Given $M$ points in $\mathbb{R}^{N}$ (where $M$ is larger than $N$), I was wondering if there is an algorithm to find a $N-1$-dimensional hyperplane which goes through the origin and also intersects as many points as possible. Specifically, does there exist an algorithm which runs faster than $O(M^{N})$ time? This is achieved by looking at all subspaces defined by each subset of $N-1$ points.Furthermore, if there is no faster exact algorithm, I was wondering if there are any constant factor approximations which run faster than $O(M^{N})$. It would be greatly appreciated if someone can point me to the correct papers or references for these.
Hyperplane through origin which goes through most number of points
algorithms;optimization;computational geometry;discrete mathematics;graphics