Discrete & Computational Geometry

, Volume 33, Issue 4, pp 593–604 | Cite as

Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries

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


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.


Computational Mathematic Decision Rule Close Point Decision Boundary Blue Point 
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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Faculty of Computer Science, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3Canada
  2. 2.Laboratory for Computer Science, MIT, 32 Vassar Street, Cambridge, MA 02139USA
  3. 3.Computer Science Department, University of Illinois, Urbana, IL 61801-2302USA
  4. 4.Department of Computer and Information Science, Polytechnic University, 6 MetroTech Center, Brooklyn, NY 11201USA
  5. 5.Charge de recherches du FNRS, Universite Libre de Bruxelles, ULB CP212, boulevard du Triomphe, 1050 Bruxelles Belgium
  6. 6.School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5BL Canada
  7. 7.School of Computer Science, McGill University, Montreal, Quebec H3A 2A7Canada

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