# Optimal Discretization is Fixed-parameter Tractable

@article{Kratsch2021OptimalDI, title={Optimal Discretization is Fixed-parameter Tractable}, author={Stefan Kratsch and Tom{\'a}{\vs} Masař{\'i}k and Irene Muzi and Marcin Pilipczuk and Manuel Sorge}, journal={ArXiv}, year={2021}, volume={abs/2003.02475} }

Given two disjoint sets $W_1$ and $W_2$ of points in the plane, the Optimal Discretization problem asks for the minimum size of a family of horizontal and vertical lines that separate $W_1$ from $W_2$, that is, in every region into which the lines partition the plane there are either only points of $W_1$, or only points of $W_2$, or the region is empty. Equivalently, Optimal Discretization can be phrased as a task of discretizing continuous variables: we would like to discretize the range of $x… Expand

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