An optimal algorithm for intersecting line segments in the plane Journal Article


Author(s): Chazelle, Bernard; Edelsbrunner, Herbert
Article Title: An optimal algorithm for intersecting line segments in the plane
Affiliation
Abstract: The main contribution of this work is an O(n log n + k)-time algorithm for computing all k intersections among n line segments in the plane. This time complexity is easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment (if any) lies right above (or below) each intersection and each endpoint. The algorithm has been implemented and performs very well. The storage requirement is on the order of n + k in the worst case, but it is considerably lower in practice. To analyze the complexity of the algorithm, an amortization argument based on a new combinatorial theorem on line arrangements is used.
Keywords: computational complexity; Combinatorial mathematics; Numerical analysis
Journal Title: Journal of the ACM
Volume: 39
Issue 1
ISSN: 0004-5411
Publisher: ACM  
Date Published: 1992-01-01
Start Page: 1
End Page: 54
DOI: 10.1145/147508.147511
Open access: no
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