this paper . Then, searching for an implementation

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Swanepoel’s comment here lead me to this paper. Then, searching for an implementation in C, I came across this, which referenced another paper on an algorithm described here.

Both papers describe integer sorting algorithms that run in O(nloglog(n)) time. What is the difference between the two? Have there been any more recent findings about this topic?

Andersson et al., 1995

Han, 2004

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  1. Editorial Team

    From the abstract of the Han Paper:

    This also improves previous best
    deterministic sorting algorithm [A.
    Andersson, T. Hagerup, S. Nilsson, R.
    Raman, in: Proc. 1995 Symposium on
    Theory of Computing (1995) 427–436; Y.
    Han, X. Shen, in: Proc. 1995
    International Computing and
    Combinatorics Conference, in: Lecture
    Notes in Comput. Sci. 959 (1995)
    324–333] which sorts in O(nloglogn)
    time but uses O(m^e) space. Our results
    also improves the result of Andersson
    et al. [A. Andersson, T. Hagerup, S.
    Nilsson, R. Raman, in: Proc. 1995
    Symposium on Theory of Computing
    (1995) 427–436] which sorts in
    O(nloglogn) time and linear space but
    uses randomization.

    So there are two Anderson et al papers. One uses O(m^e) space and other uses randomization, but linear space. Han paper is deterministic with linear space.

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