Rectangularly Dualizable Graphs: Area-Universality

TL;DR

This paper introduces a class of rectangularly dualizable graphs that can be realized as area-universal rectangular duals and provides a polynomial time algorithm for their construction.

Contribution

It identifies a new class of rectangularly dualizable graphs with area-universality and offers a polynomial time construction algorithm.

Findings

Identifies a class of area-universal rectangular duals.

Provides a polynomial time construction algorithm.

Enhances understanding of rectangular graph duality.

Abstract

A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. A rectangular dual is it area-universal if any assignment of areas to each of its regions can be realized by a combinatorially weak equivalent rectangular dual. It is still unknown that there exists no polynomial time algorithm to construct an area-universal rectangular dual for a rectangularly dualizable graph . In this paper, we describe a class of rectangularly dualizable graphs wherein each graph can be realized by an area-universal rectangular dual. We also present a polynomial time algorithm for its construction.