Average Case Analysis of Dynamic Geometric Optimization

@article{Eppstein1994AverageCA,
  title={Average Case Analysis of Dynamic Geometric Optimization},
  author={David Eppstein},
  journal={Comput. Geom.},
  year={1994},
  volume={6},
  pages={45-68}
}
We maintain the maximum spanning tree of a planar point set, as points are inserted or deleted, in O(log n) expected time per update in Mulmuley’s average-case model of dynamic geometric computation. We use as subroutines dynamic algorithms for two other geometric graphs: the farthest neighbor forest and the rotating caliper graph related to an algorithm for static computation of point set widths and diameters. We maintain the former graph in expected time O(log n) per update and the latter in… CONTINUE READING
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Dynamic algorithms for half-space reporting, proximity problems, and geometric minimum spanning trees

  • P. K. Agarwal, D. Eppstein, J. Matoušek
  • In Proc. 33rd IEEE Symp. Foundations of Computer…
  • 1992
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