Approximation of a direction of Nd in bounded coordinates

  • Authors:

  • Jean-Christophe Novelli;Gilles Schaeffer;Florent Hivert

  • Affiliations:

  • Université Paris 7, LIAFA 2, place Jussieu, 75251 Paris cedex 05, France;École Polytechnique, LIX 91128, Palaiseau cedex, France;Université Paris 7, LIAFA 2, place Jussieu, 75251 Paris cedex 05, France

  • Venue:
  • Mobile Networks and Applications - Dial m for mobility: discrete algorithms and methods for mobile computing and communication
  • Year:
  • 2001

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Abstract

In this paper, we address the following problem: a direction in Rd is given by a vector with large integral coordinates and we have to find a vector with bounded integral coordinates which realizes a good approximation of this direction. We present a short algorithm that efficiently computes an optimal approximation with respect to the distance to the direction. We then compare experimental results with those of a straightforward rounding algorithm with respect to the distance to the direction and to the angle with it.