Abstract: A computing device is provided, including a processor that receives a network graph. The processor further receives a specification of a network traffic control heuristic for a network traffic routing problem over the network graph. The processor further constructs a gap maximization problem that has, as a maximization target, a difference between an exact solution to the network traffic routing problem and a heuristic solution generated using the network traffic control heuristic. The processor further generates a Lagrange multiplier formulation of the gap maximization problem. At a convex solver, the processor further computes an estimated maximum gap as an estimated solution to the Lagrange multiplier formulation of the gap maximization problem. The processor further performs a network traffic control action based at least in part on the estimated maximum gap.