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Anchored Hyperplane Location Problems

dc.contributor.authorSchöbel, Anita
dc.date.accessioned2010-11-16T08:02:48Z
dc.date.available2010-11-16T08:02:48Z
dc.date.issued2003
dc.identifier.citationSchöbel, Anita (2003): Anchored Hyperplane Location Problems - Discrete and Computational Geometry, Vol. 29, Nr. 2, p. 229-238
dc.identifier.urihttp://resolver.sub.uni-goettingen.de/purl?gs-1/5712
dc.description.abstractThe anchored hyperplane location problem is to locate a hyperplane passing through some given points P ⊆ Rn and minimizing either the sum of weighted distances (median problem), or the maximum weighted distance (center problem) to some other points Q ⊆ Rn . This problem of computational geometry is analyzed by using nonlinear programming techniques. If the distances are measured by a norm, it will be shown that in the median case there exists an optimal hyperplane that passes through at least n − k affinely independent points of Q, if k is the maximum number of affinely independent points of P. In the center case, there exists an optimal hyperplane which is at maximum distance to at least n −k +1 affinely independent points of Q. Furthermore, if the norm is a smooth norm, all optimal hyperplanes satisfy these criteria. These results generalize known results about unrestricted hyperplane location problems.
dc.language.isoeng
dc.rightsopenAccess
dc.subjectHyperplane Location Problems
dc.subject.ddc510
dc.titleAnchored Hyperplane Location Problems
dc.typejournalArticle
dc.identifier.doi10.1007/s00454-002-0741-z
dc.type.versionsubmittedVersion
dc.bibliographicCitation.volume29
dc.bibliographicCitation.issue2
dc.bibliographicCitation.firstPage229
dc.bibliographicCitation.lastPage238
dc.type.subtypejournalArticle
dc.description.statuspeerReviewed
dc.bibliographicCitation.journalDiscrete and Computational Geometry


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