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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.
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} .
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 two-tree broadcast communicates concurrently over two binary trees that span all processors. This achieves full usage of the bandwidth in the full-duplex communication model while having a startup latency logarithmic in the number of partaking processors. [1] The algorithm can also be adapted to perform a reduction or prefix sum.
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.
prefix; prefix code; prefix computation; prefix sum; prefix traversal; preorder traversal; primary clustering; primitive recursive; Prim's algorithm; principle of optimality; priority queue; prisoner's dilemma; PRNG; probabilistic algorithm; probabilistically checkable proof; probabilistic Turing machine; probe sequence; Procedure (computer ...
Fast food gets a bad rap for being unhealthy, but there are healthy fast food options at chains like McDonald’s, Pizza Hut, and Sonic. Dietitians explain.
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 ...