# Minimum Color Spanning Circle in Imprecise Setup

Maria Saumell Mendiola, 15 Nov 2021

Let \(R\) be a set of \(n\) colored imprecise points, where each point is colored by one of \(k\) colors. Each imprecise point is specified by a unit disk in which the point lies. We study the problem of computing the smallest and the largest possible minimum color spanning circle, among all possible choices of points inside their corresponding disks. We present an \(\mathcal{O}(nk\cdot\log n)\) time algorithm to compute a smallest minimum color spanning circle. Regarding the largest minimum color spanning circle, we show that the problem is \(\mathsf{NP}\)-hard and present a \(\frac{1}{3}\)-factor approximation algorithm.

Joint work with A. Acharyya, R.K. Jallu, V. Keikha and M. Löffler