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}
}
  • R. Kannan
  • Published 1 August 1987
  • Mathematics, Computer Science
  • Math. Oper. Res.
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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