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ARCOL: Aspect Ratio Constrained Orthogonal Layout

Zainab Alsuwaykit, Yousef Rajeh, Alexandre Kouyoumdjian, Steve Kieffer, Dominik Engel, Sara Di Bartolomeo, Martin Nöllenburg, Ivan Viola

Abstract

Orthogonal graph layout algorithms aim to produce clear, compact, and readable network diagrams by arranging nodes and edges along horizontal and vertical lines, while minimizing bends and crossings. Most existing orthogonal layout methods focus primarily on quality criteria such as area usage, total edge length, and bend minimization. Explicitly controlling the global aspect ratio (AR) of the resulting layout is as of now unexplored. Existing orthogonal layout methods offer no control over the resulting AR and their rigid geometric constraints make adaptation of finished layouts difficult. With the increasing variety of aspect ratios encountered in daily life, from wide monitors to tall mobile devices or fixed-size interface panels, there is a clear need for aspect ratio control in orthogonal layout methods. To tackle this issue, we introduce Aspect Ratio-Constrained Orthogonal Layout (ARCOL). Building upon the Human-like Orthogonal Layout Algorithm (HOLA)~\cite{Kieffer2016}, we integrate aspect ratio at two different stages: (1) into the stress minimization phase, as a soft constraint, allowing the layout algorithm to gently guide node positions toward a specified target AR, while preserving visual clarity and topological faithfulness; and (2) into the tree reattachment phase, where we modify the cost function to favor placements that improve the AR. We evaluate our approach through quantitative evaluation and a user study, as well as expert interviews. Our evaluations show that ARCOL produces balanced and space efficient orthogonal layouts across diverse aspect ratios.

ARCOL: Aspect Ratio Constrained Orthogonal Layout

Abstract

Orthogonal graph layout algorithms aim to produce clear, compact, and readable network diagrams by arranging nodes and edges along horizontal and vertical lines, while minimizing bends and crossings. Most existing orthogonal layout methods focus primarily on quality criteria such as area usage, total edge length, and bend minimization. Explicitly controlling the global aspect ratio (AR) of the resulting layout is as of now unexplored. Existing orthogonal layout methods offer no control over the resulting AR and their rigid geometric constraints make adaptation of finished layouts difficult. With the increasing variety of aspect ratios encountered in daily life, from wide monitors to tall mobile devices or fixed-size interface panels, there is a clear need for aspect ratio control in orthogonal layout methods. To tackle this issue, we introduce Aspect Ratio-Constrained Orthogonal Layout (ARCOL). Building upon the Human-like Orthogonal Layout Algorithm (HOLA)~\cite{Kieffer2016}, we integrate aspect ratio at two different stages: (1) into the stress minimization phase, as a soft constraint, allowing the layout algorithm to gently guide node positions toward a specified target AR, while preserving visual clarity and topological faithfulness; and (2) into the tree reattachment phase, where we modify the cost function to favor placements that improve the AR. We evaluate our approach through quantitative evaluation and a user study, as well as expert interviews. Our evaluations show that ARCOL produces balanced and space efficient orthogonal layouts across diverse aspect ratios.

Paper Structure

This paper contains 16 sections, 7 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Orthogonal Graph Layouts
  4. Force-Directed Layout
  5. Method
  6. Preliminaries: Revisiting HOLA
  7. Normalized Stress Minimization
  8. Tree attachments
  9. Refinement
  10. Results
  11. Evaluation
  12. Graph Metrics
  13. Task-based User Study
  14. Preference-based User Study
  15. Expert Interviews
  16. ...and 1 more sections

Figures (8)

  • Figure 1: The main stages of ARCOL pipeline for the same graph for three different aspect ratios. (a) From random initial layout to core without trees. (b) stress minimization with the normalization step to guide the layout to the shape that matches the target aspect ratio. (c) core orthogonalization. (d) trees attachment (e) final graph fitted to the target aspect ratio.
  • Figure 2: Comparison of post-scaled HOLA and ARCOL for a graph from Rome dataset with different aspect ratios.
  • Figure 3: Comparison of post-scaled HOLA and ARCOL for the Sydney metro map graph with different aspect ratios.
  • Figure 4: Comparison of Kruskal Stress and Node Resolution between ARCOL and HOLA. (Higher scores are better.)
  • Figure 5: Comparison of ELD over different graph sizes.
  • ...and 3 more figures