Combinatorial optimization problems have recently emerged in the design of controllers for OLED displays. The objective is to decompose an image into subframes minimizing the addressing time and thereby also the amplitude of the electrical current through the diodes, which has a direct impact on the lifetime of such a display. To this end, we model this problem as an integer linear program. Subsequently, we refine this formulation by exploiting the combinatorial structure of the problem. We propose a fully combinatorial separation routine for the LP-relaxation based on matching techniques. It can be used as an oracle in various frameworks to derive approximation algorithms or heuristics. We establish NP-hardness and hardness of approximation. Nevertheless, we are able to work around this issue by only focusing on a subsets of the variables and provide experimental evidence that they are sufficient to come up with near optimal solutions in practice. On this basis, one can derive custom-tailored solutions adapting to technical constraints such as memory requirements. By allowing the addressing of distributed doublelines, we improve the addressing time in cases where previous approaches fall short due to their restriction to consecutive doublelines.