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In this paper, we consider the colorful $k$-center problem, which is ageneralization of the well-known $k$-center problem. Here, we are given red andblue points in a metric space, and a coverage requirement for each color. Thegoal is to find the smallest radius $\rho$, such that with $k$ balls of radius$\rho$, the desired number of points of each color can be covered. We obtain aconstant approximation for this problem in the Euclidean plane. We obtain thisresult by combining a "pseudo-approximation" algorithm that works in any metricspace, and an approximation algorithm that works for a special class ofinstances in the plane. The latter algorithm uses a novel connection to acertain matching problem in graphs.

A Constant Approximation for Colorful k-Center