The Weighted Euclidean 1-Center Problem

  title={The Weighted Euclidean 1-Center Problem},
  author={Nimrod Megiddo},
  journal={Math. Oper. Res.},
The special case where wi = 1, i = 1, . . . , n, was proposed by J. Sylvester in 1857 and amounts to finding the smallest circle that contains all the given points. The general case was introduced by Francis [3]. The most efficient algorithm known to date for the unweighted case is an O(n logn) algorithm by Shamos and Hoey [lo].' This algorithm utilizes the data structure so-called "Farthest point Voronoi diagram." It is not clear whether the generalization of this concept into weighted Voronoi… CONTINUE READING
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