Heuristic Approaches for the Quartet Method of Hierarchical Clustering

Given a set of objects and their pairwise distances, we wish to determine a visual representation of the data. We use the quartet paradigm to compute a hierarchy of clusters of the objects. The method is based on an NP-hard graph optimization problem called the Minimum Quartet Tree Cost problem. This paper presents and compares several heuristic approaches to approximate the optimal hierarchy. The performance of the algorithms is tested through extensive computational experiments and it is shown that the Reduced Variable Neighborhood Search heuristic is the most effective approach to the problem, obtaining high-quality solutions in short computational running times.