# The importance of evaluating the number of constraints

If I introduce a problem, say as an ILP formulation, should I also discuss the number of introduced constraints? If yes, why?

• If you have an exponential number of them (e.g., for the TSP, the set of constraints that forbid cycling), then you have a problem. Dec 6 '21 at 12:30
• The number of constraints may indicate how well the formulation will scale. For a given problem, a formulation with $O(n)$ constraints might work better than a formulation with $O(n^2)$ constraints for large problems even if the second formulation is tighter. See for example the various formulations for the clique problem "Worst-case analysis of clique MIPs" (Naderi et al., 2021) DOI PDF Dec 6 '21 at 15:05