A framework for cost-constrained genome rearrangement under Double Cut and Join

TL;DR

This paper introduces a polynomial-time algorithm for finding minimum cost genome rearrangement scenarios under certain constraints, extending the Double Cut and Join framework to weighted and colored breakpoint graphs.

Contribution

It generalizes the weighted 2-break distance problem, linking cycle decompositions to edit scenarios, and provides efficient algorithms for specific cost functions.

Findings

Polynomial-time algorithm for minimum cost scenarios with vertex coloring.

NP-Hardness of finding non-parsimonious minimum cost scenarios.

Connection established between cycle decompositions and genome edit scenarios.

Abstract

The study of genome rearrangement has many flavours, but they all are somehow tied to edit distances on variations of a multi-graph called the breakpoint graph. We study a weighted 2-break distance on Eulerian 2-edge-colored multi-graphs, which generalizes weighted versions of several Double Cut and Join problems, including those on genomes with unequal gene content. We affirm the connection between cycle decompositions and edit scenarios first discovered with the Sorting By Reversals problem. Using this we show that the problem of finding a parsimonious scenario of minimum cost on an Eulerian 2-edge-colored multi-graph - with a general cost function for 2-breaks - can be solved by decomposing the problem into independent instances on simple alternating cycles. For breakpoint graphs, and a more constrained cost function, based on coloring the vertices, we give a polynomial-time algorithm for finding a parsimonious 2-break scenario of minimum cost, while showing that finding a non-parsimonious 2-break scenario of minimum cost is NP-Hard.