Combinatorial Optimization Solutions for the Maximum Quartet Consistency Problem

Given a set of taxa S and a complete set of quartet topologies Q over S, the problem of determining a phylogeny that satisfies the maximum number of topologies is called the Maximum Quartet Consistency (MQC) problem. The MQC problem is an NP-problem. MQC has been solved both heuristically and exactly. Exact solutions for MQC include Constraint Programming, Answer Set Programming and Pseudo-Boolean Optimization (PBO). This paper extends the range of solutions for MQC, by developing two new PBO models and also by introducing models based on the optimization of Satisfiability Modulo Theories (SMT). The models were experimentally compared with existing exact solutions. The results show that for instances with small percentage of quartet errors, the models based on SMT can be competitive, whereas for instances with higher number of quartet errors the PB-models are more efficient.