An exact algorithm for the minimum quartet tree cost problem

Sergio Consoli*, Jan Korst, Gijs Geleijnse, Steffen Pauws

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


The minimum quartet tree cost (MQTC) problem is a graph combinatorial optimization problem where, given a set of 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.

Original languageEnglish
Pages (from-to)401-425
Number of pages25
Journal4or-A quarterly journal of operations research
Issue number4
Publication statusPublished - Jun 2019


  • Combinatorial optimization
  • Quartet trees
  • Minimum quartet tree cost
  • Exact solution algorithms
  • Cluster analysis
  • Graphs


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