A Branch-and-Cut Algorithm for the 2-Species Duplication-Loss Phylogeny Problem

TL;DR

This paper introduces a branch-and-cut algorithm for the duplication-loss alignment problem in phylogeny reconstruction, significantly improving computational efficiency over previous ILP methods.

Contribution

It presents a novel branch-and-cut algorithm, defines valid inequalities, and demonstrates the NP-hardness of the problem.

Findings

Algorithm outperforms existing ILP methods by several orders of magnitude.

Defines classes of valid inequalities and efficient separation algorithms.

Proves the NP-hardness of the duplication-loss alignment problem.

Abstract

The reconstruction of the history of evolutionary genome-wide events among a set of related organisms is of great biological interest. A simplified model that captures only content modifying operations was introduced recently. It allows the small phylogeny problem to be formulated as an alignment problem. In this work we present a branch-and-cut algorithm for this so-called duplication-loss alignment problem. Our method clearly outperforms the existing ILP based method by several orders of magnitude. We define classes of valid inequalities and provide algorithms to separate them efficiently and prove the NP-hardness of the duplication-loss alignment problem.