# Binary space partitions for fat rectangles

Published

Journal Article

We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, nonintersecting, two-dimensional rectangles in R3 such that the aspect ratio of each rectangle in S is at most α, for some constant α≥1. We present an n2O(√log n)-time algorithm to build a binary space partition of size n2O(√log n) for S. We also show that if m of the n rectangles in S have aspect ratios greater than α, we can construct a BSP of size n√m2O(√log n) for S in n√m2O(√log n) time. The constants of proportionality in the big-oh terms are linear in log α. We extend these results to cases in which the input contains nonorthogonal or intersecting objects.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Grove, EF; Murali, TM; Vitter, JS

### Published Date

- March 1, 2000

### Published In

### Volume / Issue

- 29 / 5

### Start / End Page

- 1422 - 1448

### International Standard Serial Number (ISSN)

- 0097-5397

### Digital Object Identifier (DOI)

- 10.1137/S0097539797320578

### Citation Source

- Scopus