区域通用矩形布局
Area-Universal Rectangular Layouts
摘要：
矩形布局是将一个矩形划分为一组有限的相邻不相交矩形。矩形布局出现在各种应用中：如制图学中的矩形制图图，建筑结构和VLSI设计中的平面图，以及图形绘图。区域通常与矩形布局的矩形相关联，因此如果一个矩形布局可以表示几个区域分配，则可能是期望的。一个布局是面积通用的，如果任何分配的面积矩形可以实现一个组合等效的矩形布局。我们确定了一个简单的必要和充分条件的矩形布局是面积泛的：矩形布局是面积泛的当且仅当它是单侧的。更一般地说，给定任何矩形布局L和任何区域分配到其区域，我们表明，可以有最多一个布局（水平和垂直缩放），这是组合等价于L，并实现了给定的面积分配。我们还调查了类似的问题，周边分配。矩形布局的矩形的邻接要求可以通过各种方式指定，最常见的是通过布局的对偶图。我们将展示如何找到一个区域通用布局的邻接要求，只要这样的布局存在的一组给定的。
英文摘要：
A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. Rectangular layouts appear in various applications: as rectangular cartograms in cartography, as floorplans in building architecture and VLSI design, and as graph drawings. Often areas are associated with the rectangles of a rectangular layout and it might hence be desirable if one rectangular layout can represent several area assignments. A layout is area-universal if any assignment of areas to rectangles can be realized by a combinatorially equivalent rectangular layout. We identify a simple necessary and sufficient condition for a rectangular layout to be area-universal: a rectangular layout is area-universal if and only if it is one-sided. More generally, given any rectangular layout L and any assignment of areas to its regions, we show that there can be at most one layout (up to horizontal and vertical scaling) which is combinatorially equivalent to L and achieves a given area assignment. We also investigate similar questions for perimeter assignments. The adjacency requirements for the rectangles of a rectangular layout can be specified in various ways, most commonly via the dual graph of the layout. We show how to find an area-universal layout for a given set of adjacency requirements whenever such a layout exists.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
