A \emph{generic rectangular layout} (for short, \emph{layout}) is a subdivision of an axis-aligned rectangle into axis-aligned rectangles, no four of which have a point in common. Such layouts are used in data visualization and in cartography. The contacts between the rectangles represent semantic or geographic relations. A layout is weakly (strongly) \emph{aspect ratio universal} if any assignment of aspect ratios to rectangles can be realized by a weakly (strongly) equivalent layout. We give combinatorial characterizations for weakly and strongly aspect ratio universal layouts. Furthermore, we describe a quadratic-time algorithm that decides whether a given graph is the dual graph of a strongly aspect ratio universal layout, and finds such a layout if one exists.

翻译：\emph{通用矩形布局}（简称\emph{布局}）是将一个轴对齐矩形细分为若干轴对齐小矩形，且任意四个小矩形无公共点的划分方式。此类布局广泛应用于数据可视化和地图制图领域，其中矩形间的邻接关系表示语义或地理关联。若任意宽高比赋值均能通过弱（强）等价布局实现，则称该布局是弱（强）\emph{宽高比通用}的。我们给出了弱通用与强通用布局的组合刻画特征，并描述了一种二次时间内判定给定图是否为强宽高比通用布局对偶图的算法，且能在存在此类布局时构造之。