# Partitioning arrangements of lines I: An efficient deterministic algorithm

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DOI: 10.1007/BF02187805

- Cite this article as:
- Agarwal, P.K. Discrete Comput Geom (1990) 5: 449. doi:10.1007/BF02187805

## 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.

## Copyright information

© Springer-Verlag New York Inc. 1990