Algorithmica

, Volume 60, Issue 1, pp 95–109 | Cite as

Fitting a Step Function to a Point Set

Article

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(nlog n) 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(nlog 4n). Finally, we give an O(nh2log n) algorithm for the case where h outliers are allowed. The running time of all our algorithms is independent of k.

Keywords

Algorithm Design Optimization Computational geometry Shape fitting Histogram 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Laboratoire PRiSM, CNRS UMR 8144Université de Versailles Saint-Quentin-en-YvelinesVersaillesFrance
  2. 2.UR 341 Mathématiques et Informatique AppliquéesINRAJouy-en-JosasFrance

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