Fast dynamic intersection searching in a set of isothetic line segments

doi:10.1016/0020-0190(85)90054-7

Information Processing Letters

Volume 21, Issue 4, 7 October 1985, Pages 165-171

https://doi.org/10.1016/0020-0190(85)90054-7 Get rights and content

Abstract

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(log N + 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.

References (15)

J.L. Bentley
Decomposable searching problems
Inform. Process. Lett.
(1979)
H. Edelsbrunner et al.
On the intersection of orthogonal objects
Inform. Process. Lett.
(1981)
H. Edelsbrunner et al.
Some methods of computational geometry applied to computer graphics
Computer Vision, Graphics and Image Processing
(1984)
E. Soisalon-Soininen et al.
Optimal algorithms to compute the closure of a set of iso-rectangles
J. Algorithms
(1984)
J.J. Bentley
Solutions to Klee's rectangle problems
(1977)
J.L. Bentley et al.
An optimal worst-case algorithm for reporting intersections of rectangles
IEEE Trans. Comput.
(1980)
B.M. Chazelle
Filtering search: A new approach to query answering

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Fast dynamic intersection searching in a set of isothetic line segments

Abstract

Inform. Process. Lett.

Inform. Process. Lett.

Computer Vision, Graphics and Image Processing

J. Algorithms

Solutions to Klee's rectangle problems

An optimal worst-case algorithm for reporting intersections of rectangles

IEEE Trans. Comput.

Filtering search: A new approach to query answering