Concepts inPairwise Element Computation with MapReduce
Element (mathematics)
In mathematics, an element or member of a set is any one of the distinct objects that make up that set.
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MapReduce
MapReduce is a programming model for processing large data sets, and the name of an implementation of the model by Google. MapReduce is typically used to do distributed computing on clusters of computers. The model is inspired by the map and reduce functions commonly used in functional programming, although their purpose in the MapReduce framework is not the same as their original forms. MapReduce libraries have been written in many programming languages.
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In mathematics, a partition of a set X is a division of X into non-overlapping and non-empty "parts" or "blocks" or "cells" that cover all of X. More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being partitioned.
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Evaluation strategy
In computer science, an evaluation strategy is a set of (usually deterministic) rules for evaluating expressions in a programming language. Emphasis is typically placed on functions or operators: an evaluation strategy defines when and in what order the arguments to a function are evaluated, when they are substituted into the function, and what form that substitution takes.
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Generic programming
In the simplest definition, generic programming is a style of computer programming in which algorithms are written in terms of to-be-specified-later types that are then instantiated when needed for specific types provided as parameters. This approach, pioneered by Ada in 1983, permits writing common functions or types that differ only in the set of types on which they operate when used, thus reducing duplication.
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two closely related senses: The order of a group is its cardinality, i.e. , the number of elements in its set. The order, sometimes period, of an element a of a group is the smallest positive integer m such that a = e (where e denotes the identity element of the group, and a denotes the product of m copies of a). If no such m exists, a is said to have infinite order. All elements of finite groups have finite order.
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