@inproceedings{Hershberger2003BinarySP,
title={Binary space partitions for 3D subdivisions},
author={John Hershberger and Subhash Suri},
booktitle={SODA},
year={2003}
}

We consider the following question: Given a subdivision of space into <i>n</i> convex polyhedral cells, what is the worst-case complexity of a binary space partition (BSP) for the subdivision? We show that if the subdivision is rectangular and axis-aligned, then the worstcase complexity of an axis-aligned BSP is Ω(<i>n</i><sup>4/3</sup>) and <i>O</i>(<i>n</i><sup>α</sup> log<sup>2</sup> <i>n</i>), where α = 1 + log<inf>2</inf>(4/3 ) = 1.4150375 .... By contrast, it is known that the BSP of a… CONTINUE READING