H. Fournier, A. Vigneron
Information Processing Letters, 113(3), 51-54, (2013)
Given a set of n points in the plane, each point having a positive weight, and an integer k>0k>0, we present an optimal View the MathML sourceO(nlogn)-time deterministic algorithm to compute a step function with k steps that minimizes the maximum weighted vertical distance to the input points. It matches the expected time bound of the best known randomized algorithm for this problem. Our approach relies on Coleʼs improved parametric searching technique. As a direct application, our result yields the first View the MathML sourceO(nlogn)-time algorithm for computing a k-center of a set of n weighted points on the real line.