Polynomial Bounds on the Rectangle Slicing Number.
Wed, 04/21/2010 - 15:01 — SomNambul
link: http://arxiv.org/abs/1004.3381
Abstract
Abstract
We examine the following question raised by V. Vatter: How many axis-parallel
lines does it take to slice a finite set of rectangles in the plane, if the
maximum independent set is at most $m$? For the planar case, we give a
quadratic bound on this number, thereby improving the previously known upper
bound, which was exponential in $m$. We show that under a reasonable assumption
our result can be generalized to the higher-dimensional case to show the bound
is polynomial for any fixed $d$.
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