Computational similarity

Abstract

SUMMARYThe paper enunciates the principle of computational similarity, whereby calculations with the same values for certain dimensionless ratios are said to be 'computationally similar' and as a consequence have the same optimum self-speed-up and optimum number of processors. Based on a three-parameter description of the computer hardware, two dimensionless ratios, which are only a function of the problem size and the hardware parameters, completely determine the scaling. Contours of constant self-speed-up can be drawn on a two-dimensional dimensionless universal scaling diagram (DUSD). This diagram is for a particular class of timing expressions that can be shown to represent approximately the performance of a corresponding class of computer programs or benchmarks, but it applies to all computers describable by the three hardware parameters and to all problem sizes. Thus the dimensionless ratios play a similar role in the study of computer performance, as do the Reynolds and other dimensionless numbers in fluid dynamics. This dimensional analysis of computer performance is illustrated by the case of the FFTl benchmark from the Southampton 'Genesis' distributed-memory benchmarks.

Message-passing performance of parallel computers

“…However, predicting communication performance in terms of performance parameters provided by existing Parkbench codes is not just a function of low-level parameters, measured by simple communication benchmarks. Previous studies have shown that the analytic expression (2) fits well into parallel performance data [6,3]. Unfortunately, the fitted values of parameters turn out to be very different from those determined by the low-level benchmarks.…”

A metric space for computer programs and the principle of computational least action

“…Computational force has the same units, flop/byte, as an important quantity in performance analysis called computational intensity by Hockney [6,7] and others [14] and also called balance by some other authors [4,13]. Identifying it as a force allows us to think of computation in a new framework described in the next section.…”

“…first proposed by Hockney [6][7][8][9]. It treats time t as a linear function of length n, the number of data items moved.…”

Secure similarity coefficients computation for binary data and its extensions

“…Similarity coefficients (SC) aim at quantifying the extent to which objects resemble with each other. Many researchers have proposed plenty of meaningful binary similarity coefficients in their fields, such as ecology and biogeography , privacy‐preserving data mining , biometric areas , computational similarity , and porting scientific application . One specific example is Jaccard index , which was used to cluster ecological species.…”