On the minimum quartet tree cost problem

TL;DR

This paper introduces the minimum quartet tree cost problem, a challenging task of constructing an optimal tree with minimal dissimilarity sum from pairwise data, and discusses an exact algorithm to improve existing heuristics.

Contribution

It formulates the novel MQTC problem and details an exact algorithm aimed at enhancing current heuristic methods.

Findings

Formulation of the MQTC problem

Development of an exact algorithm

Potential for more efficient hybrid approaches

Abstract

Given a set of n data objects and their pairwise dissimilarities, the goal of the minimum quartet tree cost (MQTC) problem is to construct an optimal tree from the total number of possible combinations of quartet topologies on n, where optimality means that the sum of the dissimilarities of the embedded (or consistent) quartet topologies is minimal. We provide details and formulation of this novel challenging problem, and the preliminaries of an exact algorithm under current development which may be useful to improve the MQTC heuristics to date into more efficient hybrid approaches.