The complexity of cutting complexes
Discrete & Computational Geometry
Quasi-optimal range searching in spaces of finite VC-dimension
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Ray shooting and other applications of spanning trees with low stabbing number
SIAM Journal on Computing
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Rectilinear decompositions with low stabbing number
Information Processing Letters
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Stabbing triangulations by lines in 3D
Proceedings of the eleventh annual symposium on Computational geometry
On R-trees with low query complexity
Computational Geometry: Theory and Applications
On Spanning Trees with Low Crossing Numbers
Data Structures and Efficient Algorithms, Final Report on the DFG Special Joint Initiative
Minimizing the stabbing number of matchings, trees, and triangulations
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Cost-driven octree construction schemes: an experimental study
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
The minimum stabbing triangulation problem: IP models and computational evaluation
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
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It is shown that for any orthogonal subdivision of size n in a d-dimensional Euclidean space, d ∈ℕ, d ≥ 2, there is an axis-parallel line that stabs at least Ω(log1/(d−1)n) boxes. For any integer k, 1≤ kd, there is also an axis-aligned k-flat that stabs at least Ω(log$^{\rm 1/ \lfloor (d-1)/k \rfloor }$n) boxes of the subdivision. These bounds cannot be improved.