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Given a set of n points in the plane, each point having a positive weight,and an integer k>0, we present an optimal O(n \log n)-time deterministicalgorithm to compute a step function with k steps that minimizes the maximumweighted vertical distance to the input points. It matches the expected timebound of the best known randomized algorithm for this problem. Our approachrelies on Cole's improved parametric searching technique.

A deterministic algorithm for fitting a step function to a weighted point-set