### 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) |
---|---|

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 - 2003 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

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

*2748*, 451-461.

**Output-sensitive algorithms for computing nearest-neighbour decision boundaries.** / Bremner, David; Demaine, Erik; Erickson, Jeff; Iacono, John; Langerman, Stefan; Morin, Pat; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 2748, pp. 451-461.

}

TY - JOUR

T1 - Output-sensitive algorithms for computing nearest-neighbour decision boundaries

AU - Bremner, David

AU - Demaine, Erik

AU - Erickson, Jeff

AU - Iacono, John

AU - Langerman, Stefan

AU - Morin, Pat

AU - Toussaint, Godfried

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=35248827671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248827671&partnerID=8YFLogxK

M3 - Article

VL - 2748

SP - 451

EP - 461

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -