A Faster Algorithm for Two-Variable Integer Programming

نویسندگان

  • Friedrich Eisenbrand
  • Sören Laue
چکیده

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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تاریخ انتشار 2003