An optimal algorithm for intersecting line segments in the plane (1992)
| Venue: | J. ACM |
| Citations: | 148 - 2 self |
BibTeX
@ARTICLE{Chazelle92anoptimal,
author = {Bernard Chazelle and Herbert Edelsbrunner},
title = {An optimal algorithm for intersecting line segments in the plane},
journal = {J. ACM},
year = {1992},
volume = {39},
pages = {1--54}
}
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Abstract
Abstract. Themain contribution ofthiswork is an O(nlogr ~ +k)-timeal gorithmfo rcomputingall k intersections among n line segments in the plane, This time complexity IS easdy shown to be optimal. Within thesame asymptotic cost, ouralgorithm canalso construct thesubdiwslon of theplancdefmed 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.
