# The power of parallel prefix

TL;DR: This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model) to solve the prefix computation problem, when the order of the elements is specified by a linked list.

Abstract: The prefix computation problem is to compute all n initial products a1* . . . *a1,i=1, . . ., n of a set of n elements, where * is an associative operation. An O(((logn) log(2n/p))XI(n/p)) time deterministic parallel algorithm using p≤n processors is presented to solve the prefix computation problem, when the order of the elements is specified by a linked list. For p≤O(n1-e)(e〉0 any constant), this algorithm achieves linear speedup. Such optimal speedup was previously achieved only by probabilistic algorithms. This study assumes the weakest PRAM model, where shared memory locations can only be exclusively read or written (the EREW model).

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### Cites methods from "The power of parallel prefix"

...A parallel bucket sort can be computed: (i) using ~ processors, EO(logn) parallel expected time on a priority CRCW PRAM [18] (we will discuss how this is achieved in the next paragraph); (ii) using ~ loglogn processors, O(logn) time on a priority CRCW by the algorithm of [9]; (iii) or using n 1-~ processors, O(n ~) time on an EI~EW PRAM for any c > 0 [ 10 ];...

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...We use parallel sorting [3, 5, 9, 10 ] and parallel prefix sum to implement the other...

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