A rectangular floorplan is a partition of a rectangle into smaller rectangles such that no four rectangles meet at a single point. Rectangular floorplans arise naturally in a variety of applications, including VLSI design, architectural layout, and cartography, where efficient and flexible spatial subdivisions are required. A central concept in this domain is that of area-universality: a floorplan (or more generally, a rectangular layout) is area-universal if, for any assignment of target areas to its constituent rectangles, there exists a combinatorially equivalent layout that realizes these areas. In this paper, we investigate the structural conditions under which an outerplanar graph admits an area-universal rectangular layout. We establish a necessary and sufficient condition for area-universality in this setting, thereby providing a complete characterization of admissible outerplanar graphs. Furthermore, we present an algorithmic construction that guarantees that the resulting layout is always area-universal.

翻译：矩形平面布局是将一个矩形划分为若干较小矩形的分割方式，其中任意四个矩形不会交于同一点。矩形平面布局自然出现在多种应用场景中，包括超大规模集成电路设计、建筑平面布局和制图学，这些领域都需要高效且灵活的空间划分。该领域的一个核心概念是面积通用性：一个平面布局（或更广义地说，一个矩形布局）被称为面积通用的，如果对于其组成矩形任意给定的目标面积分配，都存在一个组合结构等价的布局能够实现这些面积。本文研究了外平面图在何种结构条件下允许存在面积通用的矩形布局。我们为此类布局中的面积通用性建立了一个充分必要条件，从而完整刻画了可允许的外平面图。此外，我们提出了一种算法构造方法，确保生成的布局始终是面积通用的。