According to one exemplary embodiment, a method for parallel processing a network of nodes having at least one ordering constraint and at least one conflict constraint is provided. The method may include breaking a plurality of loops caused by the at least one ordering constraint. The method may also include determining a node order based on the at least one ordering constraint. The method may then include determining a conflict order based on the at least one conflict constraint, whereby no new loops are created in the network. The method may further include performing parallel processing of the network of nodes based on the node order and the conflict order.