Planar Rectilinear Drawings of Outerplanar Graphs in Linear Time

TL;DR

This paper presents a linear-time algorithm to determine if an outerplanar graph can be drawn with straight lines without crossings, respecting a given embedding if specified, and constructs such drawings when possible.

Contribution

It introduces the first linear-time algorithm for testing and constructing planar rectilinear drawings of outerplanar graphs, including cases with prescribed embeddings.

Findings

Linear-time testing algorithm for rectilinear drawings

Constructs drawings when they exist

Works with or without prescribed embeddings

Abstract

We show how to test in linear time whether an outerplanar graph admits a planar rectilinear drawing, both if the graph has a prescribed plane embedding that the drawing has to respect and if it does not. Our algorithm returns a planar rectilinear drawing if the graph admits one.