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An exact algorithm for the minimum quartet tree cost problem

Author

Listed:
  • Sergio Consoli

    (Philips Research)

  • Jan Korst

    (Philips Research)

  • Gijs Geleijnse

    (Netherlands Comprehensive Cancer Organisation (IKNL))

  • Steffen Pauws

    (Philips Research
    Tilburg University)

Abstract

The minimum quartet tree cost (MQTC) problem is a graph combinatorial optimization problem where, given a set of $$n \ge 4$$n≥4 data objects and their pairwise costs (or distances), one wants to construct an optimal tree from the $$3 \cdot {n \atopwithdelims ()4}$$3·n4 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.

Suggested Citation

  • Sergio Consoli & Jan Korst & Gijs Geleijnse & Steffen Pauws, 2019. "An exact algorithm for the minimum quartet tree cost problem," 4OR, Springer, vol. 17(4), pages 401-425, December.
    • Handle: RePEc:spr:aqjoor:v:17:y:2019:i:4:d:10.1007_s10288-018-0394-2
    DOI: 10.1007/s10288-018-0394-2
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    References listed on IDEAS

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    1. Michael Steel, 1992. "The complexity of reconstructing trees from qualitative characters and subtrees," Journal of Classification, Springer;The Classification Society, vol. 9(1), pages 91-116, January.
    2. George Furnas, 1984. "The generation of random, binary unordered trees," Journal of Classification, Springer;The Classification Society, vol. 1(1), pages 187-233, December.
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    Cited by:

    1. Sergio Consoli & Jan Korst & Steffen Pauws & Gijs Geleijnse, 2020. "Improved metaheuristics for the quartet method of hierarchical clustering," Journal of Global Optimization, Springer, vol. 78(2), pages 241-270, October.

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