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).
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Eisenbrand, F., Laue, S. A linear algorithm for integer programming in the plane. Math. Program. 102, 249–259 (2005). https://doi.org/10.1007/s10107-004-0520-0
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DOI: https://doi.org/10.1007/s10107-004-0520-0