, Volume 5, Issue 1, pp 449-483

Partitioning arrangements of lines I: An efficient deterministic algorithm

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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 N00014-87-K-0129, by National Science Foundation Grant DCR-83-20085, 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.