Paper by Erik D. Demaine

David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, and Godfried Toussaint, “Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries”, Discrete & Computational Geometry, volume 33, number 4, April 2005, pages 593–604.

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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Related papers:
VoronoiBoundary_WADS2003 (Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries)

See also other papers by Erik Demaine.
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Last updated July 25, 2017 by Erik Demaine.