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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.
Generalized suffix arrays can be used to solve the pattern matching problem: [5]. Given a pattern and a text , find all occurrences of in .; Using the generalized suffix array of , then first, the suffixes that have as a prefix need to be found.
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.
It stores the lengths of the longest common prefixes (LCPs) between all pairs of consecutive suffixes in a sorted suffix array. For example, if A := [ aab , ab , abaab , b , baab ] is a suffix array, the longest common prefix between A [1] = aab and A [2] = ab is a which has length 1, so H [2] = 1 in the LCP array H .
For long messages, the hypercube (Hypercube (communication pattern) § Prefix sum, Prefix sum § Distributed memory: Hypercube algorithm) topology is not suitable, since all processing units are active in every step and therefore pipelining can't be used.
The topology allows for an efficient implementation of some basic communication primitives such as Broadcast, All-Reduce, and Prefix sum. [1] The processing elements are numbered 0 {\displaystyle 0} through 2 d − 1 {\displaystyle 2^{d}-1} .
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Suffix arrays are closely related to suffix trees: . Suffix arrays can be constructed by performing a depth-first traversal of a suffix tree. The suffix array corresponds to the leaf-labels given in the order in which these are visited during the traversal, if edges are visited in the lexicographical order of their first character.