A Pseudo-Boolean Solution to the Maximum Quartet Consistency Problem

Determining the evolutionary history of a given biological data is an important task in biological sciences. Given a set of quartet topologies over a set of taxa, the Maximum Quartet Consistency (MQC) problem consists of computing a global phylogeny that satisfies the maximum number of quartets. A number of solutions have been proposed for the MQC problem, including Dynamic Programming, Constraint Programming, and more recently Answer Set Programming (ASP). ASP is currently the most efficient approach for optimally solving the MQC problem. This paper proposes encoding the MQC problem with pseudo-Boolean (PB) constraints. The use of PB allows solving the MQC problem with efficient PB solvers, and also allows considering different modeling approaches for the MQC problem. Initial results are promising, and suggest that PB can be an effective alternative for solving the MQC problem.

💡 Research Summary

The paper addresses the Maximum Quartet Consistency (MQC) problem, a fundamental task in phylogenetics where one seeks a global tree that satisfies the largest possible subset of quartet topologies derived from a set of taxa. While several approaches have been explored—including dynamic programming, constraint programming, and, most recently, Answer Set Programming (ASP)—ASP currently offers the most efficient exact solutions. The authors propose a novel formulation of MQC using Pseudo‑Boolean (PB) constraints, thereby enabling the use of state‑of‑the‑art PB solvers.

The core of the approach is to represent a rooted phylogeny through an ultrametric matrix M. For a taxa set S of size n, M is an n × n symmetric matrix where M(i,i)=0 and each off‑diagonal entry M(i,j) takes an integer value in the range