Worbel: Aggregating Point Labels into Word Clouds.

Point feature labeling is a classical problem in cartography and GIS that has been extensively studied for geospatial point data. At the same time, word clouds are a popular visualization tool to show the most important words in text data which has also been extended to visualize geospatial data (Buchin et al. PacificVis 2016). In this article, we study a hybrid visualization, which combines aspects of word clouds and point labeling. In the considered setting, the input data consist of a set of points grouped into categories and our aim is to place multiple disjoint and axis-aligned rectangles, each representing a category, such that they cover points of (mostly) the same category under some natural quality constraints. In our visualization, we then place category names inside the computed rectangles to produce a labeling of the covered points which summarizes the predominant categories globally (in a word-cloud-like fashion) while locally avoiding excessive misrepresentation of points (i.e., retaining the precision of point labeling). We show that computing a minimum set of such rectangles is NP -hard. Hence, we turn our attention to developing a heuristic with (optional) exact components using SAT models to compute our visualizations. We evaluate our algorithms quantitatively, measuring running time and quality of the produced solutions, on several synthetic and real-world data sets. Our experiments show that the fully heuristic approach produces solutions of comparable quality to heuristics combined with exact SAT models, while running much faster.