Given a mixed integer linear program with $m$ constraints and $n$ variables how much time do we need to solve this?
I know that MIPs like IPs are in general NP-hard. Nevertheless for IPs one can show that the problem $\lbrace \min c^T x | Ax=b, x \geq 0, x \in \mathbb{Z}^n \rbrace $ can be solved in time $(m \Delta)^{O(m)} ||b||_\infty^2$ where $\Delta$ is an upper bound on each absolute value of an entry in $A$ (Source: https://arxiv.org/abs/1707.00481). Does there exists a similar result for MIPs? Or is there a way to use this result?
On the other hand in practice Branch-and-Bound or Branch-And-Cut algorithms are mostly used for solving MIPs. Unfortunately I cannot find explicit running times, just the statement that in the worst case these algorithms have exponential running time (This means $m^n?$).