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We consider the problem of layering Directed Acyclic Graphs, an NP-hard problem. We show that some useful variants of the problem are also NP-hard. We provide an Integer Linear Programming formulation of a generalization of the standard problem and discuss how a banch-and-bound algorithm could be improved upon with cutting planes. We then describe a separation algorithm for two classes of valid inequalities that we have identified - one of which is facet-defining - and discuss their efficacy

A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem