Area-universality in Outerplanar Graphs

TL;DR

This paper characterizes when outerplanar graphs can be realized as area-universal rectangular layouts, providing a complete structural criterion and an algorithm to construct such layouts.

Contribution

It offers a necessary and sufficient condition for area-universality in outerplanar graphs and presents an algorithmic method for constructing these layouts.

Findings

Established a complete characterization of area-universality in outerplanar graphs.

Developed an algorithm to construct area-universal rectangular layouts.

Proved the structural conditions necessary and sufficient for such layouts.

Abstract

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.