Publisher's Synopsis
Excerpt from Robotic Research Technical Report: On Vertical Visibility in Arrangements of Segments and the Queue Size in the Bentley-Ottman Line Sweeping Algorithm
We also consider a weaker variant of the problem (which has nothing to do with the bentley-ottman algorithm), in which we are given an arbitrary collection of n segments and wish to estimate the number of pairs of non-intersecting vertically visible segments, dropping the condition that these pairs intersect when extended to the right (and that the segments all have to end on the same vertical line). We show that the number of these pairs in this gen eral case is and can be ?(u4'3) in the worst case. (thus the innocent looking extra conditions that are assumed in the bentley-ottman case appear to be crucial for.
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