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Binary space partitions for fat rectangles

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4 Author(s)
Agarwal, Pankaj K. ; Dept. of Comput. Sci., Duke Univ., Durham, NC, USA ; Grove, E.F. ; Murali, T.M. ; Vitter, J.S.

The authors 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 a α⩾1. They present an n2O(√logn)-time algorithm to build a binary space partition of size n2O(√logn) for S. They also show that if m of the n rectangles in S have aspect ratios greater than α, they can contact a BSP of size n√m2O(√logn) for S in n√2O(√logn) time. The constants of proportionality in the big-oh terms are linear in log α. They extend these results to cases in which the input contains non-orthogonal or intersecting objects

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996