Large scale systems have large numbers of inputs and outputs, and include whole chemical plants as well as some unit operations, such as paper machines, polymer film extruders, and adhesive coaters. The importance of ensuring robustness of the closed loop system to model uncertainties increases as the process dimensionality increases; hence developing algorithms for computing robustness margins for large scale systems is of immense practical importance. Computational complexity is a tool of computer scientists which has had impact in understanding large scale optimization problems, both theoretically and in terms of finding computational solutions. Computational complexity theory is used to determine the level of accuracy and computational speed that are obtainable by algorithms for computing robustness margins, and as to which algorithms are likely for providing practical robustness margin computation for large scale systems.