Compact Layered Drawings of General Directed Graphs

  • Adalat JabrayilovEmail author
  • Sven Mallach
  • Petra Mutzel
  • Ulf Rüegg
  • Reinhard von Hanxleden
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)


We consider the problem of layering general directed graphs under height and possibly also width constraints. Given a directed graph \(G=(V,A)\) and a maximal height, we propose a layering approach that minimizes a weighted sum of the number of reversed arcs, the arc lengths, and the width of the drawing. We call this the Compact Generalized Layering Problem (CGLP). Here, the width of a drawing is defined as the maximum sum of the number of vertices placed on a layer and the number of dummy vertices caused by arcs traversing the layer. The CGLP is \(\mathcal {NP}\)-hard. We present two MIP models for this problem. The first one (EXT) is our extension of a natural formulation for directed acyclic graphs as suggested by Healy and Nikolov. The second one (CGL) is a new formulation based on partial orderings. Our computational experiments on two benchmark sets show that the CGL formulation can be solved much faster than EXT using standard commercial MIP solvers. Moreover, we suggest a variant of CGL, called MML, that can be seen as a heuristic approach. In our experiments, MML clearly improves on CGL in terms of running time while it does not considerably increase the average arc lengths and widths of the layouts although it solves a slightly different problem where the dummy vertices are not taken into account.


Layer-based layout Layer assignment Mixed integer programming 



This work was supported by the German Research Foundation under the project Compact Graph Drawing with Port Constraints (ComDraPor, DFG HA 4407/8-1 and MU 1129/9-1).


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Adalat Jabrayilov
    • 1
    Email author
  • Sven Mallach
    • 3
  • Petra Mutzel
    • 1
  • Ulf Rüegg
    • 2
  • Reinhard von Hanxleden
    • 2
  1. 1.Department of Computer ScienceTechnische Universität DortmundDortmundGermany
  2. 2.Department of Computer ScienceKiel UniversityKielGermany
  3. 3.Department of Computer ScienceUniversität zu KölnKölnGermany

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