A note on binary plane partitions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Binary space partitions for line segments with a limited number of directions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Binary space partitions of orthogonal subdivisions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
On the union of κ-round objects
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Binary plane partitions for disjoint line segments
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Approximate range searching using binary space partitions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in ${\Bbb R}^3$ such that the aspect ratio of each rectangle in $S$ is at most $\alpha$, for some constant $\alpha \geq 1$. We present an $n2^{O(\sqrt{\log n})}$-time algorithm to build a binary space partition of size $n2^{O(\sqrt{\log n})}$ for $S$. We also show that if $m$ of the $n$ rectangles in $S$ have aspect ratios greater than $\alpha$, we can construct a BSP of size $n\sqrt{m}2^{O(\sqrt{\log n})}$ for $S$ in $n\sqrt{m}2^{O(\sqrt{\log n})}$ time. The constants of proportionality in the big-oh terms are linear in $\log \alpha$. We extend these results to cases in which the input contains nonorthogonal or intersecting objects.