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 is linked to an NP-complete problem which we approach with 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元素的简洁方式，即使缺乏经验的读者也能轻松理解。特别值得关注的是将集合表示为对齐矩形的欧拉图。本研究将此类矩形欧拉图的存在性问题与关联序关系的序维数相联系。为此，我们分别考察一维和二维情形下的欧拉图。在一维情形中，这种对应关系为我们提供了计算欧拉图的多项式时间算法；而二维情形则关联于一个NP完全问题，我们通过指数时间算法对其进行求解。