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Lower Bounds for Line Stabbing McGill University
 

Summary: Lower Bounds for Line Stabbing
D. Avis
McGill University
J.M. Robert
McGill University
R. Wenger
Universit'e de Montr'eal
March 25, 1997
Abstract
We present an \Omega\Gamma 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 of a family of k + 1
translates where every k translates have a line transversal but the
entire family has no line transversal.
A line which intersects every member in a family of objects is known as

  

Source: Avis, David - School of Computer Science, McGill University

 

Collections: Computer Technologies and Information Sciences