Dynamic Maintenance of the Lower Envelope of Pseudo-Lines

Wolfgang Mulzer

FU Berlin

Abstract

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 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.

Based on joint work with Pankaj K. Agarwal,, Ravid Cohen, and Dan Halperin.