Fast 2-variable integer programming

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Abstract

We show that a 2-variable integer program defined by m constraints involving coeffcients with at most s bits can be solved with O(m+s logm) arithmetic operations or with O(m+logmlogs)M(s) bit operations, where M(s) is the time needed for s-bit integer multiplication.

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Eisenbrand, F., & Rote, G. (2001). Fast 2-variable integer programming. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2081, pp. 78–89). Springer Verlag. https://doi.org/10.1007/3-540-45535-3_7

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