The planar minimum linear arrangement problem is different from the minimum linear arrangement problem

TL;DR

This paper clarifies that the planar minimum linear arrangement problem (planar minLA) is distinct from the general minimum linear arrangement problem (minLA), correcting a common misconception in existing literature.

Contribution

It demonstrates that planar minLA and minLA are different problems, providing clarification and correction to prior assumptions in the research community.

Findings

Planar minLA is not equivalent to minLA.

Previous claims of solvability on outerplanar graphs are incorrect for planar minLA.

The paper distinguishes the two problems clearly.

Abstract

In various research papers, such as [2], one will find the claim that the minLA is optimally solvable on outerplanar graphs, with a reference to [1]. However, the problem solved in that publication, which we refer to as the planar minimum linear arrangement problem (planar minLA), is different from the minimum linear arrangement problem (minLA), as we show in this article.