Improved nonconservative sequential and parallel integer sorting

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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, mϵ+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.

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Supported in part by the Deutsche Forschungsgemeinschaft, SFB 124, TP B2, VLSI Entwurfmethoden und Parallelität, and in part by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM).

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Supported by the Finsoft III Research Program.

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