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

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dc.contributor.authorSadílek, Václavcs
dc.contributor.authorVořechovský, Miroslavcs
dc.coverage.issue5cs
dc.coverage.volume24cs
dc.date.issued2018-09-21cs
dc.description.abstractCartesian 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 nave 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.en
dc.formattextcs
dc.format.extent410-423cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of civil engineering and management. 2018, vol. 24, issue 5, p. 410-423.en
dc.identifier.doi10.3846/jcem.2018.5189cs
dc.identifier.issn1392-3730cs
dc.identifier.orcid0000-0001-6695-2168cs
dc.identifier.orcid0000-0002-3366-5557cs
dc.identifier.other150120cs
dc.identifier.researcheridF-8950-2018cs
dc.identifier.researcheridA-1759-2010cs
dc.identifier.scopus26027265100cs
dc.identifier.scopus57260228700cs
dc.identifier.urihttp://hdl.handle.net/11012/85339
dc.language.isoencs
dc.publisherVGTU Presscs
dc.relation.ispartofJournal of civil engineering and managementcs
dc.relation.urihttps://www.tede.vgtu.lt/index.php/JCEM/article/view/5189cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1392-3730/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectfull factorial designen
dc.subjectdesign of experimentsen
dc.subjectpairwise distancesen
dc.subjectAudze-Egljs criterionen
dc.subjectoptimizationen
dc.subjectperiodic spaceen
dc.titleEvaluation of pairwise distances among points forming a regular orthogonal grid in a hypercubeen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionacceptedVersionen
sync.item.dbidVAV-150120en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:45:39en
sync.item.modts2025.01.17 15:27:32en
thesis.grantorVysoké učení technické v Brně. Fakulta stavební. Ústav stavební mechanikycs
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