### 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 ℝ ^{2}. 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.

Original language | English (US) |
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Pages (from-to) | 451-461 |

Number of pages | 11 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 2748 |

State | Published - Dec 1 2003 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*2748*, 451-461.