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Visualizing Treewidth

Authors Alvin Chiu , Thomas Depian , David Eppstein, Michael T. Goodrich , Martin Nöllenburg

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Dynamic programming
  • Human-centered computing → Graph drawings
Keywords
  • Graph drawing
  • witness drawings
  • pathwidth
  • treewidth

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Abstract

A witness drawing of a graph is a visualization that clearly shows a given property of a graph. We study and implement various drawing paradigms for witness drawings to clearly show that graphs have bounded pathwidth or treewidth. Our approach draws the tree decomposition or path decomposition as a tree of bags, with induced subgraphs shown in each bag, and with "tracks" for each graph vertex connecting its copies in multiple bags. Within bags, we optimize the vertex layout to avoid crossings of edges and tracks. We implement a visualization prototype for crossing minimization using dynamic programming for graphs of small width and heuristic approaches for graphs of larger width. We introduce a taxonomy of drawing styles, which render the subgraph for each bag as an arc diagram with one or two pages or as a circular layout with straight-line edges, and we render tracks either with straight lines or with orbital-radial paths.

Cite As Get BibTex

Alvin Chiu, Thomas Depian, David Eppstein, Michael T. Goodrich, and Martin Nöllenburg. Visualizing Treewidth. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.17

Author Details

Alvin Chiu
  • University of California, Irvine, CA, USA
Thomas Depian
  • TU Wien, Austria
David Eppstein
  • University of California, Irvine, CA, USA
Michael T. Goodrich
  • University of California, Irvine, CA, USA
Martin Nöllenburg
  • TU Wien, Austria

Funding

  • Depian, Thomas: Supported by Vienna Science and Technology Fund (WWTF) [10.47379/ICT22029].
  • Eppstein, David: Supported by NSF grant 2212129.
  • Goodrich, Michael T.: Supported by NSF grant 2212129.
  • Nöllenburg, Martin: Supported by Vienna Science and Technology Fund (WWTF) [10.47379/ICT22029].

Supplementary Materials

References

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