Shape Fitting with Outliers
Sariel Har-Peled, Yusu Wang · SIAM Journal on Computing · 2004
Given a set $\mathcal{H}$ of n hyperplanes in ${\Bbb R}^d$, we present an algorithm that $\eps$-approximates the extent between the top and bottom k levels of the arrangement of $\mathcal{H}$ in time $O(n + (k/\eps)^c)$, where c is a constant depending on d. The algorithm relies on computing a subset of $\mathcal{H}$ of size $O(k/\eps^{d-1})$, in near linear time, such that the k-level of the arrangement of the subset approximates that of the original arrangement. Using this algorithm, we propose efficient approximation algorithms for shape fitting with outliers for various shapes. These are the first algorithms to handle outliers efficiently for the shape fitting problems considered.