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