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We show that a unit-cost RAM with a word length ofwbits can sortnintegers in the range 0…2w−1 inO(nloglogn) time for arbitraryw⩾logn, a significant improvement over the bound ofO(nlogn) achieved by the fusion trees of Fredman and Willard. Provided thatw⩾(logn)2+εfor some fixedε>0, the sorting can even be accomplished in linear expected time with a randomized algorithm. Both of our algorithms parallelize...
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