We consider an optimization problem arising in the design of controllers for OLED displays. Our objective is to minimize the current amplitude which has a direct impact on the lifetime of such a display. Modeling the problem in mathematical terms yields a class of network flow problems where the arcs are partitioned into groups and only the arc with the highest flow in each group is charged. We present an equivalent formulation as a covering (integer) linear program with an exponential number of constraints. We develop routines that solve the corresponding separation problem in linear time. Moreover, we identify a subset of the constraints yielding good starting solutions computable in linear time. We propose (fully)
combinatorial approximation heuristics suitable for being implemented in the hardware of a control device that drives an OLED display. In practice, we find approximate solutions very close to the optimum in realtime.