Short Plane Supports for Spatial Hypergraphs

A graph $G=(V,E)$ is a support of a hypergraph $H=(V,S)$ if every hyperedge induces a connected subgraph in $G$. Supports are used for certain types of hypergraph visualizations. In this paper we consider visualizing spatial hypergraphs, where each vertex has a fixed location in the plane. This is the case, e.g., when modeling set systems of geospatial locations as hypergraphs. By applying established aesthetic quality criteria we are interested in finding supports that yield plane straight-line drawings with minimum total edge length on the input point set $V$. We first show, from a theoretical point of view, that the problem is NP-hard already under rather mild conditions as well as a negative approximability results. Therefore, the main focus of the paper lies on practical heuristic algorithms as well as an exact, ILP-based approach for computing short plane supports. We report results from computational experiments that investigate the effect of requiring planarity and acyclicity on the resulting support length. Further, we evaluate the performance and trade-offs between solution quality and speed of several heuristics relative to each other and compared to optimal solutions.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

MetroSets: Visualizing Sets as Metro Maps

We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph $\mathcal{H} = (V, \mathcal{S})$, consisting of a set $V$ of vertices and a set $\mathcal{S}$, which contains subsets of $V$ called hyperedges. Our system then computes a metro map representation of $\mathcal{H}$, where each hyperedge $E$ in $\mathcal{S}$ corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with \new{easy-to-use preset configurations.} % many real-world datasets. Furthermore, \new{using several real-world datasets}, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system, see http://metrosets.ac.tuwien.ac.a

Euler diagrams drawn with ellipses area‑proportionally (Edeap)

Background: Area-proportional Euler diagrams are frequently used to visualize data from Microarray experiments, but are also applied to a wide variety of other data from biosciences, social networks and other domains. Results: This paper details Edeap, a new simple, scalable method for drawing areaproportional Euler diagrams with ellipses. We use a search-based technique optimizing a multi-criteria objective function that includes measures for both area accuracy and usability, and which can be extended to further user-defned criteria. The Edeap software is available for use on the web, and the code is open source. In addition to describing our system, we present the frst extensive evaluation of software for producing area-proportional Euler diagrams, comparing Edeap to the current state-of-the-art; circle-based method, venneuler, and an alternative ellipse-based method, eulerr. Conclusions: Our evaluation—using data from the Gene Ontology database via GoMiner, Twitter data from the SNAP database, and randomly generated data sets—shows an ordering for accuracy (from best to worst) of eulerr, followed by Edeap and then venneuler. In terms of runtime, the results are reversed with venneuler being the fastest, followed by Edeap and fnally eulerr. Regarding scalability, eulerr cannot draw non-trivial diagrams beyond 11 sets, whereas no such limitation is present in Edeap or venneuler, both of which draw diagrams up to the tested limit of 20 sets

Scalable Set Visualizations (Dagstuhl Seminar 17332)

This report documents the program and outcomes of Dagstuhl Seminar 17332 "Scalable Set Visualizations", which took place August 14--18, 2017. The interdisciplinary seminar brought together 26 researchers from different areas in computer science and beyond such as information visualization, human-computer interaction, graph drawing, algorithms, machine learning, geography, and life sciences. During the seminar we had five invited overview talks on different aspects of set visualizations as well as a few ad-hoc presentations of ongoing work. The abstracts of these talks are contained in this report. Furthermore, we formed five working groups, each of them discussing intensively about a selected open research problem that was proposed by the seminar participants in an open problem session. The second part of this report contains summaries of the groups\u27 findings