# Have fixed parameter integer program algorithms ever been implemented for research use?

Have any fixed parameter integer programming algorithms described in Integer programming with a fixed number of variables been implemented? Is there a reference code that researchers can use?

One of the key steps in Lenstra's algorithm uses basis reduction (BR) to locate "thin directions" for the polytope. Branching on such a direction produces only a small (i.e., polynomial number) of subproblems. In a series of papers, Aardal and coauthors essentially applied this BR step to help solve (using standard MIP solvers) otherwise hard-to-solve IP instances (see, e.g., this paper and this paper). We (also see arXiv) have studied a similar, but arguably simpler and more general, approach (full disclosure: self-citation here!) to solve IP feasibility problems: apply BR to the constraint matrix $A$ of the IP feasibility problem (of the form $\{\mathbf{l} \leq A \mathbf{x} \leq \mathbf{u}, \mathbf{x} \in \mathbb{Z}^n\}$), and use standard techniques to solve the resulting reformulated IP feasibility problem. The BR could be performed using standard software tools such as NTL.