Fast integer sorting in linear space

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 log m = Ω ((log n)2).