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.

翻译：线性图通过矩阵中的水平线段来可视化集系统，其中每个集合表示为一行，每个元素表示为一列。集合的每个线段显示在矩阵单元格的连续水平范围内，表明对应列中的元素属于该集合。由于每个集合在矩阵中占据独立的一行，最终可视化结果的总高度与实例中的集合数量成正比。这种线性图可能视觉稀疏，且包含同一元素的相交集合可能分布在相距较远的行中。为解决此类不良效应，我们提出LinSets.zip——一种实现线性图更紧凑表示的新方法。首先，通过重排列顺序最小化水平线段中的间隔总数，该准则已被证明能提升线性图的可读性。LinSets.zip与线性图的主要区别在于：多个不相交的集合可被置于矩阵的同一行中。此外，我们针对基于矩阵的表示提出了若干利用所提行压缩技术的不同渲染变体。我们采用整数线性规划与旨在实现实际快速计算的合适启发式方法，将方法的不同步骤集成到可视化流程中。通过定量评估与小规模用户实验，我们比较了压缩线性图的效果。