Visualizations of set systems frequently use enclosing geometries for the sets in combination with reduced representations of the elements, such as short text labels, small glyphs, or points. Hence they are generally unable to adequately represent sets whose elements are larger text fragments, images, or charts. In this paper we introduce BlockSets, a novel set visualization technique specifically designed for sets with large elements. BlockSets places the elements on a grid and uses rectilinear shapes as enclosing geometries. We describe integer linear programs that find high-quality layouts of the elements on the grid. Since not all set systems allow a compact contiguous representation in this form, we also present an algorithm that splits the visualization into parts when needed; our visual encoding highlights the parts for the user in the final visualization. BlockSets utilizes orthoconvex shapes which offer a good trade-off between compactness and readability. Finally, BlockSets renders the enclosing geometries as stacked opaque shapes. We describe an algorithm that finds a stacking order such that all shapes can be inferred. Such a stacking does not have to exist, but our algorithm did find a stacking for all real-world data sets that we tested.

翻译：集合系统的可视化通常采用几何包围结构来表示集合，同时使用简化元素表示（如短文本标签、小型符号或点）。因此，这类方法通常无法充分表示元素为较长文本片段、图像或图表的集合。本文提出BlockSets——一种专为大元素集合设计的新型可视化技术。该方法将元素排列于网格之上，并采用直线多边形作为几何包围结构。我们描述了通过整数线性规划寻找高质量网格布局的数学模型。由于并非所有集合系统都能以紧凑连续形式呈现，我们还提出了一种在必要时对可视化进行分区的算法；最终可视化中通过视觉编码向用户突出显示这些分区。BlockSets采用正交凸形状，在紧凑性与可读性之间实现了良好平衡。最后，该方法通过堆叠不透明形状呈现包围结构。我们提出了一种寻找可推断所有形状的堆叠顺序的算法。虽然这种堆叠顺序并非必然存在，但我们的算法在所有测试的真实数据集中均找到了有效堆叠方案。