Paper by Erik D. Demaine

Reference:

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.

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.

Comments:

This paper is also available from SpringerLink.

Availability:

The paper is available in PostScript (646k), gzipped PostScript (177k), and PDF (223k).

See information on file formats.

[Google Scholar search]

Related papers:

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