Locating a general minisum 'circle' on a plane

Publication: Research - peer-reviewJournal article – Annual report year: 2011

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We approximate a set of given points in the plane by the boundary of a convex and symmetric set which is the unit circle of some norm. This generalizes previous work on the subject which considers Euclidean circles only. More precisely, we examine the problem of locating and scaling the unit circle of some given norm k with respect to given points on the plane such that the sum of weighted distances (as measured by the same norm k) between the circumference of the circle and the points is minimized. We present general results and are able to identify a finite dominating set in the case that k is a polyhedral norm.
Original languageEnglish
Journal4 O R
Volume9
Issue number4
Pages (from-to)351-370
ISSN1619-4500
DOIs
StatePublished - 2011
Peer-reviewedYes
CitationsWeb of Science® Times Cited: 2

Keywords

  • facility location, general norm, circle
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