Dynamic Maintenance of the Lower Envelope of Pseudo-Lines.
arXiv: Computational Geometry(2019)
摘要
We present a fully dynamic data structure for the maintenance of lower envelopes of pseudo-lines. The structure has $O(log^2 n)$ update time and $O(log n)$ vertical ray shooting query time. To achieve this performance, we devise a new algorithm for finding the intersection between two lower envelopes of pseudo-lines in $O(log n)$ time, using emph{tentative} binary search; the lower envelopes are special in that at $x=-infty$ any pseudo-line contributing to the first envelope lies below every pseudo-line contributing to the second envelope. The structure requires $O(n)$ storage space.
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