Efficient dynamic algorithms are presented for four geometric intersection problems. These include: (1) reporting the subset of a set S of nonintersecting segments in the plane that are intersected by a query segment of fixed slope; (2) reporting the segments of S that are intersected by a query segment whose supporting line passes through a fixed point; (3) the orthogonal segment intersection search problem; and (4) the point enclosure problem for isothetic hyper-rectangles in d-dimensional space, d ≥ 2. These algorithms are the first linear-space solutions to Problems 1-3 and for Problem 4 in the plane. For Problem 3, the update time improves upon the previous best algorithm by a logarithmic factor without affecting the query time. For Problem 4, the update time either matches or improves upon the previous best algorithms, but the query time is larger by a logarithmic factor. No dynamic algorithms were known previously for Problems 1 and 2.
Bibliographical noteFunding Information:
* Research supported in part by a grant-in-aid of research from the Graduate School of the University of Minnesota. The second author was also supported in part by NSF grant CCR-8808574.
- Analysis of algorithms
- computational complexity
- computational geometry
- data structures
- design of algorithms