Axis-Aligned Subdivisions with Low Stabbing Numbers
Csaba D. Tóth · SIAM Journal on Discrete Mathematics · 2008
It is shown that for every subdivision of the d-dimensional Euclidean space, $d\geq 2$, into n axis-aligned boxes, there is an axis-parallel line that stabs at least $\Omega(\log^{1/(d-1)} n)$ boxes, and this bound is best possible. In general, it is also shown that for every integer k, $0