Chunky Chains: Graph Drawings on Small Screens

Tim Hegemann; Dominik Jilg; Marie Diana Sieper; Samuel Wolf

Home/Archive/arXiv

arXiv · 2607.06029

Chunky Chains: Graph Drawings on Small Screens

Tim Hegemann·Dominik Jilg·Marie Diana Sieper·Samuel Wolf

View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

cs.DS

Keep this discovery

BibTeX RIS

Tim Hegemann, Dominik Jilg, Marie Diana Sieper, Samuel Wolf. 2026-07-07. Chunky Chains: Graph Drawings on Small Screens. https://arxiv.org/abs/2607.06029

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗

arXiv2026

A deterministic $(1+\varepsilon)^n$ approximation for the permanent of a nonnegative matrix

For every fixed $0<\varepsilon\le1$, we give a deterministic strongly polynomial algorithm that, given a nonnegative matrix $A\in\mathbb{R}_{\ge0}^{n\times n}$, returns $Q$ satisfying $\operatorname{per} A\le Q\le(1+\varepsilon)^n\operatorname{per} A$.

cs.DS↗

arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