Improved nonconservative sequential and parallel integer sorting

Abstract

We consider the problem of deterministic integer sorting on unit-cost sequential and parallel machines with a large word length and show that n integers drawn from {0,..., m-1} can be sorted using a word length of O( m log n) bits either in O( n) time on a unit-cost RAM or in O(log n) time on a unit-cost EREW PRAM with O( n/log n) processors. Spending O(log log log m) additional sequential or parallel time, we can reduce the necessary word length to O(min} n log n log m + (log m) 1+ϵ, m ϵ+log n}) bits, for any fixed ϵ>0. Previous algorithms with a linear time-processor count either cannot so arbitrary integers or require a much larger word length.