Red-Blue Point Separation for Points on a Circle
Abstract
Given a set R of red points and a set B of blue points in the plane, the Red-Blue point separation problem asks if there are at most k lines that separate R from B, that is, each cell induced by the lines of the solution is either empty or monochromatic (containing points of only one color). A common variant of the problem is when the lines are required to be axis-parallel. The problem is known to be NP-complete for both scenarios, and W[1]-hard parameterized by k in the former setting and FPT in the latter. We demonstrate a polynomial-time algorithm for the special case when the points lie on a circle. Further, we also demonstrate the W-hardness of a related problem in the axis-parallel setting, where the question is if there are p horizontal and q vertical lines that separate R from B. The hardness here is shown in the parameter p.
Cite
@article{arxiv.2005.06046,
title = {Red-Blue Point Separation for Points on a Circle},
author = {Neeldhara Misra and Harshil Mittal and Aditi Sethia},
journal= {arXiv preprint arXiv:2005.06046},
year = {2020}
}