LinSets.zip: Compressing Linear Set Diagrams.

Linear diagrams are used to visualize set systems by depicting set memberships as horizontal line segments in a matrix, where each set is represented as a row and each element as a column. Each such line segment of a set is shown in a contiguous horizontal range of cells of the matrix indicating that the corresponding elements in the columns belong to the set. As each set occupies its own row in the matrix, the total height of the resulting visualization is as large as the number of sets in the instance. Such a linear diagram can be visually sparse and intersecting sets containing the same element might be represented by distant rows. To alleviate such undesirable effects, we present LinSets.zip, a new approach that achieves a more space-efficient representation of linear diagrams. First, we minimize the total number of gaps in the horizontal segments by reordering columns, a criterion that has been shown to increase readability in linear diagrams. The main difference of LinSets.zip to linear diagrams is that multiple non-intersecting sets can be positioned in the same row of the matrix. Furthermore, we present several different rendering variations for a matrix-based representation that utilize the proposed row compression. We implemented the different steps of our approach in a visualization pipeline using integer-linear programming, and suitable heuristics aiming at sufficiently fast computations in practice. We conducted both a quantitative evaluation and a small-scale user experiment to compare the effects of compressing linear diagrams.

Splitting Vertices in 2-Layer Graph Drawings.

Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines (layers), and their relationships (edges) are represented by segments connecting vertices. Methods for constructing 2-layer drawings often try to minimize the number of edge crossings. We use vertex splitting to reduce the number of crossings, by replacing selected vertices on one layer by two (or more) copies and suitably distributing their incident edges among these copies. We study several optimization problems related to vertex splitting, either minimizing the number of crossings or removing all crossings with fewest splits. While we prove that some variants are ${\mathsf {NP}}$NP-complete, we obtain polynomial-time algorithms for others. We run our algorithms on a benchmark set of bipartite graphs representing the relationships between human anatomical structures and cell types.

MosaicSets: Embedding Set Systems into Grid Graphs.

Visualizing sets of elements and their relations is an important research area in information visualization. In this paper, we present MosaicSets: a novel approach to create Euler-like diagrams from non-spatial set systems such that each element occupies one cell of a regular hexagonal or square grid. The main challenge is to find an assignment of the elements to the grid cells such that each set constitutes a contiguous region. As use case, we consider the research groups of a university faculty as elements, and the departments and joint research projects as sets. We aim at finding a suitable mapping between the research groups and the grid cells such that the department structure forms a base map layout. Our objectives are to optimize both the compactness of the entirety of all cells and of each set by itself. We show that computing the mapping is NP-hard. However, using integer linear programming we can solve real-world instances optimally within a few seconds. Moreover, we propose a relaxation of the contiguity requirement to visualize otherwise non-embeddable set systems. We present and discuss different rendering styles for the set overlays. Based on a case study with real-world data, our evaluation comprises quantitative measures as well as expert interviews.

Multicriteria Optimization for Dynamic Demers Cartograms.

Cartograms are popular for visualizing numerical data for administrative regions in thematic maps. When there are multiple data values per region (over time or from different datasets) shown as animated or juxtaposed cartograms, preserving the viewer's mental map in terms of stability between multiple cartograms is another important criterion alongside traditional cartogram criteria such as maintaining adjacencies. We present a method to compute stable stable Demers cartograms, where each region is shown as a square scaled proportionally to the given numerical data and similar data yield similar cartograms. We enforce orthogonal separation constraints using linear programming, and measure quality in terms of keeping adjacent regions close (cartogram quality) and using similar positions for a region between the different data values (stability). Our method guarantees the ability to connect most lost adjacencies with minimal-length planar orthogonal polylines. Experiments show that our method yields good quality and stability on multiple quality criteria.

Multi-Level Area Balancing of Clustered Graphs.

We present a multi-level area balancing technique for laying out clustered graphs to facilitate a comprehensive understanding of the complex relationships that exist in various fields, such as life sciences and sociology. Clustered graphs are often used to model relationships that are accompanied by attribute-based grouping information. Such information is essential for robust data analysis, such as for the study of biological taxonomies or educational backgrounds. Hence, the ability to smartly arrange textual labels and packing graphs within a certain screen space is therefore desired to successfully convey the attribute data . Here we propose to hierarchically partition the input screen space using Voronoi tessellations in multiple levels of detail. In our method, the position of textual labels is guided by the blending of constrained forces and the forces derived from centroidal Voronoi cells. The proposed algorithm considers three main factors: (1) area balancing, (2) schematized space partitioning, and (3) hairball management. We primarily focus on area balancing, which aims to allocate a uniform area for each textual label in the diagram. We achieve this by first untangling a general graph to a clustered graph through textual label duplication, and then coupling with spanning-tree-like visual integration. We illustrate the feasibility of our approach with examples and then evaluate our method by comparing it with well-known conventional approaches and collecting feedback from domain experts.

Mixed Labeling: Integrating Internal and External Labels.

In this article, we present an algorithm capable of mixed labeling of 2D and 3D objects. In mixed labeling, the given objects are labeled with both internal labels placed (at least partially) over the objects and external labels placed in the space around the objects and connected with the labeled objects with straight-line leaders. The proposed algorithm determines the position and type of each label based on the user-specified ambiguity threshold and eliminates overlaps between the labels, as well as between the internal labels and the straight-line leaders of external labels. The algorithm is a screen-space technique; it operates in an image where the 2D objects or projected 3D objects are encoded. In other words, we can use the algorithm whenever we can render the objects to an image, which makes the algorithm fit for use in many domains. The algorithm operates in real-time, giving the results immediately. Finally, we present results from an expert evaluation, in which a professional illustrator has evaluated the label layouts produced with the proposed algorithm.

