A 3-approximation algorithm for computing a parsimonious first speciation in the gene duplication model

TL;DR

This paper introduces a polynomial-time 3-approximation algorithm for the Minimum Duplication Bipartition Problem, which aims to identify a speciation event that minimizes pre-speciation gene duplications across genomes.

Contribution

It presents the first polynomial-time approximation algorithm with a guaranteed approximation ratio for the problem, leveraging submodular function minimization techniques.

Findings

The algorithm achieves a 3-approximation ratio.

It operates in polynomial time and space.

Provides a practical approach for gene duplication analysis.

Abstract

We consider the following problem: from a given set of gene families trees on a set of genomes, find a first speciation, that splits these genomes into two subsets, that minimizes the number of gene duplications that happened before this speciation. We call this problem the Minimum Duplication Bipartition Problem. Using a generalization of the Minimum Edge-Cut Problem, known as Submodular Function Minimization, we propose a polynomial time and space 3-approximation algorithm for the Minimum Duplication Bipartition Problem.