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Improved parallel integer sorting without concurrent writing
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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) time. This improves our previous result [Y. Han, Inform. and Comput. 170 (1) (2001) 81-94] which sorts in O(n log log n log log log n) time and linear space. 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(n log log n) time but uses O(mε)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(nlog log n)time and linear space but uses randomization.