Output-sensitive algorithms for computing nearest-neighbour decision boundaries

David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint

Research output: Contribution to journalArticle

Abstract

Given a set R of red points and a set B of blue points, the nearest-neighbour decision rule classifies a new point q as red (respectively, blue) if the closest point to q in R ∪ B comes from R (respectively, B). This rule implicitly partitions space into a red set and a blue set that are separated by a red-blue decision boundary. In this paper we develop output-sensitive algorithms for computing this decision boundary for point sets on the line and in ℝ2. Both algorithms run in time O(n log k), where k is the number of points that contribute to the decision boundary. This running time is the best possible when parameterizing with respect to n and k.

Original languageEnglish (US)
Pages (from-to)593-604
Number of pages12
JournalDiscrete and Computational Geometry
Volume33
Issue number4
DOIs
StatePublished - Apr 2005

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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