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

A balanced V-shape is a polygonal region in the plane contained in the union of two crossing equal-width strips. It is delimited by two pairs of parallel rays that emanate from two points x, y, are contained in the strip boundaries, and are mirror-symmetric with respect to the line xy. The width of a balanced V-shape is the width of the strips. We first present an O(n^2logn) 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+@e)-approximation of this V-shape in time O((n/@e)logn+(n/@e^3^/^2)log^2(1/@e)). A much simpler constant-factor approximation algorithm is also described.

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