# Minkowski's Convex Body Theorem and Integer Programming

@article{Kannan1987MinkowskisCB, title={Minkowski's Convex Body Theorem and Integer Programming}, author={Ravi Kannan}, journal={Math. Oper. Res.}, year={1987}, volume={12}, pages={415-440} }

The paper presents an algorithm for solving Integer Programming problems whose running time depends on the number n of variables as nOn. This is done by reducing an n variable problem to 2n5i/2 problems in n-i variables for some i greater than zero chosen by the algorithm. The factor of On5/2 “per variable” improves the best previously known factor which is exponential in n. Minkowski's Convex Body theorem and other results from Geometry of Numbers play a crucial role in the algorithm. Several…

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