Computing Balanced Islands in Two Colored Point Sets in the Plane

Oswin Aichholzer, Nieves Atienza, José M. Díaz-Báñez, Ruy Fabila-Monroy, David Flores-Peñaloza, Pablo Pérez-Lantero, Birgit Vogtenhuber, Jorge Urrutia Galicia

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)28 - 32
JournalInformation Processing Letters
Volume135
DOIs
Publication statusPublished - 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