The region approach for computing relative neighbourhood graphs in the Lp metric

@article{Katajainen1988TheRA,
  title={The region approach for computing relative neighbourhood graphs in the Lp metric},
  author={Jyrki Katajainen},
  journal={Computing},
  year={1988},
  volume={40},
  pages={147-161}
}
The following geometrical proximity concepts are discussed: relative closeness and geographic closeness. Consider a setV={v 1,v 2, ...,v n } of distinct points in atwo-dimensional space. The pointv j is said to be arelative neighbour ofv i ifd p (v i ,v j )≤max{d p (v j ,v k ),d p (v j ,v k )} for allv k ∈V, whered p denotes the distance in theL p metric, 1≤p≤∞. After dividing the space around the pointv i into eight sectors (regions) of equal size, a closest point tov i in some region is… CONTINUE READING
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