Order diagrams allow human analysts to understand and analyze structural properties of ordered data. While an experienced expert can create easily readable order diagrams, the automatic generation of those remains a hard task. In this work, we adapt force-directed approaches, which are known to generate aesthetically-pleasing drawings of graphs, to the realm of order diagrams. Our algorithm ReDraw thereby embeds the order in a high dimension and then iteratively reduces the dimension until a two-dimensional drawing is achieved. To improve aesthetics, this reduction is equipped with two force-directed steps where one optimizes on distances of nodes and the other on distances of lines in order to satisfy a set of a priori fixed conditions. By respecting an invariant about the vertical position of the elements in each step of our algorithm we ensure that the resulting drawings satisfy all necessary properties of order diagrams. Finally, we present the results of a user study to demonstrate that our algorithm outperforms comparable approaches on drawings of lattices with a high degree of distributivity.

中文翻译：

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使用尺寸约简的力图定向图

顺序图使人类分析师能够理解和分析顺序数据的结构特性。尽管经验丰富的专家可以创建易于阅读的订单图，但是自动生成订单图仍然是一项艰巨的任务。在这项工作中，我们将力导向方法（用于生成美观的图形图）调整到顺序图的领域。因此，我们的算法ReDraw将订单嵌入到高维中，然后迭代减小维，直到实现二维绘图为止。为了提高美观度，此归约方法配备了两个力导向步骤，其中一个步骤在节点的距离上进行优化，而另一个在线的距离上进行优化，以满足一组先验的固定条件。在我们算法的每个步骤中，通过考虑元素垂直位置的不变性，我们确保生成的图形满足顺序图的所有必要属性。最后，我们提出了一项用户研究的结果，以证明我们的算法在具有高度分布性的点阵图上优于可比方法。