### Abstract

Let $S$ be a set of $n$ points in general position in the plane, $r$ of which are red and $b$ of which are blue. In this paper we present algorithms to find convex sets containing a balanced number of red and blue points. We provide an $O(n^4)$ time algorithm that for a given $alpha in left [ 0,12 right ]$ finds a convex set containing exactly $lceil alpha r red points and exactly $lceil alpha b blue points of $S$. If $lceil alpha rlceil alpha b is not much larger than $13n$, we improve the running time to $O(n log n)$. We also provide an $O(n^2log n)$ time algorithm to find a convex set containing exactly $left lceil r+12right red points and exactly $left lceil b+12right blue points of $S$, and show that balanced islands with more points do not always exist.

Original language | English |
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Pages (from-to) | 28 - 32 |

Journal | Information Processing Letters |

Volume | 135 |

DOIs | |

Publication status | Published - 2018 |

### Keywords

- Equipartition, Islands, Convex sets, Computational geometry

## Cite this

Aichholzer, O., Atienza, N., Díaz-Báñez, J. M., Fabila-Monroy, R., Flores-Peñaloza, D., Pérez-Lantero, P., ... Urrutia Galicia, J. (2018). Computing Balanced Islands in Two Colored Point Sets in the Plane.

*Information Processing Letters*,*135*, 28 - 32. https://doi.org/10.1016/j.ipl.2018.02.008