Strong IP Formulations Need Large Coefficients

The development of practically well-behaving integer programming formulations is an important aspect of solving linear optimization problems over a set $X \subseteq \{0,1\}^n$. In practice, one is often interested in strong integer formulations with additional properties, e.g., bounded coefficients to avoid numerical instabilities. This article presents a lower bound on the size of coefficients in … Read more

On the Size of Integer Programs with Bounded Coefficients or Sparse Constraints

Integer programming formulations describe optimization problems over a set of integer points. A fundamental problem is to determine the minimal size of such formulations, in particular, if the size of the coefficients or sparsity of the constraints is bounded. This article considers lower and upper bounds on these sizes both in the original and in … Read more