Summary: In Proceedings 27th ACM Symposium on Theory of Computing, pages 427-436. ACM Press, 1995.
Sorting in Linear Time?
We show that a unit-cost RAM with a word length of £ bits
can sort ¤ integers in the range ¥§¦¨¦© in ¤"!$#&%'!$#&%(¤0)
time, for arbitrary £213!$#&%(¤ , a significant improvement
over the bound of 4¤05 !$#&%6¤0) achieved by the fusion trees
of Fredman and Willard. Provided that £7189!$#&%@¤0)BADCFE , for
some fixed GIHP¥ , 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 £ bits. The first one yields