On the Continuous Fermat-Weber Problem

@article{Fekete2005OnTC,
  title={On the Continuous Fermat-Weber Problem},
  author={S{\'a}ndor P. Fekete and Joseph B. M. Mitchell and Karin Beurer},
  journal={ArXiv},
  year={2005},
  volume={cs.CG/0310027}
}
We give the firstexact algorithmic study of facility location problems that deal with finding a median for acontinuum of demand points. In particular, we consider versions of the "continuousk-median (Fermat-Weber) problem" where the goal is to select one or more center points that minimize the average distance to a set of points in a demandregion. In such problems, the average is computed as an integral over the relevant region, versus the usual discrete sum of distances. The resulting facility… 
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