Martin Nöllenburg

Thomas Depian, Carolina Haase, Martin Nöllenburg et al.

A linkage $\mathcal{L}$ consists of a graph $G=(V,E)$ and an edge-length function $\ell$. Deciding whether $\mathcal{L}$ can be realized as a planar straight-line embedding in $\mathbb{R}^2$ with edge length $\ell(e)$ for all $e \in E$ is $\exists\mathbb{R}$-complete [Abel et al., JoCG'25], even if $\ell \equiv 1$, but a considerable part of $\mathcal{L}$ is rigid. In this paper, we study the computational complexity of the realization question for structurally simpler, less rigid linkages inside an open polygonal domain $P$, where the placement of some vertices may be specified in the input. We show XP-membership and W[1]-hardness with respect to the size of $G$, even if $\ell \equiv 1$ and no vertex positions are prescribed. Furthermore, we consider the case where $G$ is a path with prescribed start and end position and $\ell \equiv 1$. Despite the absence of any rigid components, we obtain NP-hardness in general, and provide a linear-time algorithm for arbitrary $\ell$ if $G$ has only three edges and $P$ is convex.

Zainab Alsuwaykit, Yousef Rajeh, Alexandre Kouyoumdjian et al.

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.