Cell Complexities in Hyperplane Arrangements

  • Authors:

  • Boris Aronov;Micha Sharir

  • Affiliations:

  • Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201-3840, USA;School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA

  • Venue:
  • Discrete & Computational Geometry
  • Year:
  • 2004

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Abstract

We derive improved bounds on the complexity, i.e., the total number of faces of all dimensions, of many cells in arrangements of hyperplanes in higher dimensions, and use these bounds to obtain a very simple proof of an earlier bound, due to Aronov, Matousek, and Sharir, on the sum of squares of cell complexities in such an arrangement.