## Sorting in Linear Time? (1995)

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Citations: | 86 - 14 self |

### BibTeX

@MISC{Andersson95sortingin,

author = {Arne Andersson and Torben Hagerup and Stefan Nilsson},

title = {Sorting in Linear Time?},

year = {1995}

}

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### Abstract

We show that a unit-cost RAM with a word length of w bits can sort n integers in the range 0 : : 2 w \Gamma1 in O(n log log n) time, for arbitrary w log n, a significant improvement over the bound of O(n p log n) achieved by the fusion trees of Fredman and Willard. Provided that w (log n) 2+ffl for some fixed ffl ? 0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize without loss on a unit-cost PRAM with a word length of w bits. The first one yields an algorithm that uses O(logn) time and O(n log log n) operations on a deterministic CRCW PRAM. The second one yields an algorithm that uses O(log n) expected time and O(n) expected operations on a randomized EREW PRAM, provided that w (log n) 2+ffl for some fixed ffl ? 0. Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words. ...