@MISC{Linear_, author = {Sorting Linear and Time Arne and Hagerupy Stefan and Nilsson\lambda Rajeev Ramanz}, title = {}, year = {} }

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Abstract

Abstract We show that a unit-cost RAM with a word length of w bitscan sort n integers in the range 0: : 2w \Gamma 1 in O(n log log n)time, for arbitrary w * log n, a significant improvementover the bound of O(nplog n) achieved by the fusion treesof Fredman and Willard. Provided that w * (log n)2+ffl, forsome fixed ffl? 0, the sorting can even be accomplished inlinear 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 yieldsan algorithm that uses O(log n) time and O(n log log n) op-erations 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 problemof sorting multiple-precision integers represented in several words. 1 Introduction Sorting is one of the most fundamental computational prob-lems, and n keys can be sorted in O(n log n) time by anyof a number of well-known sorting algorithms. These algorithms operate in the comparison-based setting, i.e., they ob-tain information about the relative order of keys exclusively through pairwise comparisons. It is easy to show that a run-ning time of