# On Equal Point Separation by Planar Cell Decompositions

@article{Marda2017OnEP, title={On Equal Point Separation by Planar Cell Decompositions}, author={Nikhil Marda}, journal={arXiv: Combinatorics}, year={2017} }

In this paper, we investigate the problem of separating a set $X$ of points in $\mathbb{R}^{2}$ with an arrangement of $K$ lines such that each cell contains an asymptotically equal number of points (up to a constant ratio). We consider a property of curves called the stabbing number, defined to be the maximum countable number of intersections possible between the curve and a line in the plane. We show that large subsets of $X$ lying on Jordan curves of low stabbing number are an obstacle to… CONTINUE READING

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