We consider the following problem: Given a point set in space find a largest subset that is in convex position and whose convex hull is empty. We show that the (decision version of the) problem is W[1]-hard.
Cite
@article{arxiv.1304.0247,
title = {Finding a largest empty convex subset in space is W[1]-hard},
author = {Panos Giannopoulos and Christian Knauer},
journal= {arXiv preprint arXiv:1304.0247},
year = {2013}
}