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Locating a minisum circle in the plane. (English) Zbl 1163.90010
Discrete Appl. Math. 157, No. 5, 901-912 (2009); erratum to ibid. 158, No. 18, 2088 (2010).
Summary: We consider the problem of locating a circle with respect to existing facilities in the plane such that the sum of weighted distances between the circle and the facilities is minimized, i.e., we approximate a set of given points by a circle regarding the sum of weighted distances. If the radius of the circle is a variable we show that there always exists an optimal circle passing through two of the existing facilities. For the case of a fixed radius we provide characterizations of optimal circles in special cases. Solution procedures are suggested.

MSC:
90B80 Discrete location and assignment
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
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[1] Brimberg, J.; Juel, H.; Schöbel, A., Locating a minisum circle in the plane, Discrete applied mathematics, 157, 901-912, (2009) · Zbl 1163.90010
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