On the Weighted Quartet Consensus problem

TL;DR

This paper proves the NP-hardness of the Weighted Quartet Consensus problem in phylogenetics, provides a 1/2-factor approximation, derandomizes a 1/3-factor algorithm, and explores fixed-parameter tractability.

Contribution

It establishes the computational complexity of the problem, offers improved approximation algorithms, and investigates parameterized complexity.

Findings

Weighted Quartet Consensus is NP-hard.

A 1/2-factor approximation algorithm is proposed.

A derandomized 1/3-factor approximation is developed.

Abstract

In phylogenetics, the consensus problem consists in summarizing a set of phylogenetic trees that all classify the same set of species into a single tree. Several definitions of consensus exist in the literature; in this paper we focus on the Weighted Quartet Consensus problem, a problem with unknown complexity status so far. Here we prove that the Weighted Quartet Consensus problem is NP-hard and we give a 1/2-factor approximation for this problem. During the process, we propose a derandomization procedure of a previously known randomized 1/3-factor approximation. We also investigate the fixed-parameter tractability of this problem.