# Visualizing Treewidth

## TL;DR

This paper presents visualization techniques for graph witness drawings that effectively display bounded treewidth or pathwidth, using tree decompositions, optimized layouts, and various drawing styles to minimize crossings.

## Contribution

It introduces new visualization paradigms for witness drawings of graphs with bounded treewidth, including a taxonomy of styles and algorithms for crossing minimization.

## Key findings

- Implemented a prototype for crossing minimization using dynamic programming and heuristics.
- Developed a taxonomy of drawing styles for witness graphs, including arc, circular, and straight-line layouts.
- Demonstrated effective visualization of graphs with small and large treewidth.

## 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.