In

(Mathematical expressions are simplified in this html-dokument. They should be readable enough to get the flavour.)

We show that a unit-cost RAM with a word length of w bits can sort $n$ integers in the range 0.. 2^(w-1) in O(n log\og n) time, for arbitrary w >= log n, a significant improvement over the bound of O(n sqrt(log n) achieved by the fusion trees of Fredman and Willard. Provided that $w >=(log n)^(2+epsilon), for some fixed epsilon>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(log n) time and O(n loglog 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+epsilon) for some fixed epsilon>0.

Our deterministic and randomized sequential and parallel algorithms generalize to the lexicographic sorting problem of sorting multiple-precision integers represented in several words.