Euler diagrams are a tool for the graphical representation of set relations. Due to their simple way of visualizing elements in the sets by geometric containment, they are easily readable by an inexperienced reader. Euler diagrams where the sets are visualized as aligned rectangles are of special interest. In this work, we link the existence of such rectangular Euler diagrams to the order dimension of an associated order relation. For this, we consider Euler diagrams in one and two dimensions. In the one-dimensional case, this correspondence provides us with a polynomial-time algorithm to compute the Euler diagrams, while the two-dimensional case results in an exponential-time algorithm.

翻译：欧拉图是一种用于图形化表示集合关系的工具。由于其通过几何包含关系直观展示集合中元素的特性，即使缺乏经验的读者也能轻松理解。其中，以对齐矩形形式可视化集合的欧拉图具有特殊研究价值。本研究将此类矩形欧拉图的存在性问题与关联序关系的偏序维数建立联系。为此，我们分别考察了一维和二维两种情况下的欧拉图。在一维情形下，该对应关系使我们能够提出多项式时间算法来构造欧拉图；而在二维情形下，则得到指数时间算法。