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}
}
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