# Integer programming and Groebner basis

I enjoyed reading different papers about using Groebner basis to solve integer programming.

Is there any literature about the complexity and/or comparison with other (more classical) methods like gomory, branch and bound?

• The worst case complexity of Groebner bases is really bad: something like $d^{2^n}$ where $n$ is the number of variables and $d$ the maximum total degree of the inputs. That doesn't prevent this approach from being useful in particular instances. – Robert Israel Aug 7 '16 at 17:47

For a typical Integer Programming problem, assume it has the form: $\min {c*z} ~ \text{ s.t.} ~ A*z=b$