A Generalization of the Directed Graph Layering Problem
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.
KeywordsLayer-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).
- 4.Dwyer, T., Koren, Y.: DIG-COLA: directed graph layout through constrained energy minimization. In: Proceedings of the IEEE Symposium on Information Visualization (INFOVIS 2005), pp. 65–72, October 2005Google Scholar
- 8.Gutwenger, C., von Hanxleden, R., Mutzel, P., Rüegg, U., Spönemann, M.: Examining the compactness of automatic layout algorithms for practical diagrams. In: Proceedings of the Workshop on Graph Visualization in Practice (GraphViP 2014), Melbourne, Australia, July 2014Google Scholar
- 11.Healy, P., Nikolov, N.S.: Hierarchical drawing algorithms. In: Tamassia, R. (ed.) Handbook of Graph Drawing and Visualization, pp. 409–453. CRC Press, Boca Raton (2013)Google Scholar
- 12.McAllister, A.J.: A new heuristic algorithm for the linear arrangement problem. University of New Brunswick, Technical report (1999)Google Scholar
- 14.Nikolov, N.S., Tarassov, A., Branke, J.: In search for efficient heuristics for minimum-width graph layering with consideration of dummy nodes. J. Exp. Algorithmics 10 (2005)Google Scholar
- 16.Rüegg, U., Ehlers, T., Spönemann, M., von Hanxleden, R.: A generalization of the directed graph layering problem. Technical report 1501, Kiel University, Department of Computer Science, ISSN 2192–6247, February 2015Google Scholar
- 17.Rüegg, U., Ehlers, T., Spönemann, M., von Hanxleden, R.: A generalization of the directed graph layering problem, August 2016. arXiv:1608.07809 [cs.OH]