Abstract
Let S = {l1, l2, l3, . . . , ln} be a set of n vertical line segments in the plane. Though not essential, to simplify proofs we assume that no two li ’s are on the same vertical line. A convex polygon weakly intersects S if it contains a point of each line segment on its boundary or interior. In this paper, we propose an O(n logn) algorithm for the problem of finding a minimum area convex polygon that weakly intersects S. The principal motivation behind this paper is the open problem proposed by Tamir [5] at the fourth Computational Geometry day at NYU to decide if there exists a convex polygon whose boundary intersects a set of arbitrarily oriented line segments.
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