Partitioning arrangements of lines I: An efficient deterministic algorithm

Abstract

In this paper we consider the following problem: Given a set ℒ of n lines in the plane, partition the plane into O(r2) 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. © 1990 Springer-Verlag New York Inc.