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Locating a general minisum ‘circle’ on the plane

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Abstract

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.

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Authors and Affiliations

  1. Royal Military College of Canada and Groupe d’Études et de Recherche en Analyse des Décisions, Kingston, ON, Canada

    Jack Brimberg

  2. Technical University of Denmark, Copenhagen, Denmark

    Henrik Juel

  3. Georg-August-Universität Göttingen, Göttingen, Germany

    Mark-Christoph Körner & Anita Schöbel

Authors
  1. Jack Brimberg
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  2. Henrik Juel
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  3. Mark-Christoph Körner
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  4. Anita Schöbel
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Correspondence to Jack Brimberg.

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Brimberg, J., Juel, H., Körner, MC. et al. Locating a general minisum ‘circle’ on the plane. 4OR-Q J Oper Res 9, 351–370 (2011). https://doi.org/10.1007/s10288-011-0169-5

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  • DOI: https://doi.org/10.1007/s10288-011-0169-5

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