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.

Zoomless Maps: External Labeling Methods for the Interactive Exploration of Dense Point Sets at a Fixed Map Scale.

Visualizing spatial data on small-screen devices such as smartphones and smartwatches poses new challenges in computational cartography. The current interfaces for map exploration require their users to zoom in and out frequently. Indeed, zooming and panning are tools suitable for choosing the map extent corresponding to an area of interest. They are not as suitable, however, for resolving the graphical clutter caused by a high feature density since zooming in to a large map scale leads to a loss of context. Therefore, in this paper, we present new external labeling methods that allow a user to navigate through dense sets of points of interest while keeping the current map extent fixed. We provide a unified model, in which labels are placed at the boundary of the map and visually associated with the corresponding features via connecting lines, which are called leaders. Since the screen space is limited, labeling all features at the same time is impractical. Therefore, at any time, we label a subset of the features. We offer interaction techniques to change the current selection of features systematically and, thus, give the user access to all features. We distinguish three methods, which allow the user either to slide the labels along the bottom side of the map or to browse the labels based on pages or stacks. We present a generic algorithmic framework that provides us with the possibility of expressing the different variants of interaction techniques as optimization problems in a unified way. We propose both exact algorithms and fast and simple heuristics that solve the optimization problems taking into account different criteria such as the ranking of the labels, the total leader length as well as the distance between leaders. In experiments on real-world data we evaluate these algorithms and discuss the three variants with respect to their strengths and weaknesses proving the flexibility of the presented algorithmic framework.