Aspect Ratio Universal Rectangular Layouts

TL;DR

This paper introduces combinatorial criteria and an efficient algorithm to determine and construct rectangular layouts that can realize any aspect ratio assignment, enhancing flexibility in data visualization and cartography.

Contribution

It provides the first combinatorial characterizations and a quadratic-time algorithm for identifying strongly aspect ratio universal layouts.

Findings

Characterizations for weakly and strongly aspect ratio universal layouts.

A quadratic-time algorithm to decide and construct such layouts.

Application potential in data visualization and geographic mapping.

Abstract

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.