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DOI: 10.4230/LIPIcs.GD.2025.17

Visualizing Treewidth

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

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

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.

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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)

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@InProceedings{chiu_et_al:LIPIcs.GD.2025.17,
  author =	{Chiu, Alvin and Depian, Thomas and Eppstein, David and Goodrich, Michael T. and N\"{o}llenburg, Martin},
  title =	{{Visualizing Treewidth}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{17:1--17:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.17},
  URN =		{urn:nbn:de:0030-drops-250034},
  doi =		{10.4230/LIPIcs.GD.2025.17},
  annote =	{Keywords: Graph drawing, witness drawings, pathwidth, treewidth}
}

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Poster Abstract

DOI: 10.4230/LIPIcs.GD.2024.52

Polygonally Anchored Graph Drawing (Poster Abstract)

Authors: Alvin Chiu, Ahmed Eldawy, and Michael T. Goodrich

Published in: LIPIcs, Volume 320, 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)

Abstract

We investigate force-directed graph drawing techniques under the constraint that some nodes must be anchored to stay within a given polygonal region associated with it (i.e. some positional information is known). The low energy layouts produced by such algorithms may reveal geographic information about nodes with no such knowledge a priori. Some applications of graph drawing with partial positional information include location-based social networks and rail networks, where the geographical locations need not be precise.

Cite as

Alvin Chiu, Ahmed Eldawy, and Michael T. Goodrich. Polygonally Anchored Graph Drawing (Poster Abstract). In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 52:1-52:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chiu_et_al:LIPIcs.GD.2024.52,
  author =	{Chiu, Alvin and Eldawy, Ahmed and Goodrich, Michael T.},
  title =	{{Polygonally Anchored Graph Drawing}},
  booktitle =	{32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)},
  pages =	{52:1--52:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-343-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{320},
  editor =	{Felsner, Stefan and Klein, Karsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2024.52},
  URN =		{urn:nbn:de:0030-drops-213369},
  doi =		{10.4230/LIPIcs.GD.2024.52},
  annote =	{Keywords: polygonal anchors, force-directed}
}

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Documents authored by Chiu, Alvin

Visualizing Treewidth

Abstract

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Polygonally Anchored Graph Drawing (Poster Abstract)

Abstract

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