Planar Rectilinear Drawings of Outerplanar Graphs in Linear Time
Fabrizio Frati

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.
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