A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem
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.
- 4.P. Healy and N. S. Nikolov. How to layer a directed acyclic graph. In P. Mutzel, M. Jünger, and S. Leipert, editors, Graph Drawing: Proceedings of 9th International Symposium,GD 2001, volume 2265 of LNCS, pages 16–30. Springer-Verlag, 2002.Google Scholar
- 5.P. Healy and N. S. Nikolov. Facets of the directed acyclic graph layering polytope. In Luděk Kučera, editor, Graph Theoretical Concepts in Computer Science: WG2002, LNCS. Springer-Verlag, (To appear.).Google Scholar