Let $M$ be an $r\times c$ table with each cell weighted by a nonzero positive number. A StreamTable visualization of $M$ represents the columns as non-overlapping vertical streams and the rows as horizontal stripes such that the area of intersection between a column and a row is equal to the weight of the corresponding cell. To avoid large wiggle of the streams, it is desirable to keep the consecutive cells in a stream to be adjacent. Let $B$ be the smallest axis-aligned bounding box containing the StreamTable. Then the difference between the area of $B$ and the sum of the weights is referred to as the excess area. We examine the complexity of optimizing various table aesthetics (minimizing excess area, or maximizing cell adjacencies in streams) in a StreamTable visualization. (A) If the row permutation is fixed and the row heights are given as a part of the input, then we provide an $O(rc)$-time algorithm that optimizes these aesthetics. (B) If the row permutation is fixed but the row heights can be chosen, then we discuss a technique to compute an aesthetic StreamTable by solving a quadratically constrained quadratic program, followed by iterative improvements. (C) If row permutations can be chosen, then we show that it is NP-hard to find a row permutation that optimizes the area or adjacency aesthetics.

中文翻译：

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StreamTable：具有流动流的表的区域比例可视化

假设$ M $是一个$ r \ times $$表，每个像元均以非零正数加权。$ M $的StreamTable可视化效果将列表示为不重叠的垂直流，将行表示为水平条纹，以使列和行之间的相交面积等于相应单元格的权重。为了避免流的大幅度摆动，期望将流中的连续单元保持为相邻。令$ B $为包含StreamTable的最小的与轴对齐的边界框。然后，$ B $的面积与权重之和之间的差称为多余面积。我们研究了在StreamTable可视化中优化各种表的美观性（最小化多余的区域或最大化流中的单元格邻接）的复杂性。（A）如果行排列是固定的，并且行高作为输入的一部分给出，那么我们将提供$ O（rc）$-time算法，以优化这些美观度。（B）如果行排列是固定的，但可以选择行高，则我们讨论一种通过求解二次约束二次程序来计算美观的StreamTable的技术，然后进行迭代改进。（C）如果可以选择行排列，那么我们表明找到能够优化面积或邻接美学的行排列是NP难的。其次是迭代改进。（C）如果可以选择行排列，那么我们表明找到能够优化面积或邻接美学的行排列是NP难的。其次是迭代改进。（C）如果可以选择行排列，那么我们表明找到能够优化面积或邻接美学的行排列是NP难的。