A correction on Shiloach's algorithm for minimum linear arrangement of trees

TL;DR

This paper corrects a small error in Shiloach's longstanding algorithm for the minimum linear arrangement of trees and discusses its impact on related research, also improving notation clarity.

Contribution

It identifies and fixes a specific error in Shiloach's algorithm and refines the notation used, clarifying the algorithm's correctness and influence.

Findings

The correction ensures the algorithm's accuracy.

The fix impacts subsequent research relying on the original algorithm.

Notation improvements enhance understanding and implementation.

Abstract

More than 30 years ago, Shiloach published an algorithm to solve the minimum linear arrangement problem for undirected trees. Here we fix a small error in the original version of the algorithm and discuss its effect on subsequent literature. We also improve some aspects of the notation.