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# A Polynomial Algorithm for the Two-Variable Integer Programming Problem

@article{Kannan1980APA, title={A Polynomial Algorithm for the Two-Variable Integer Programming Problem}, author={Ravi Kannan}, journal={J. ACM}, year={1980}, volume={27}, pages={118-122} }

- Published 1980 in J. ACM
DOI:10.1145/322169.322179

A polynomial time algorithm is presented for solving the following two-variable integer programming problem maximize ClXl + c2x2 subject to a, lxl + a,2x2 =< b,, I = 1, 2, , n, and x~, x2 => O, integers, where a,j, cj, and b, are assumed to be nonnegattve integers This generahzes a result of Htrschberg and Wong, who developed a polynomial algorithm for the same problem with only one constraint (l e, where n = 1) However, the techniques used here are quite different