A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

TL;DR

This paper presents a novel 2-approximation algorithm for the NP-hard Maximum Agreement Forest problem on rooted binary trees, improving previous approximation ratios by leveraging LP duality in its analysis.

Contribution

It introduces the first LP duality-based approximation algorithm for the problem, achieving a better approximation ratio than prior methods.

Findings

Achieves a 2-approximation ratio for the problem

First to use LP duality in analysis of this problem

Improves upon previous 2.5-approximation algorithm

Abstract

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree Prune-and-Regraft (SPR) distance between two phylogenetic trees. Our result improves on the very recent 2.5-approximation algorithm due to Shi, Feng, You and Wang (2015). Our algorithm is the first approximation algorithm for this problem that uses LP duality in its analysis.