Chunky Chains Graph Drawings on Small Screens

Q: What problem does the framework optimize using the bucket capacity parameter c?

With capacity c limiting how many vertices fit per bucket, it may be impossible for every edge to be short. Bucket Integrity minimizes the number of long edges while keeping the drawing width at most c.

Jul 16, 2026

Upload by Riley

Chunky Chains presents a graph drawing style tailored to small screens like smartphones, where vertical scrolling is the primary interaction. It models each drawing as a vertical chain of chord-diagram buckets with bounded width. Vertices are placed as arcs on bucket boundaries, while edges are drawn within buckets or via gate nodes between consecutive buckets. A bucket arrangement based on capacity c minimizes the number of long edges, yielding a combinatorial framework with exact and heuristic algorithms validated on real-world graphs.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages29

Reading Time1 h 13 min

Introduction

Problem Statement

Problem 1: Bucketwidth

Problem 2: Bucket Integrity

Related Work

Chunky Chains: Graph Drawings on Small Screens Tim Hegemann \# 􀀚 Universität Würzburg, Germany Dominik Jilg \# 􀀚 Universität Würzburg, Germany Marie Diana Sieper \# 􀀚 Universität Würzburg, Germany Samuel Wolf \# 􀀚 Universität Würzburg, Germany Figure 1 Chunky Chain visualization of spatial color co-occurrences in Vincent van Gogh’s “Starry Night Over the Rhône”. When turned 90° , the drawing fits the narrow screen of a smartphone. ~~ Abstract ~~ We introduce Chunky Chains, a graph drawing style designed for small screens such as smartphones, where vertical scrolling is the dominant means of interaction. A Chunky Chain consists of a vertical chain of chord diagrams, called buckets. Vertices are placed as circular arcs on bucket boundaries, and edges are drawn inside a bucket or through gate nodes connecting consecutive buckets. Since every bucket contains only a bounded number of vertices, the drawing has bounded width. The combinatorial core is the choice of a bucket arrangement. Given a capacity c, the vertices are partitioned into an ordered set of buckets, each of size at most c. Edges whose endpoints lie in the same or in adjacent buckets are short. Edges that are “skipping” at least one bucket are long, and we draw them only partially. The goal is to minimize the number of long edges. We present a combinatorial framework for producing high quality Chunky Chains and analyze the complexity of its steps. We develop exact and heuristic algorithms, and experimentally evaluate their effectiveness. Our experiments show that many real-world graphs have good Chunky Chain visualizations. In a case study, we discuss Chunky Chains for graphs with certain temporal features. 2012 ACM Subject Classification Theory of computation → Graph algorithms analysis; Humancentered computing → Graph drawings Keywords and phrases Hybrid visualization, chord-link, chord diagram, chunky chains, bucketwidth, bandwidth, bucket integrity, experimental analysis Supplementary Material Collection: [https://chunkychains.github.io](https://chunkychains.github.io) [34] Software (Source Code): [https://github.com/hegetim/chunky-chains](https://github.com/hegetim/chunky-chains) Acknowledgements We thank Vasil Alistarov for many fruitful discussions and his prior work on how to avoid node duplication in ChordLink [2] . 2 Chunky Chains: Graph Drawings on Small Screens 1 Introduction Smartphone screens are arguably the most common type of screen that displays information nowadays. Due to their limited size, content rarely fits entirely on the screen, requiring users to explore it through zooming, panning, and (vertical) scrolling. In many applications, such as social media feeds, scrolling is the dominant mode of navigation. Following this trend, graph visualizations with small width (but possibly large height) are natural to consider. Hence, the task (T1) is to visualize graphs on narrow screens in a linear fashion that promotes vertical scrolling to explore the drawing. To this end, we present Chunky Chains. Intuitively, a Chunky Chain is a graph drawing that places vertices on a vertical chain of circles. We call them buckets and draw them as chord diagrams. Adjacent vertices should ideally be assigned to the same or adjacent buckets. See Figure 1 for an example of a Chunky Chain that visualizes the spatial color co-occurrences in Vincent van Gogh’s“Starry Night Over the Rhône”(see Appendix A for details) . Naturally, such a constraint on the aspect ratio benefits the visualization of sequential or weakly branching structures the most. We aim to (T2) reveal these structures with Chunky Chains. Interestingly, in Figure 1 our algorithm unveils a hidden correlation between the colors as our algorithm apparently ordered the colors from blue, over teal and green, to ocher. Problem Statement. From a combinatorial perspective, we want to find a bucket arrangement of a given graph G. A bucket arrangement is a partition of V (G)

FAQs

What is a Chunky Chain and why is it designed for small screens?

A Chunky Chain is a graph drawing style that organizes vertices into a vertical chain of chord-diagram buckets. It is designed for narrow screens where vertical scrolling is dominant, enabling exploration in a linear layout.

How are “short” and “long” edges determined in Chunky Chains?

Given a bucket arrangement, an edge is short if its endpoints lie in the same or adjacent buckets (|i−j|<2). Edges that span more buckets become long and are only partially drawn to reduce clutter.

What problem does the framework optimize using the bucket capacity parameter c?

With capacity c limiting how many vertices fit per bucket, it may be impossible for every edge to be short. Bucket Integrity minimizes the number of long edges while keeping the drawing width at most c.

Jul 16, 2026

Upload by Riley