DC Field | Value | Language |
---|---|---|
dc.contributor.author | Fulek, R | ko |
dc.contributor.author | Holmsen, Andreas F | ko |
dc.contributor.author | Pach, J | ko |
dc.date.accessioned | 2013-03-08T16:43:42Z | - |
dc.date.available | 2013-03-08T16:43:42Z | - |
dc.date.created | 2012-02-06 | - |
dc.date.created | 2012-02-06 | - |
dc.date.issued | 2009-10 | - |
dc.identifier.citation | DISCRETE & COMPUTATIONAL GEOMETRY, v.42, no.3, pp.343 - 358 | - |
dc.identifier.issn | 0179-5376 | - |
dc.identifier.uri | http://hdl.handle.net/10203/93616 | - |
dc.description.abstract | What is the smallest number tau = tau(n) such that for any collection of n pairwise disjoint convex sets in d-dimensional Euclidean space, there is a point such that any ray (half-line) emanating from it meets at most tau sets of the collection? This question of Urrutia is closely related to the notion of regression depth introduced by Rousseeuw and Hubert ( 1996). We show the following: Given any collection C of n pairwise disjoint compact convex sets in d-dimensional Euclidean space, there exists a point p such that any ray emanating from p meets at most dn+1/d+1 members of C. There exist collections of n pairwise disjoint (i) equal-length segments or (ii) disks in the Euclidean plane such that from any point there is a ray that meets at least 2n/3-2 of them. We also determine the asymptotic behavior of tau(n) when the convex bodies are fat and of roughly equal size. | - |
dc.language | English | - |
dc.publisher | SPRINGER | - |
dc.subject | DEPTH | - |
dc.subject | POINTS | - |
dc.title | Intersecting Convex Sets by Rays | - |
dc.type | Article | - |
dc.identifier.wosid | 000267824300002 | - |
dc.identifier.scopusid | 2-s2.0-70349747032 | - |
dc.type.rims | ART | - |
dc.citation.volume | 42 | - |
dc.citation.issue | 3 | - |
dc.citation.beginningpage | 343 | - |
dc.citation.endingpage | 358 | - |
dc.citation.publicationname | DISCRETE & COMPUTATIONAL GEOMETRY | - |
dc.contributor.localauthor | Holmsen, Andreas F | - |
dc.contributor.nonIdAuthor | Fulek, R | - |
dc.contributor.nonIdAuthor | Pach, J | - |
dc.type.journalArticle | Article; Proceedings Paper | - |
dc.subject.keywordAuthor | Convex sets | - |
dc.subject.keywordAuthor | Geometric transversals | - |
dc.subject.keywordAuthor | Depth in hyperplane arrangements | - |
dc.subject.keywordAuthor | Regression depth | - |
dc.subject.keywordPlus | DEPTH | - |
dc.subject.keywordPlus | POINTS | - |
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