Output-sensitive algorithms for computing nearest-neighbour decision boundaries
David Avis, Erik D. Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint · 2003
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 R . 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.