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A linear-time algorithm for linearL 1 approximation of points

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Abstract

In this paper we present a linear-time algorithm for approximating a set ofn points by a linear function, or a line, that minimizes theL 1 norm. The algorithmic complexity of this problem appears not to have been investigated, although anO(n 3) naive algorithm can be easily obtained based on some simple characteristics of an optimumL 1 solution. Our linear-time algorithm is optimal within a constant factor and enables us to use linearL 1 approximation of many points in practice. The complexity ofL 1 linear approximation of a piecewise linear function is also touched upon.

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Authors and Affiliations

  1. Department of Computer Science and Communication Engineering, Kyushu University, 812, Fukuoka, Japan

    Hiroshi Imai, Kenji Kato & Peter Yamamoto

  2. School of Computer Science, McGill University, H3A 2K6, Montreal, Quebec, Canada

    Peter Yamamoto

Authors
  1. Hiroshi Imai
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  2. Kenji Kato
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  3. Peter Yamamoto
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Additional information

Communicated by Chee-Keng Yap.

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Imai, H., Kato, K. & Yamamoto, P. A linear-time algorithm for linearL 1 approximation of points. Algorithmica 4, 77–96 (1989). https://doi.org/10.1007/BF01553880

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  • DOI: https://doi.org/10.1007/BF01553880

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