### 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) | 593-604 |

Number of pages | 12 |

Journal | Discrete and Computational Geometry |

Volume | 33 |

Issue number | 4 |

DOIs | |

State | Published - 2005 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics
- Discrete Mathematics and Combinatorics
- Geometry and Topology

### Cite this

*Discrete and Computational Geometry*,

*33*(4), 593-604. https://doi.org/10.1007/s00454-004-1152-0

**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

*Discrete and Computational Geometry*, vol. 33, no. 4, pp. 593-604. https://doi.org/10.1007/s00454-004-1152-0

}

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 - 2005

Y1 - 2005

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=17444374947&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17444374947&partnerID=8YFLogxK

U2 - 10.1007/s00454-004-1152-0

DO - 10.1007/s00454-004-1152-0

M3 - Article

VL - 33

SP - 593

EP - 604

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 4

ER -