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Partitioning arrangements of lines I: An efficient deterministic algorithm
 Pankaj K. Agarwal
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In this paper we consider the following problem: Given a set ℒ ofn lines in the plane, partition the plane intoO(r ^{2}) triangles so that no triangle meets more thanO(n/r) lines of ℒ. We present a deterministic algorithm for this problem withO(nr logn/r) running time, whereω is a constant <3.33.
Work on this paper has been supported by Office of Naval Research Grant N0001487K0129, by National Science Foundation Grant DCR8320085, and by grants from the Digital Equipment Corporation and the IBM Corporation. A preliminary version of this paper appears in theProceedings of the 5th Annual Symposium on Computational Geometry, 1989, pp. 11–22.
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 Title
 Partitioning arrangements of lines I: An efficient deterministic algorithm
 Journal

Discrete & Computational Geometry
Volume 5, Issue 1 , pp 449483
 Cover Date
 19901201
 DOI
 10.1007/BF02187805
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Pankaj K. Agarwal ^{(1)}
 Author Affiliations

 1. Courant Institute of Mathematical Sciences, New York University, 10012, NY, USA