A matrix is produced for a semiconductor design. Interactions between mask edges in forming semiconductor shapes are determined and a graph created that shows those interactions. The graph is then partitioned into groups using a coloring algorithm, with each group representing one or more non-interacting mask edges. A lithography simulation is performed for each group, with the edges of that group perturbed, but the edges of other groups unmoved. The partial derivatives are calculated for the edges of a group based on the simulation with those edges perturbed, and used to populate locations in a Jacobian matrix. The Jacobian matrix is then used to solve an Optical Proximity Correction (OPC) problem by finding a mask edge correction vector for a given wafer targeting error vector.