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

  • Patrick Healy
  • Nikola S. Nikolov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)


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.


  1. 1.
    O. Bastert and C. Matuszewski. Layered drawings of digraphs. In M. Kaufman and D. Wagner, editors, Drawing Graphs: Method and Models, volume 2025 of LNCS, pages 87–120. Springer-Verlag, 2000.CrossRefGoogle Scholar
  2. 2.
    J. Branke, S. Leppert, M. Middendorf, and P. Eades. Width-restriced layering of acyclic digraphs with consideration of dummy nodes. Information Processing Letters, 81(2):59–63, January 2002.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    P. Eades and K. Sugiyama. How to draw a directed graph. Journal of Information Processing, 13(4):424–437, 1990.MATHGoogle Scholar
  4. 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. 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
  6. 6.
    K. Sugiyama, S. Tagawa, and M. Toda. Methods for visual understanding of hierarchical system structures. IEEE Transaction on Systems,Man,and Cybernetics, 11(2):109–125, February 1981.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Patrick Healy
  • Nikola S. Nikolov
    • 1
  1. 1.CSIS DepartmentUniversity of LimerickLimerickRepublic of Ireland

Personalised recommendations