We consider the practical problem of constructing binary space partitions (BSPs) for a set S of n orthogonal, non-intersecting, two-dimensional rectangles in R 3 such that the aspect ratio of each rectangle in S is at most ff, for some constant ff 1. We present an n2 O( p log n ) -time algorithm to build a binary space partition of size n2 O( p log n ) for S. We also show that if m of the n rectangles in S have aspect ratios greater than ff, we can construct a BSP of size n p m2 O( p log n ) for S in n p m2 O( p log n ) time. The constants of proportionality in the big-oh terms are linear in log ff. We extend these results to cases in which the input contains non-orthogonal or intersecting objects. A preliminary version of this paper appeared in the Proceedings of the 37th Annual Symposium on Foundations of Computer Science, 1996. y Support was provided by National Science Foundation research grant CCR--93--01259, by Army Research Office MURI grant DAAH04--9...

We present the rst systematic comparison of the performance of algorithms that construct Binary Space Partitions for orthogonal rectangles in R 3. We compare known algorithms with our implementation of a variant of a recent algorithm of Agarwal et al. [1]. We show via an empirical study that their algorithm constructs BSPs of near-linear size in practice and performs better than most of the other algorithms in the literature. 1