DC Field | Value | Language |
---|---|---|
dc.contributor.author | Choi, Ilkyoo | ko |
dc.contributor.author | Joo, Weonyoung | ko |
dc.contributor.author | Kim, Minki | ko |
dc.date.accessioned | 2021-03-26T01:53:42Z | - |
dc.date.available | 2021-03-26T01:53:42Z | - |
dc.date.created | 2020-08-31 | - |
dc.date.issued | 2020-10 | - |
dc.identifier.citation | DISCRETE MATHEMATICS, v.343, no.10 | - |
dc.identifier.issn | 0012-365X | - |
dc.identifier.uri | http://hdl.handle.net/10203/281872 | - |
dc.description.abstract | For a finite point set in R-d, we consider a peeling process where the vertices of the convex hull are removed at each step. The layer number L(X) of a given point set X is defined as the number of steps of the peeling process in order to delete all points in X. It is known that if X is a set of random points in R-d, then the expectation of L(X) is Theta(vertical bar X vertical bar(2/(d+1))) and recently it was shown that if X is a point set of the square grid on the plane, then L(X) = Theta(vertical bar X vertical bar(2/3)). In this paper, we investigate the layer number of alpha-evenly distributed point sets for alpha > 1; these point sets share the regularity aspect of random point sets but in a more general setting. The set of lattice points is also an alpha-evenly distributed point set for some alpha > 1. We find an upper bound of O(vertical bar X vertical bar(3/4)) for the layer number of an alpha-evenly distributed point set X in a unit disk on the plane for some alpha > 1, and provide an explicit construction that shows the growth rate of this upper bound cannot be improved. In addition, we give an upper bound of O(vertical bar X vertical bar(d+1/2d)) for the layer number of an a-evenly distributed point set X in a unit ball in R-d for some alpha > 1 and d >= 3. | - |
dc.language | English | - |
dc.publisher | ELSEVIER | - |
dc.title | The layer number of alpha-evenly distributed point sets | - |
dc.type | Article | - |
dc.identifier.wosid | 000558591300032 | - |
dc.identifier.scopusid | 2-s2.0-85086570371 | - |
dc.type.rims | ART | - |
dc.citation.volume | 343 | - |
dc.citation.issue | 10 | - |
dc.citation.publicationname | DISCRETE MATHEMATICS | - |
dc.identifier.doi | 10.1016/j.disc.2020.112029 | - |
dc.contributor.nonIdAuthor | Choi, Ilkyoo | - |
dc.contributor.nonIdAuthor | Kim, Minki | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordAuthor | Convex layer | - |
dc.subject.keywordAuthor | Peeling sequence | - |
dc.subject.keywordAuthor | Evenly-distributed point set | - |
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