A path-deformation framework for determining weighted genome rearrangement distance

TL;DR

This paper introduces a novel group-theoretic framework utilizing the Knuth--Bendix algorithm to compute minimal weighted genome rearrangement distances, generalizing previous methods to accommodate arbitrary inversion weights.

Contribution

It extends existing group-theoretic approaches by incorporating rewriting systems and the Knuth--Bendix algorithm to handle weighted genome rearrangement distances.

Findings

First application of Knuth--Bendix in genome rearrangement

Generalizes inversion distance calculation to arbitrary weights

Provides a method to deform initial paths to optimal solutions

Abstract

Measuring the distance between two bacterial genomes under the inversion process is usually done by assuming all inversions to occur with equal probability. Recently, an approach to calculating inversion distance using group theory was introduced, and is effective for the model in which only very short inversions occur. In this paper, we show how to use the group-theoretic framework to establish minimal distance for any weighting on the set of inversions, generalizing previous approaches. To do this we use the theory of rewriting systems for groups, and exploit the Knuth--Bendix algorithm, the first time this theory has been introduced into genome rearrangement problems. The central idea of the approach is to use existing group theoretic methods to find an initial path between two genomes in genome space (for instance using only short inversions), and then to deform this path to optimality using a confluent system of rewriting rules generated by the Knuth--Bendix algorithm.