Abstract
We present an Ω( n log n) fixed order algebraic decision tree lower bound for determining the existence of a line stabber for a family of n line segments in the plane. We give the same lower bound for determining the existence of a line stabber for n translates of a circle in the plane. In proving this lower bound, we show that this problem is equivalent to determining if the width of a set of points is less than or equal to w. Through this transformation we can reexamine an old example by Hadwiger, Debrunner and Klee (1964) of a family of k+1 translates where every k translates have a line transversal but the entire family has no line transversal.
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