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- W2893345561 abstract "Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration." @default.
- W2893345561 created "2018-10-05" @default.
- W2893345561 creator A5042834617 @default.
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- W2893345561 date "2018-09-24" @default.
- W2893345561 modified "2023-09-30" @default.
- W2893345561 title "EVALUATION OF PAIRWISE DISTANCES AMONG POINTS FORMING A REGULAR ORTHOGONAL GRID IN A HYPERCUBE" @default.
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- W2893345561 doi "https://doi.org/10.3846/jcem.2018.5189" @default.
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