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. © 2005 Springer Science+Business Media, Inc.
CITATION STYLE
Bremner, D., Demaine, E., Erickson, J., Iacono, J., Langerman, S., Morin, P., & Toussaint, G. (2005). Output-sensitive algorithms for computing nearest-neighbour decision boundaries. Discrete and Computational Geometry, 33(4), 593–604. https://doi.org/10.1007/s00454-004-1152-0
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