A Generalization of the Directed Graph Layering Problem

  • Ulf RüeggEmail author
  • Thorsten Ehlers
  • Miro Spönemann
  • Reinhard von Hanxleden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)


The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set Problem (FASP) to make the graph acyclic before a layering is determined.

Here we present the Generalized Layering Problem (GLP), which solves the combination of DLP and FASP simultaneously, allowing general graphs as input. We present an integer programming model and a heuristic to solve the NP-complete GLP and perform thorough evaluations on different sets of graphs and with different implementations for the steps of the layer-based approach.

We observe that GLP reduces the number of dummy nodes significantly, can produce more compact drawings, and improves on graphs where DLP yields poor aspect ratios.


Layer-based layout Layer assignment Linear arrangement Feedback arc set Integer programming 



We thank Chris Mears for support regarding the initial IP formulation. We further thank Tim Dwyer and Petra Mutzel for valuable discussions. This work was supported by the German Research Foundation under the project Compact Graph Drawing with Port Constraints (ComDraPor, DFG HA 4407/8-1).


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Ulf Rüegg
    • 1
    Email author
  • Thorsten Ehlers
    • 1
  • Miro Spönemann
    • 2
  • Reinhard von Hanxleden
    • 1
  1. 1.Department of Computer ScienceKiel UniversityKielGermany
  2. 2.TypeFox GmbHKielGermany

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