Highly Influenced

# The Weighted Euclidean 1-Center Problem

@article{Megiddo1983TheWE, title={The Weighted Euclidean 1-Center Problem}, author={Nimrod Megiddo}, journal={Math. Oper. Res.}, year={1983}, volume={8}, pages={498-504} }

- Published 1983 in Math. Oper. Res.
DOI:10.1287/moor.8.4.498

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