  Motivated by applications in instance selection, we introduce the \emph{star
discrepancy subset selection problem}, which consists of finding a subset of
\(m\) out of \(n\) points that minimizes the star discrepancy. We introduce two
mixed integer linear formulations (MILP) and a combinatorial branch-and-bound
(BB) algorithm for this problem and we evaluate our approaches against random
subset selection and a greedy construction on different use-cases in dimension
two and three. Our results show that one of the MILPs and BB are efficient in
dimension two for large and small $m/n$ ratio, respectively, and for not too
large $n$. However, the performance of both approaches decays strongly for
larger dimensions and set sizes.
  As a side effect of our empirical comparisons we obtain point sets of
discrepancy values that are much smaller than those of common low-discrepancy
sequences, random point sets, and of Latin Hypercube Sampling. This suggests
that subset selection could be an interesting approach for generating point
sets of small discrepancy value.
