Multiple forecast visualizations (MFVs) present curated sets of forecasts to support decision-making under uncertainty. However, the research community knows little about how people interpret and integrate competing forecasts. In this study, we investigate the strategies individuals use when predicting hypothetical future events with MFVs across five visualization types (median, 95% CIs, standard deviation intervals, density plots, and hypothetical outcome plots) and multiple probability distributions in two preregistered experiments (n = 500 each). Analysis of 18 participant strategies and open responses shows that whereas many participants attempted to visually average across forecasts, others adopted a winner-takes-all approach (e.g., selecting a single forecast as the most likely outcome), which deviates from rational agent expectations. We also observed reliance on visual artifacts, such as intersection points or end caps. These findings underscore the complexity of interpreting a range of forecasts and help explain why individuals may privilege particular predictions in real-world decision contexts.

Layered network visualizations assign each node to one of several parallel axes. They can convey sequence or flow data, hierarchies, or multiple data classes, but edge crossings and long edges often impair readability. Layout algorithms can reduce edge crossings and shorten edges using quick heuristics or optimal methods that prioritize human readability over computation speed. This work uses an optimization metaheuristic to provide the best of both worlds: high-quality layouts within a predetermined execution time. Our adaptation of the large neighborhood search (LNS) metaheuristic repeatedly selects fixed-sized subgraphs to lay out optimally. We conducted a computational evaluation using 450 synthetic networks to compare five ways of selecting candidate nodes, four ways of selecting their neighboring subgraph, and three criteria for determining subgraph size. LNS generally halved the number of crossings versus the barycentric heuristic while maintaining a reasonable runtime. Our best approach randomly selected candidate nodes, used degree centrality to pick cluster-like neighborhoods, and chose smaller neighborhoods that could be optimally laid out in 0.6 or 1.2 seconds (versus 6 seconds). In a case study visualizing 13 control flow graphs, most with over 1000 nodes, we show that our method can be employed to create visualizations with fewer crossings than Tabu Search, another metaheuristic, and vastly outperforms an ILP solver when runtime is bounded.

A layered graph is an important category of graph in which every node is assigned to a layer, and layers are drawn as parallel or radial lines. They are commonly used to display temporal data or hierarchical graphs. Previous research has demonstrated that minimizing edge crossings is the most important criterion to consider when looking to improve the readability of such graphs. While heuristic approaches exist for crossing minimization, we are interested in optimal approaches to the problem that prioritize human readability over computational scalability. We aim to improve the usefulness and applicability of such optimal methods by understanding and improving their scalability to larger graphs. This paper categorizes and evaluates the state-of-the-art linear programming formulations for exact crossing minimization and describes nine new and existing techniques that could plausibly accelerate the optimization algorithm. Through a computational evaluation, we explore each technique's effect on calculation time and how the techniques assist or inhibit one another, allowing researchers and practitioners to adapt them to the characteristics of their graphs. Our best-performing techniques yielded a median improvement of 2.5-17 × depending on the solver used, giving us the capability to create optimal layouts faster and for larger graphs. We provide an open-source implementation of our methodology in Python, where users can pick which combination of techniques to enable according to their use case. A free copy of this paper and all supplemental materials, datasets used, and source code are available at https://osf.io/5vq79.

Abstract Evaluations—encompassing computational evaluations, benchmarks and user studies—are essential tools for validating the performance and applicability of graph and network layout algorithms (also known as graph drawing). These evaluations not only offer significant insights into an algorithm's performance and capabilities, but also assist the reader in determining if the algorithm is suitable for a specific purpose, such as handling graphs with a high volume of nodes or dense graphs. Unfortunately, there is no standard approach for evaluating layout algorithms. Prior work holds a ‘Wild West’ of diverse benchmark datasets and data characteristics, as well as varied evaluation metrics and ways to report results. It is often difficult to compare layout algorithms without first implementing them and then running your own evaluation. In this systematic review, we delve into the myriad of methodologies employed to conduct evaluations—the utilized techniques, reported outcomes and the pros and cons of choosing one approach over another. Our examination extends beyond computational evaluations, encompassing user‐centric evaluations, thus presenting a comprehensive understanding of algorithm validation. This systematic review—and its accompanying website—guides readers through evaluation types, the types of results reported, and the available benchmark datasets and their data characteristics. Our objective is to provide a valuable resource for readers to understand and effectively apply various evaluation methods for graph layout algorithms. A free copy of this paper and all supplemental material is available at osf.io , and the categorized papers are accessible on our website at https://visdunneright.github.io/gd‐comp‐eval/ .