Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries

  • David Bremner
  • Erik Demaine
  • Jeff Erickson
  • John Iacono
  • Stefan Langerman
  • Pat Morin
  • Godfried Toussaint
Conference paper

DOI: 10.1007/978-3-540-45078-8_39

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)
Cite this paper as:
Bremner D. et al. (2003) Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries. In: Dehne F., Sack JR., Smid M. (eds) Algorithms and Data Structures. WADS 2003. Lecture Notes in Computer Science, vol 2748. Springer, Berlin, Heidelberg

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • David Bremner
    • 1
  • Erik Demaine
    • 2
  • Jeff Erickson
    • 3
  • John Iacono
    • 4
  • Stefan Langerman
    • 5
  • Pat Morin
    • 6
  • Godfried Toussaint
    • 7
  1. 1.Faculty of Computer ScienceUniversity of New Brunswick 
  2. 2.MIT Laboratory for Computer Science 
  3. 3.Computer Science DepartmentUniversity of Illinois 
  4. 4.Polytechnic University 
  5. 5.Chargé de recherches du FNRSUniversité Libre de Bruxelles 
  6. 6.School of Computer ScienceCarleton University 
  7. 7.School of Computer ScienceMcGill University 

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