Approximation of a direction of Nd in bounded coordinates

Jean Christophe Novelli; Gilles Schaeffer; Florent Hivert

doi:10.1023/A:1011818306681

Approximation of a direction of N^d in bounded coordinates

Jean Christophe Novelli
, Gilles Schaeffer
, Florent Hivert

Laboratoire de Probabilités et Modèles Aléatoires

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we address the following problem: a direction in R^d 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.

Original language	English
Pages (from-to)	547-550
Number of pages	4
Journal	Mobile Networks and Applications
Volume	6
Issue number	6
DOIs	https://doi.org/10.1023/A:1011818306681
Publication status	Published - 1 Jan 2001

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title = "Approximation of a direction of Nd in bounded coordinates",

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.",

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N2 - 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.

AB - 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.

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DO - 10.1023/A:1011818306681

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JO - Mobile Networks and Applications

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Approximation of a direction of N^d in bounded coordinates

Abstract

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