STRATISFIMAL LAYOUT: A modular optimization model for laying out layered node-link network visualizations

Sara Di Bartolomeo, Mirek Riedewald, Wolfgang Gatterbauer, Cody Dunne

Abstract: Node-link visualizations are a familiar and powerful tool for displaying the relationships in a network. The readability of these visualizations highly depends on the spatial layout used for the nodes. In this paper, we focus on computing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">layered</i> layouts, in which nodes are aligned on a set of parallel axes to better expose hierarchical or sequential relationships. Heuristic-based layouts are widely used as they scale well to larger networks and usually create readable, albeit sub-optimal, visualizations. We instead use a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">layout optimization model</i> that prioritizes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">optimality</i> - as compared to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalability</i> - because an optimal solution not only represents the best attainable result, but can also serve as a baseline to evaluate the effectiveness of layout heuristics. We take an important step towards powerful and flexible network visualization by proposing S <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">tratisfimal</small> L <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ayout</small> , a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">modular integer-linear-programming formulation</i> that can consider several important readability criteria <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">simultaneously</i> — crossing reduction, edge bendiness, and nested and multi-layer groups. The layout can be adapted to diverse use cases through its modularity. Individual features can be enabled and customized depending on the application. We provide open-source and documented implementations of the layout, both for web-based and desktop visualizations. As a proof-of-concept, we apply it to the problem of visualizing complicated SQL queries, which have features that we believe cannot be addressed by existing layout optimization models. We also include a benchmark network generator and the results of an empirical evaluation to assess the performance trade-offs of our design choices. A full version of this paper with all appendices, data, and source code is available at osf.io/qdyt9 with live examples at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://visdunneright.github.io/stratisfimal/</uri> .