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Small-size -Nets for Axis-Parallel Rectangles and Boxes Boris Aronov
 

Summary: Small-size -Nets for Axis-Parallel Rectangles and Boxes
Boris Aronov
Esther Ezra
Micha Sharir§
November 17, 2008
Abstract
We show the existence of -nets of size O 1
log log 1
for planar point sets and axis-parallel
rectangular ranges. The same bound holds for points in the plane with "fat" triangular ranges,
and for point sets in R3
and axis-parallel boxes; these are the first known non-trivial bounds for
these range spaces. Our technique also yields improved bounds on the size of -nets in the more
general context considered by Clarkson and Varadarajan. For example, we show the existence
of -nets of size O 1
log log log 1
for the dual range space of "fat" regions and planar point
sets (where the regions are the ground objects and the ranges are subsets stabbed by points).
Plugging our bounds into the technique of Bršonnimann and Goodrich, we obtain improved
approximation factors (computable in randomized polynomial time) for the hitting set or the

  

Source: Aronov, Boris - Department of Computer and Information Science, Polytechnic University

 

Collections: Computer Technologies and Information Sciences