Integer linear programming as a tool for constructing trees from quartet data

Weyer-Menkhoff, Jan; Devauchelle, Claudine; Großmann, A.; Grünewald, Stefan

doi:10.1016/j.compbiolchem.2005.04.001

Cited by 9 publications

(11 citation statements)

References 22 publications

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“…They presented two "quartet cleaning" algorithms for correcting bounded numbers of quartet errors for many popular quartet methods. Exact approaches to the MQC problem are presented in [2], where the problem is solved by using dynamic programming and a geometric algorithm, and in [26], where the problem is reformulated as an integer linear programming problem. However, these approaches are not able to solve problems with more than 15-20 objects.…”

Section: The Quartet Methods Of Hierarchical Clusteringmentioning

confidence: 99%

Heuristic Approaches for the Quartet Method of Hierarchical Clustering

Consoli¹,

Darby‐Dowman²,

Geleijnse

et al. 2010

IEEE Trans. Knowl. Data Eng.

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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.

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Section: The Quartet Methods Of Hierarchical Clusteringmentioning

confidence: 99%

Heuristic Approaches for the Quartet Method of Hierarchical Clustering

Consoli¹,

Darby‐Dowman²,

Geleijnse

et al. 2010

IEEE Trans. Knowl. Data Eng.

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show abstract

“…incorrect inferences of simple quartet topologies) for many popular quartet methods. Exact approaches to the MQC problem are presented in (Ben-Dor et al, 1998), where the problem is solved by using dynamic programming and a geometric algorithm, and in (Weyer-Menkhoff et al, 2005), where the problem is reformulated as an integer linear programming problem. However, these approaches are not able to solve problems with more than 15-20 taxa.…”

Section: The Quartet Methods Of Hierarchical Clusteringmentioning

confidence: 99%

The development and application of metaheuristics for problems in graph theory: a computational study

Consoli¹

2011

4OR-Q J Oper Res

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“…1(b), and several methods for tree reconstruction rely on this fact (see e.g. [13,19,22]). With this in mind, let Q(X) denote the set of all bipartitions of the form a 1 a 2 |b 1 b 2 , where a 1 , a 2 , b 1 , b 2 are distinct elements of X , i.e., Q(X) is the set of quartets on X .…”

Section: Introductionmentioning

confidence: 99%

Characterizing weak compatibility in terms of weighted quartets

Grünewald

Huber

Moulton

et al. 2009

Advances in Applied Mathematics

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In phylogenetics there are various methods available for understanding the evolutionary history of a set of species based on the analysis of its 4-element subsets. Guided by biological data, such techniques usually require the initial computation of a quartet-weight function, i.e., a function that assigns a weight to each bipartition of each 4-element subset into two parts of size two, from which a phylogenetic tree or network is subsequently deduced. It is therefore of interest to characterize quartet-weight functions that correspond precisely to phylogenetic trees or networks. Recently, such characterizations have been presented for phylogenetic trees. Here we provide a 5-point condition for characterizing more general structures called weakly compatible split systems. Such split systems underly the construction of split networks, a special class of phylogenetic networks. This 5-point condition also yields a new characterization of quartet-weight functions that correspond to phylogenetic trees.

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Integer linear programming as a tool for constructing trees from quartet data

Cited by 9 publications

References 22 publications

Heuristic Approaches for the Quartet Method of Hierarchical Clustering

Heuristic Approaches for the Quartet Method of Hierarchical Clustering

The development and application of metaheuristics for problems in graph theory: a computational study

Characterizing weak compatibility in terms of weighted quartets

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