Binary plane partitions for disjoint line segments
Proceedings of the twenty-fifth annual symposium on Computational geometry
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
| Hi-index | 0.00 |
We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space-filling packings of boxes) in $d$-space. We show that a subdivision with $n$ boxes can be refined into a BSP of size $O(n^{(d+1)/{3}})$ for all $d \geq 3$ and that such a partition can be computed in time ${O(K\log n)}$, where $K$ is the size of the BSP produced. Our upper bound on the BSP size is tight for $3$-dimensional subdivisions; in higher dimensions, this is the first nontrivial result for general full-dimensional boxes. We also present a lower bound construction for a subdivision of $n$ boxes in $d$-space for which every axis-aligned BSP has $\Omega(n^{\beta(d)})$ size, where $\beta(d)$ converges to $(1+\sqrt{5})/2$ as $d \rightarrow \infty$.