Summary: In Proceedings 27th ACM Symposium on Theory
ofComputing, pages 427436. ACM Press, 1995.
Sorting in Linear Time?
Arne Andersson \Lambda Torben Hagerup y Stefan Nilsson \Lambda Rajeev Raman z
We show that a unitcost RAM with a word length of w bits
can sort n integers in the range 0 : : 2 w \Gamma 1 in O(n log log n)
time, for arbitrary w – log n, a significant improvement
over the bound of O(n
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) op
erations on a deterministic CRCW PRAM. The second one
yields an algorithm that uses O(logn) expected time and
O(n) expected operations on a randomized EREW PRAM,