Edge-Path Bundling: A Less Ambiguous Edge Bundling Approach.

Edge bundling techniques cluster edges with similar attributes (i.e. similarity in direction and proximity) together to reduce the visual clutter. All edge bundling techniques to date implicitly or explicitly cluster groups of individual edges, or parts of them, together based on these attributes. These clusters can result in ambiguous connections that do not exist in the data. Confluent drawings of networks do not have these ambiguities, but require the layout to be computed as part of the bundling process. We devise a new bundling method, Edge-Path bundling, to simplify edge clutter while greatly reducing ambiguities compared to previous bundling techniques. Edge-Path bundling takes a layout as input and clusters each edge along a weighted, shortest path to limit its deviation from a straight line. Edge-Path bundling does not incur independent edge ambiguities typically seen in all edge bundling methods, and the level of bundling can be tuned through shortest path distances, Euclidean distances, and combinations of the two. Also, directed edge bundling naturally emerges from the model. Through metric evaluations, we demonstrate the advantages of Edge-Path bundling over other techniques.

On the Readability of Abstract Set Visualizations.

Set systems are used to model data that naturally arises in many contexts: social networks have communities, musicians have genres, and patients have symptoms. Visualizations that accurately reflect the information in the underlying set system make it possible to identify the set elements, the sets themselves, and the relationships between the sets. In static contexts, such as print media or infographics, it is necessary to capture this information without the help of interactions. With this in mind, we consider three different systems for medium-sized set data, LineSets, EulerView, and MetroSets, and report the results of a controlled human-subjects experiment comparing their effectiveness. Specifically, we evaluate the performance, in terms of time and error, on tasks that cover the spectrum of static set-based tasks. We also collect and analyze qualitative data about the three different visualization systems. Our results include statistically significant differences, suggesting that MetroSets performs and scales better.

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 H=(V, S), consisting of a set V of vertices and a set S, which contains subsets of V called hyperedges. Our system then computes a metro map representation of H, where each hyperedge E in 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 easy-to-use preset configurations. Furthermore, 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.

A Survey on Transit Map Layout - from Design, Machine, and Human Perspectives.

Transit maps are designed to present information for using public transportation systems, such as urban railways. Creating a transit map is a time-consuming process, which requires iterative information selection, layout design, and usability validation, and thus maps cannot easily be customised or updated frequently. To improve this, scientists investigate fully- or semi-automatic techniques in order to produce high quality transit maps using computers and further examine their corresponding usability. Nonetheless, the quality gap between manually-drawn maps and machine-generated maps is still large. To elaborate the current research status, this state-of-the-art report provides an overview of the transit map generation process, primarily from Design, Machine, and Human perspectives. A systematic categorisation is introduced to describe the design pipeline, and an extensive analysis of perspectives is conducted to support the proposed taxonomy. We conclude this survey with a discussion on the current research status, open challenges, and future directions.

Photonic-integrated circuits with non-planar topologies realized by 3D-printed waveguide overpasses.

Complex photonic-integrated circuits (PIC) may have strongly non-planar topologies that require waveguide crossings (WGX) when realized in single-layer integration platforms. The number of WGX increases rapidly with the complexity of the circuit, in particular when it comes to highly interconnected optical switch topologies. Here, we present a concept for WGX-free PIC that relies on 3D-printed freeform waveguide overpasses (WOP). We experimentally demonstrate the viability of our approach using the example of a 4 × 4 switch-and-select (SAS) circuit realized on the silicon photonic platform. We further present a comprehensive graph-theoretical analysis of different n × n SAS circuit topologies. We find that for increasing port counts n of the SAS circuit, the number of WGX increases with n4, whereas the number of WOP increases only in proportion to n2.

Metabopolis: scalable network layout for biological pathway diagrams in urban map style.

BACKGROUND: Biological pathways represent chains of molecular interactions in biological systems that jointly form complex dynamic networks. The network structure changes from the significance of biological experiments and layout algorithms often sacrifice low-level details to maintain high-level information, which complicates the entire image to large biochemical systems such as human metabolic pathways. RESULTS: Our work is inspired by concepts from urban planning since we create a visual hierarchy of biological pathways, which is analogous to city blocks and grid-like road networks in an urban area. We automatize the manual drawing process of biologists by first partitioning the map domain into multiple sub-blocks, and then building the corresponding pathways by routing edges schematically, to maintain the global and local context simultaneously. Our system incorporates constrained floor-planning and network-flow algorithms to optimize the layout of sub-blocks and to distribute the edge density along the map domain. We have developed the approach in close collaboration with domain experts and present their feedback on the pathway diagrams based on selected use cases. CONCLUSIONS: We present a new approach for computing biological pathway maps that untangles visual clutter by decomposing large networks into semantic sub-networks and bundling long edges to create space for presenting relationships systematically.

Drawing Large Graphs by Multilevel Maxent-Stress Optimization.

Drawing large graphs appropriately is an important step for the visual analysis of data from real-world networks. Here we present a novel multilevel algorithm to compute a graph layout with respect to the maxent-stress metric proposed by Gansner et al. (2013) that combines layout stress and entropy. As opposed to previous work, we do not solve the resulting linear systems of the maxent-stress metric with a typical numerical solver. Instead we use a simple local iterative scheme within a multilevel approach. To accelerate local optimization, we approximate long-range forces and use shared-memory parallelism. Our experiments validate the high potential of our approach, which is particularly appealing for dynamic graphs. In comparison to the previously best maxent-stress optimizer, which is sequential, our parallel implementation is on average 30 times faster already for static graphs (and still faster if executed on a single thread) while producing a comparable solution quality.