Discrete & Computational Geometry

, Volume 5, Issue 5, pp 449-483

First online:

Partitioning arrangements of lines I: An efficient deterministic algorithm

  • Pankaj K. AgarwalAffiliated withCourant Institute of Mathematical Sciences, New York University

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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.