Area-universality in Outerplanar Graphs

2026-01-20

AI Summary

This study investigates the structural conditions under which outerplanar graphs admit area-universal rectangular layouts—layouts that, for any prescribed assignment of rectangle areas, admit a combinatorially equivalent realization. By integrating techniques from graph theory, computational geometry, and combinatorial optimization, the work establishes necessary and sufficient structural conditions for an outerplanar graph to be area-universal and presents a constructive algorithm to generate such layouts. This paper provides the first complete characterization of area-universality for outerplanar graphs, thereby filling a fundamental gap in the theory of area-universal layout representations. The proposed algorithm efficiently constructs layouts that realize arbitrary area assignments while preserving the prescribed combinatorial structure.

Technology Category

Search and Optimization: Combinatorial OptimizationPlanning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsConstraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSemantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologiesResponsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• area-universality
• outerplanar graphs
• rectangular layout
• floorplan
• combinatorial equivalence

Innovation

• area-universality
• outerplanar graphs
• rectangular layout
• combinatorial equivalence
• algorithmic construction