We consider the problem of partitioning a directed acyclic graph into layers such that all edges point unidirectionally. We perform an experimental analysis of some of the existing layering algorithms and then propose a new algorithm that is more realistic in the sense that it is possible to incorporate specific information about node and edge widths into the algorithm. The goal is to minimize the total sum of edge spans subject to dimension constraints on the drawing. We also present some preliminary results from experiments we have conducted using our layering algorithm on over 5900 example directed acyclic graphs.

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We consider the problem of layering Directed Acyclic Graphs, an N P-hard problem. We show that some useful variants of the problem are also N P-hard. We provide an Integer Linear Programming formulation of a generalization of the standard problem and discuss how a branch-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.

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