  In the $d$-Scattered Set problem we are asked to select at least $k$ vertices
of a given graph, so that the distance between any pair is at least $d$. We
study the problem's (in-)approximability and offer improvements and extensions
of known results for Independent Set, of which the problem is a generalization.
  Specifically, we show:
  - A lower bound of $\Delta^{\lfloor d/2\rfloor-\epsilon}$ on the
approximation ratio of any polynomial-time algorithm for graphs of maximum
degree $\Delta$ and an improved upper bound of $O(\Delta^{\lfloor d/2\rfloor})$
on the approximation ratio of any greedy scheme for this problem.
  - A polynomial-time $2\sqrt{n}$-approximation for bipartite graphs and even
values of $d$, that matches the known lower bound by considering the only
remaining case.
  - A lower bound on the complexity of any $\rho$-approximation algorithm of
(roughly) $2^{\frac{n^{1-\epsilon}}{\rho d}}$ for even $d$ and
$2^{\frac{n^{1-\epsilon}}{\rho(d+\rho)}}$ for odd $d$ (under the randomized
ETH), complemented by $\rho$-approximation algorithms of running times that
(almost) match these bounds.
