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Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries

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Algorithms and Data Structures (WADS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2748))

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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.

This research was partly funded by the Alexander von Humboldt Foundation and The Natural Sciences and Engineering Research Council of Canada.

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, University of New Brunswick,  

    David Bremner

  2. MIT Laboratory for Computer Science,  

    Erik Demaine

  3. Computer Science Department, University of Illinois,  

    Jeff Erickson

  4. Polytechnic University,  

    John Iacono

  5. Chargé de recherches du FNRS, Université Libre de Bruxelles,  

    Stefan Langerman

  6. School of Computer Science, Carleton University,  

    Pat Morin

  7. School of Computer Science, McGill University,  

    Godfried Toussaint

Authors
  1. David Bremner
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  2. Erik Demaine
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  3. Jeff Erickson
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  4. John Iacono
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  5. Stefan Langerman
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  6. Pat Morin
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  7. Godfried Toussaint
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Editor information

Editors and Affiliations

  1. Carleton University, Ottawa, Canada

    Frank Dehne

  2. School of Computer Science, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada

    Jörg-Rüdiger Sack

  3. School of Computer Science, Carleton University, K1S 5B6, Ottawa, ON, Canada

    Michiel Smid

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© 2003 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/978-3-540-45078-8_39

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  • DOI: https://doi.org/10.1007/978-3-540-45078-8_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40545-0

  • Online ISBN: 978-3-540-45078-8

  • eBook Packages: Springer Book Archive

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