Fast dynamic intersection searching in a set of isothetic line segments

We reconsider the (isothetic) line segment intersection searching problem: Given a set S of n horizontal and vertical line segments and a query segment q, find all t segments in S intersecting q. We describe the first dynamic solution for this problem which achieves O(log n + t) query time. This, however, has to be paid by O(n log² n) space requirements and O(log³ n) update time. If segments are defined over a grid of size N × N (the semidynamic case), then the problem can be solved in O(logN + t) query time, O(n log² N) space and O(log² N) update time. The solution is based on the use of segment tree and range tree and the halfobject technique.