Computing shortest transversals of sets

Given a family of objecte in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(nlogn) time algorithms for computing a shortest transversal of a family of n lines, a family of n line segments, and a family of convex polygons with a total of n vertices, In general, fiading a line transversal for a family of n objects takes O(n log n,) time. This time bound holds for a family of n line segments as well as for a family of convex polygons with a total of n vertices. Hence, our shortest tra.nsvergal algorithms for these families are optimal. Keyuonh: Computational Geometry, shortest transver'sal, envelope, butterfly polygon.