Dynamic Maintenance of the Lower Envelope of Pseudo-Lines
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We present a fully dynamic data structure for the maintenance of lower envelopes of pseudo-lines. The structure has O(^2 n) update time and O( 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( n) time, using tentative binary search; the lower envelopes are special in that at x=-∞ 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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