LNCS 2748 Output Sensitive Algorithms for Computing Nearest Neighbour Decision Boundaries 1st Edition by David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint ISBN 3540450785 9783540450788
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Authors:David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin; Godfried Toussaint , Tags:Algorithms and Data Structures , Author sort:David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin & Toussaint, Godfried , Languages:Languages:eng , Published:Published:Jun 2003
LNCS 2748 – Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries 1st Edition by David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint – Ebook PDF Instant Download/Delivery. 3540450785, 9783540450788
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Product details:
ISBN 10: 3540450785
ISBN 13: 9783540450788
Author: David Bremner, Erik Demaine, Jeff Erickson, John Iacono, Stefan Langerman, Pat Morin, Godfried Toussaint
LNCS 2748 – Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries 1st Edition:
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.
This research was partly funded by the Alexander von Humboldt Foundation and The Natural Sciences and Engineering Research Council of Canada.
LNCS 2748 – Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries 1st Edition Table of contents:
1 Introduction
2 A 1-Dimensional Algorithm
3 A 2-Dimensional Algorithm
3.1 The High Level Algorithm
3.2 Pivots
3.3 Finding the First Edge
3.4 Finding More Points
4 Conclusions
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