A branch-and-cut approach to the directed acyclic graph layering problem

Abstract

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 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. © Springer-Verlag Berlin Heidelberg 2002.