Journal of Information Processing
Drawing graphs
Width-restricted layering of acyclic digraphs with consideration of dummy nodes
Information Processing Letters
How to Layer a Directed Acyclic Graph
GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
Facets of the Directed Acyclic Graph Layering Polytope
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Graph layering by promotion of nodes
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Journal of Experimental Algorithmics (JEA)
Graph layering by promotion of nodes
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
GD'07 Proceedings of the 15th international conference on Graph drawing
GD'09 Proceedings of the 17th international conference on Graph Drawing
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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 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.