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The complexity of greatest common divisor computations

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Algorithmic Number Theory (ANTS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 877))

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Abstract

We study the complexity of expressing the greatest common divisor of n positive numbers as a linear combination of the numbers. We prove the NP-completeness of finding an optimal set of multipliers with respect to either the L 0 metric or the L ∞ norm. We present and analyze a new method for expressing the gcd of n numbers as their linear combination and give an upper bound on the size of the largest multiplier produced by this method, which is optimal.

partially supported by the Australian Research Council.

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Authors and Affiliations

  1. Key Centre for Software Technology Department of Computer Science, The University of Queensland, 4072, Queensland, Australia

    Bohdan S. Majewski & George Havas

Authors
  1. Bohdan S. Majewski
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  2. George Havas
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Editor information

Leonard M. Adleman Ming-Deh Huang

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© 1994 Springer-Verlag Berlin Heidelberg

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Majewski, B.S., Havas, G. (1994). The complexity of greatest common divisor computations. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_56

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  • DOI: https://doi.org/10.1007/3-540-58691-1_56

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58691-3

  • Online ISBN: 978-3-540-49044-9

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