Abstract
We consider the problem of fitting a step function to a set of points. More precisely, given an integer k and a set P of n points in the plane, our goal is to find a step function f with k steps that minimizes the maximum vertical distance between f and all the points in P. We first give an optimal Θ(n logn) algorithm for the general case. In the special case where the points in P are given in sorted order according to their x-coordinates, we give an optimal Θ(n) time algorithm. Then, we show how to solve the weighted version of this problem in time O(n log4 n). Finally, we give an O(n h 2 logh) algorithm for the case where h outliers are allowed, and the input is sorted. The running time of all our algorithms is independent of k.
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Fournier, H., Vigneron, A. (2008). Fitting a Step Function to a Point Set. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_37
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DOI: https://doi.org/10.1007/978-3-540-87744-8_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87743-1
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