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Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.
A Fenwick tree or binary indexed tree (BIT) is a data structure that stores an array of values and can efficiently compute prefix sums of the values and update the values. It also supports an efficient rank-search operation for finding the longest prefix whose sum is no more than a specified value.
List ranking can equivalently be viewed as performing a prefix sum operation on the given list, in which the values to be summed are all equal to one. The list ranking problem can be used to solve many problems on trees via an Euler tour technique, in which one forms a linked list that includes two copies of each edge of the tree, one in each direction, places the nodes of this list into an ...
dimensional hypercube is a network topology for parallel computers with processing elements. The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. [1]
Prefix sum, in computing; Pushout (category theory) (also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domainor pushout, leading to a fibered sum in category theory; QCD sum rules, in quantum field theory
In computer science, a segmented scan is a modification of the prefix sum with an equal-sized array of flag bits to denote segment boundaries on which the scan should be performed. [ 1 ] Example
If my functional programming knowledge correctly serves me, the statement in the first section about prefix sum being the fold of addition is incorrect. I believe it is a scan of addition, however wikipedia does not have a page for scan. 128.138.230.183 15:14, 31 January 2012 (UTC)
Information flow of Prefix-Sum/Scan operation performed on three nodes. The operator + can be any associative operator. The prefix-sum or scan operation [ 7 ] is used to collect data or partial results from different processing units and to compute intermediate results by an operator, which are stored on those processing units.