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A Faster Algorithm for Two-Variable Integer Programming

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Algorithms and Computation (ISAAC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2906))

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Abstract

We show that a 2-variable integer program, defined by m constraints involving coefficients with at most ϕ bits can be solved with O(m + ϕ) arithmetic operations on rational numbers of size O(ϕ).

This result closes the gap between the running time of two-variable integer programming with the sum of the running times of the Euclidean algorithm on ϕ-bit integers and the problem of checking feasibility of an integer point for m constraints.

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Author information

Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Friedrich Eisenbrand & Sören Laue

Authors
  1. Friedrich Eisenbrand
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  2. Sören Laue
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Editor information

Editors and Affiliations

  1. School of Science and Technology, Kwansei Gakuin University, Sanda, Japan

    Toshihide Ibaraki

  2. Department of Architecture and Architectural Engineering, Kyoto University, 615-8540, Nishikyo-ku, Kyoto, Japan

    Naoki Katoh

  3. Department of Computer Science and Communication Engineering, Kyushu University, 812-8581, Fukuoka, Japan

    Hirotaka Ono

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Eisenbrand, F., Laue, S. (2003). A Faster Algorithm for Two-Variable Integer Programming. In: Ibaraki, T., Katoh, N., Ono, H. (eds) Algorithms and Computation. ISAAC 2003. Lecture Notes in Computer Science, vol 2906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24587-2_31

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  • DOI: https://doi.org/10.1007/978-3-540-24587-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20695-8

  • Online ISBN: 978-3-540-24587-2

  • eBook Packages: Springer Book Archive

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