This problem was presented by Barany and Onn in 1997 and it is still not known if a polynomial-time algorithm for the problem exists. The monochrome version of this problem, expressing p as a convex combination of points in a set S, is a traditional linear programming feasibility problem. The colourful Caratheodory Theorem, due to Barany in 1982, provides a sufficient condition for the existence of a colourful set of points containing p in its convex hull. Barany's result was generalized by Holmsen et al. in 2008 and by Arocha et al. in 2009 before being recently further generalized by...
This problem was presented by Barany and Onn in 1997 and it is still not known if a polynomial-time algorithm for the problem exists. The monochrome v...