Concepts inSpace-efficient online computation of quantile summaries
Sequence
In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements), and the number of ordered element (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function. For example, (C, R, Y) is a sequence of letters that differs from (Y, C, R), as the ordering matters.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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Computation
Computation is any type of calculation or the use of computer technology in Information processing. Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc. Computation is also a major subject matter of computer science: it investigates what can or cannot be done in a computational manner. 40x40px Look up computation in Wiktionary, the free dictionary.
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Online algorithm
In computer science, an online algorithm is one that can process its input piece-by-piece in a serial fashion, i.e. , in the order that the input is fed to the algorithm, without having the entire input available from the start. In contrast, an offline algorithm is given the whole problem data from the beginning and is required to output an answer which solves the problem at hand.
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Euclidean space
In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions. The term “Euclidean” distinguishes these spaces from the curved spaces of non-Euclidean geometry and Einstein's general theory of relativity, and is named for the Greek mathematician Euclid of Alexandria.
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A priori and a posteriori
The terms a priori ("from the earlier") and a posteriori ("from the later") are used in philosophy to distinguish two types of knowledge, justifications or arguments. A priori knowledge or justification is independent of experience (for example "All bachelors are unmarried"); a posteriori knowledge or justification is dependent on experience or empirical evidence (for example "Some bachelors are very happy").
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Deterministic algorithm
In computer science, a deterministic algorithm is an algorithm which, in informal terms, behaves predictably. Given a particular input, it will always produce the same output, and the underlying machine will always pass through the same sequence of states. Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently.
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Quantile
Quantiles are points taken at regular intervals from the cumulative distribution function (CDF) of a random variable. Dividing ordered data into essentially equal-sized data subsets is the motivation for -quantiles; the quantiles are the data values marking the boundaries between consecutive subsets.
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