A computer implemented system produces an optimization graph in an online advertising system. The system presents at a computer, a supply of advertising inventory and advertising demand contracts, where each advertising inventory is presented as a supply node and each advertising demand contract is presented as a demand node. The system processes the supply of advertising inventory and the advertising demand contracts. For example, the system partitions the supply nodes into supply partitions and determines whether each supply node is eligible for each demand node. In addition, the system determines the number of eligible supply nodes to be drawn from each supply partition for each demand node.