, Volume 9, Issue 4, pp 351–370 | Cite as

Locating a general minisum ‘circle’ on the plane

  • Jack BrimbergEmail author
  • Henrik Juel
  • Mark-Christoph Körner
  • Anita Schöbel
Research paper


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.


Facility location General norm Circle 

MSC classification (2000)

90B85 90C26 90C90 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Jack Brimberg
    • 1
    Email author
  • Henrik Juel
    • 2
  • Mark-Christoph Körner
    • 3
  • Anita Schöbel
    • 3
  1. 1.Royal Military College of Canada and Groupe d’Études et de Recherche en Analyse des DécisionsKingstonCanada
  2. 2.Technical University of DenmarkCopenhagenDenmark
  3. 3.Georg-August-Universität GöttingenGöttingenGermany

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