Minimum-cost coverage of point sets by disks

@inproceedings{Alt2006MinimumcostCO,
  title={Minimum-cost coverage of point sets by disks},
  author={Helmut Alt and Esther M. Arkin and Herv{\'e} Br{\"o}nnimann and Jeff Erickson and S{\'a}ndor P. Fekete and Christian Knauer and Jonathan Lenchner and Joseph B. M. Mitchell and Kim Whittlesey},
  booktitle={SCG '06},
  year={2006}
}
We consider a class of geometric facility location problems in which the goal is to determine a set <i>X</i> of disks given by their centers <i>(t<sub>j</sub>)</i> and radii <i>(r<sub>j</sub>)</i> that cover a given set of demand points <i>Y∈R</i><sup>2</sup> at the smallest possible cost. We consider cost functions of the form Ε<i><sub>j</sub>f(r<sub>j</sub>)</i>, where <i>f(r)=r</i><sup>α</sup> is the cost of transmission to radius <i>r</i>. Special cases arise for α=1 (sum of radii) and α=2… 
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