Given a set of points <i>P</i> ⊂ <i>R</i><sup><i>d</i></sup> and value ∊ > 0, an ∊-core-set <i>S</i> ⊂ <i>P</i> has the property that the smallest ball containing <i>S</i> is an ∊-approximation of the smallest ball containing <i>P</i>. This paper shows that any point-set has an ∊-core-set of size [2/∊]. We also give a fast algorithm that finds this core-set. These results imply the existence of small core-sets for solving approximate <i>k</i>-center clustering and related problems. The sizes of… CONTINUE READING