Improved Fast Integer Sorting in Linear Space

Yijie Han
2001 Information and Computation  
We present a fast deterministic algorithm for integer sorting in linear space. Our algorithm sorts n integers in the range {0, 1, 2, . . . , m − 1} in linear space in O(n log log n log log log n) time. When log m ≥ log 2+ n, > 0, we can further achieve O(n log log n) time. This improves the O(n(log log n) 2 ) time bound given in M. Thorup (1998) in "Proc. 1998 ACM-SIAM Symp. on Discrete Algorithms (SODA'98)," pp. 550-555). This result is obtained by combining our new technique with that of
more » ... p's. are also used for the design of our algorithms. We provide an approach and techniques which 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 = ((log n) 2 ). C
doi:10.1006/inco.2001.3053 fatcat:une6vw3ur5hadlcirwzegr242y