Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries
- Cite this paper as:
- Bremner D. et al. (2003) Output-Sensitive Algorithms for Computing Nearest-Neighbour Decision Boundaries. In: Dehne F., Sack JR., Smid M. (eds) Algorithms and Data Structures. WADS 2003. Lecture Notes in Computer Science, vol 2748. Springer, Berlin, Heidelberg
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.
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