Optimal randomized incremental construction for guaranteed logarithmic planar point location

@article{Hemmer2016OptimalRI,
  title={Optimal randomized incremental construction for guaranteed logarithmic planar point location},
  author={Michael Hemmer and Michal Kleinbort and Dan Halperin},
  journal={Comput. Geom.},
  year={2016},
  volume={58},
  pages={110-123}
}
  • Michael Hemmer, Michal Kleinbort, Dan Halperin
  • Published 2016
  • Computer Science, Mathematics
  • Comput. Geom.
  • Given a planar map of n segments in which we wish to efficiently locate points, we present the first randomized incremental construction of the well-known trapezoidal-map search-structure that only requires expected O ( n log ź n ) preprocessing time while deterministically guaranteeing worst-case linear storage space and worst-case logarithmic query time. The best previously known randomized construction time of the search structure, which is based on a directed acyclic graph, so-called the… CONTINUE READING
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