Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Článek WoS

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.

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.

full factorial design, design of experiments, pairwise distances, Audze-Eglãjs criterion, optimization, periodic space

full factorial design, design of experiments, pairwise distances, Audze-Eglãjs criterion, optimization, periodic space

SADÍLEK, V.; VOŘECHOVSKÝ, M.

2019

21.09.2018

VGTU Press

1392-3730

Journal of Civil Engineering and Management

24

5

Litevská republika

410

423

14

https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189

http://hdl.handle.net/11012/85339

40j