Abstract
We present a fast deterministic algorithm for integer sorting in linear space. Our algorithm sorts n integers in linear space in O(n(log log n)1.5) time. This improves the O(n(log log n)2) time bound given in [11]. This result is obtained by combining our new technique with that of Thorup’s [11]. The approach and technique we provide are totally different from previous approaches and techniques for the problem. As a consequence our technique can be extended to apply to nonconservative sorting and parallel sorting. Our nonconservative sorting algorithm sorts n integers in 0, 1, ..., m − 1 in time O(n(log log n)2/(log k+log log log n)) using word length k log(m + n), where k ≤ log n. Our EREW parallel algorithm sorts n integers in 0, 1, ..., m − 1 in O((log n)2) time and O(n(log log n)2/log log log n) operations provided logm = π ((log n)2).
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Han, Y. (2000). Fast Integer Sorting in Linear Space. In: Reichel, H., Tison, S. (eds) STACS 2000. STACS 2000. Lecture Notes in Computer Science, vol 1770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46541-3_20
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DOI: https://doi.org/10.1007/3-540-46541-3_20
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