# Binary plane partitions for disjoint line segments

@inproceedings{Tth2009BinaryPP, title={Binary plane partitions for disjoint line segments}, author={Csaba D. T{\'o}th}, booktitle={Symposium on Computational Geometry}, year={2009} }

- Published 2009 in Symposium on Computational Geometry
DOI:10.1145/1542362.1542375

A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition, where each step partitions the space (and some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open halfspaces. The size of a BSP is defined as the number of resulting fragments of the input objects. It is shown that every set of n disjoint line segments in the plane admits a BSP of size O(n log n / log log n). This bound is best possible apart… CONTINUE READING