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

Hervé Fournier, Antoine E. Vigneron

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

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(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 Coles improved parametric searching technique. As a direct application, our result yields the first O(nlogn)-time algorithm for computing a k-center of a set of n weighted points on the real line. © 2012 Elsevier B.V.
Original languageEnglish (US)
Pages (from-to)51-54
Number of pages4
JournalInformation Processing Letters
Volume113
Issue number3
DOIs
StatePublished - Feb 2013

ASJC Scopus subject areas

  • Signal Processing
  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications

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