Computational Geometry Column 68

This column is devoted to geometric clustering and covering problems in Rd. As exact solutions for these problems are usually out of reach (unless d = 1), one is forced to deal with approximations. Here we mostly consider online algorithms, as the online setting introduces additional difficulty due to uncertainty about the future. One representative problem is the following (so-called Unit Covering): given a set of n points in Rd, cover the points by balls of unit diameter, so as to minimize the number of balls used.