Balanced Vertices in Trees and a Simpler Algorithm to Compute the Genomic Distance

TL;DR

This paper introduces a simplified algorithm for computing genomic distance using white-grey trees, featuring a new tree center concept that enhances understanding and efficiency in genome rearrangement analysis.

Contribution

It provides a more transparent solution for the covering cost of white-grey trees and introduces a novel tree center notion relevant to genome comparison algorithms.

Findings

Linear-time computation of rearrangement distance

Simpler algorithm for white-grey trees

New concept of tree center

Abstract

This paper provides a short and transparent solution for the covering cost of white-grey trees which play a crucial role in the algorithm of Bergeron {\it et al.}\ to compute the rearrangement distance between two multichromosomal genomes in linear time ({\it Theor. Comput. Sci.}, 410:5300-5316, 2009). In the process it introduces a new {\em center} notion for trees, which seems to be interesting on its own.