  In the General Position Subset Selection (GPSS) problem, the goal is to find
the largest possible subset of a set of points such that no three of its
members are collinear. If $s_{\mathrm{GPSS}}$ is the size of the optimal
solution, $\sqrt{s_{\mathrm{GPSS}}}$ is the current best guarantee for the size
of the solution obtained using a polynomial time algorithm. In this paper we
present an algorithm for GPSS to improve this bound based on the number of
collinear pairs of points. We experimentally evaluate this and few other GPSS
algorithms; the result of these experiments suggests further opportunities for
obtaining tighter lower bounds for GPSS.
