An exact algorithm for the minimum quartet tree cost problem

• Published in: 4OR Vol. 17; no. 4; pp. 401 - 425
• Main Authors: Consoli, Sergio, Korst, Jan, Geleijnse, Gijs, Pauws, Steffen
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Cluster analysis; Clustering; Combinatorial analysis; Construction costs; Cost engineering; Costs; Domains; Exact solutions; Industrial and Production Engineering; Mathematical analysis; Operations research; Operations Research/Decision Theory; Optimization; Research Paper; Topology; Cluster analysis; Quartet trees; Exact solution algorithms; Minimum quartet tree cost; 05C30; 90C27; Combinatorial optimization; 92E10; Graphs; 62H30; 05A05; 68R10; 05A15
• ISSN: 1619-4500; 1614-2411
• DOI: 10.1007/s10288-018-0394-2

The minimum quartet tree cost (MQTC) problem is a graph combinatorial optimization problem where, given a set of n ≥ 4 data objects and their pairwise costs (or distances), one wants to construct an optimal tree from the 3 · n 4 quartet topologies on n , where optimality means that the sum of the costs of the embedded (or consistent) quartet topologies is minimal. The MQTC problem is the foundation of the quartet method of hierarchical clustering, a novel hierarchical clustering method for non tree-like (non-phylogeny) data in various domains, or for heterogeneous data across domains. The MQTC problem is NP-complete and some heuristics have been already proposed in the literature. The aim of this paper is to present a first exact solution approach for the MQTC problem. Although the algorithm is able to get exact solutions only for relatively small problem instances, due to the high problem complexity, it can be used as a benchmark for validating the performance of any heuristic proposed for the MQTC problem.