How to cover a point set with a V-shape of minimum width

We first present an O(n2logn) time algorithm to compute, given a set of n points P, a minimum-width balanced V-shape covering P. We then describe a PTAS for computing a (1+ε)-approximation of this V-shape in time O((n/ε)logn+(n/ε3/2)log2(1/ε)). A much simpler constant-factor approximation algorithm is also described.