Binary Space Partitions for Fat Rectangles
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(\...
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| Vydáno v: | SIAM journal on computing Ročník 29; číslo 5; s. 1422 - 1448 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Philadelphia, PA
Society for Industrial and Applied Mathematics
01.01.2000
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| Témata: | |
| ISSN: | 0097-5397, 1095-7111 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | 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. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0097-5397 1095-7111 |
| DOI: | 10.1137/S0097539797320578 |