Given a finite configuration of points A in R^k endowed with the Manhattan distance, we prove that the ratio of the sum of the distances from a centroid of A over the sum of the distances from the Steiner center of A is bounded by 1 + (k − 1) k. Furthermore, this bound can be attained. This fact extends to an arbitrary finite dimension k ≥ 2 a result proved by Fekete and Meijer for k = 2,3.
An extension to R^k of a result by Fekete and Meijer
GIARLOTTA, Alfio;URSINO, Pietro
2012-01-01
Abstract
Given a finite configuration of points A in R^k endowed with the Manhattan distance, we prove that the ratio of the sum of the distances from a centroid of A over the sum of the distances from the Steiner center of A is bounded by 1 + (k − 1) k. Furthermore, this bound can be attained. This fact extends to an arbitrary finite dimension k ≥ 2 a result proved by Fekete and Meijer for k = 2,3.File in questo prodotto:
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