Output-sensitive algorithms for computing nearest-neighbour decision boundaries

David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)593-604
Number of pages12
JournalDiscrete and Computational Geometry
Volume33
Issue number4
DOIs
StatePublished - 2005

Fingerprint

Nearest Neighbor
Computing
Output
Decision Rules
Point Sets
Classify
Partition
Line

ASJC Scopus subject areas

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

Cite this

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

In: Discrete and Computational Geometry, Vol. 33, No. 4, 2005, p. 593-604.

Research output: Contribution to journalArticle

Bremner, David ; Demaine, Erik ; Erickson, Jeff ; Iacono, John ; Langerman, Stefan ; Morin, Pat ; Toussaint, Godfried. / Output-sensitive algorithms for computing nearest-neighbour decision boundaries. In: Discrete and Computational Geometry. 2005 ; Vol. 33, No. 4. pp. 593-604.
@article{df2533f19d1d4b4b88c7c08e44690217,
title = "Output-sensitive algorithms for computing nearest-neighbour decision boundaries",
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.",
author = "David Bremner and Erik Demaine and Jeff Erickson and John Iacono and Stefan Langerman and Pat Morin and Godfried Toussaint",
year = "2005",
doi = "10.1007/s00454-004-1152-0",
language = "English (US)",
volume = "33",
pages = "593--604",
journal = "Discrete and Computational Geometry",
issn = "0179-5376",
publisher = "Springer New York",
number = "4",

}

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 -