Closest-point problems

  title={Closest-point problems},
  author={M. Shamos and Dan Hoey},
  journal={16th Annual Symposium on Foundations of Computer Science (sfcs 1975)},
  • M. Shamos, Dan Hoey
  • Published 1975
  • Mathematics, Computer Science
  • 16th Annual Symposium on Foundations of Computer Science (sfcs 1975)
  • A number of seemingly unrelated problems involving the proximity of N points in the plane are studied, such as finding a Euclidean minimum spanning tree, the smallest circle enclosing the set, k nearest and farthest neighbors, the two closest points, and a proper straight-line triangulation. For most of the problems considered a lower bound of O(N log N) is shown. For all of them the best currently-known upper bound is O(N2) or worse. The purpose of this paper is to introduce a single geometric… CONTINUE READING
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