NDLI: Binary Space Partitions for Axis-Aligned Fat Rectangles

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tth, Csaba D.
Copyright Year	2008
Abstract	It is shown that for any n disjoint axis-aligned fat rectangles in three-space there is a binary space partition (BSP) of $O(n\log^8 n)$ size and $O(\log^5 n)$ height and it can be constructed in $O(n \,\mathrm{polylog}\, n)$ time. This improves earlier bounds of Agarwal et al. [SIAM J. Comput., 29 (2000), pp. 14221448]. On the other hand, for every $n\in \mathbb{N}$, there are n disjoint axis-aligned fat rectangles in $\mathbb{R}^3$ such that their smallest axis-aligned BSP has $\Omega(n\log n)$ size.
Starting Page	429
Ending Page	447
Page Count	19
File Format	PDF
ISSN	00975397
DOI	10.1137/06065934X
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	38
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-05-21
Access Restriction	Subscribed
Subject Keyword	fat objects binary space partition Computer graphics; computational geometry Combinatorial complexity of geometric structures Partitions of sets axis-aligned rectangles convex partition
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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Binary Space Partitions for Axis-Aligned Fat Rectangles