Discrete & Computational Geometry

, Volume 5, Issue 5, pp 449–483

Partitioning arrangements of lines I: An efficient deterministic algorithm


  • Pankaj K. Agarwal
    • Courant Institute of Mathematical SciencesNew York University

DOI: 10.1007/BF02187805

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


In this paper we consider the following problem: Given a set ℒ ofn lines in the plane, partition the plane intoO(r2) 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.

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© Springer-Verlag New York Inc. 1990