# Partitioning arrangements of lines I: An efficient deterministic algorithm

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## Abstract

In this paper we consider the following problem: Given a set ℒ of*n* lines in the plane, partition the plane into*O*(*r*^{2}) triangles so that no triangle meets more than*O*(*n/r*) lines of ℒ. We present a deterministic algorithm for this problem with*O*(*nr* log*n/r*) running time, where*ω* is a constant <3.33.

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© Springer-Verlag New York Inc. 1990