Comparison of labeled trees with valency three

Robinson, D. F.

doi:10.1016/0095-8956(71)90020-7

Cited by 187 publications

(174 citation statements)

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“…For example, the tbr operation depicted in Figure 2 is not an spr operation. Also note that it was shown in Robinson (1971) that for two arbitrary phylogenetic trees T and T on the same leaf set X there exists a sequence of nni operations that transform T into T . Therefore, for any operation op ∈ {nni, spr, tbr}, the distance d op (T , T ) between T and T defined as the minimum number of operations of type op that suffice to transform T into T is finite.…”

Section: Operationsmentioning

confidence: 99%

“…The nni neighborhood N nni (T ) and the spr neighborhood N spr (T ) of T are defined analogously; we clearly have N nni (T ) ⊆ N spr (T ) ⊆ N tbr (T ). Moreover, it is known that, for any phylogenetic tree T on X with |X| = n, we have |N nni (T )| = 2n − 6 (Robinson, 1971), |N spr (T )| = 2(n − 3)(2n − 7) (Allen and Steel, 2001) and…”

Section: The Size Of Tree Operation Neighborhoodsmentioning

confidence: 99%

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Neighborhoods of Trees in Circular Orderings

et al. 2014

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In phylogenetics a common strategy used to construct an evolutionary tree for a set of species X is to search in the space of all such trees for one that optimizes some given score function (such as the minimum evolution, parsimony or likelihood score). As this can be computationally intensive, it was recently proposed to restrict such searches to the set of all those trees that are compatible with some circular ordering of the set X.To inform the design of efficient algorithms to perform such searches, it is therefore of interest to find bounds for the number of trees compatible with a fixed ordering in the neighborhood of a tree that is determined by certain tree operations commonly used to search for trees: the nearest neighbor interchange (nni), the subtree prune and regraft (spr) and the tree bisection and reconnection (tbr) operations. We show that the size of such a neighborhood of a binary tree associated to the nni operation is independent of the tree's topology, but that this is not the case for the spr and tbr operations. We also give tight upper and lower bounds for the size of the neighborhood of a binary tree for the spr and tbr operations and characterize those trees for which these bounds are attained.Keywords phylogenetic tree · nearest neighbor interchange · subtree prune and regraft · tree bisection and reconnection · NeighborNet · circular ordering

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Section: Operationsmentioning

confidence: 99%

Section: The Size Of Tree Operation Neighborhoodsmentioning

confidence: 99%

Neighborhoods of Trees in Circular Orderings

et al. 2014

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“…The nni (nearest neighbor interchange) and the mast (maximum agreement subtree) are two of the most used metrics. nni has been introduced independently in [18] and [19] and its NP-completeness has been recently proved [20,21]. mast has been proposed in [22], and [23] describes an efficient algorithm for computing this metrics on binary trees.…”

Section: Comparing Binary Treesmentioning

confidence: 99%

Boolean Property Encoding for Local Set Pattern Discovery: An Application to Gene Expression Data Analysis

Pensa¹,

Boulicaut²

2005

Lecture Notes in Computer Science

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Abstract. In the domain of gene expression data analysis, several researchers have recently emphasized the promising application of local pattern (e.g., association rules, closed sets) discovery techniques from boolean matrices that encode gene properties. Detecting local patterns by means of complete constraint-based mining techniques turns to be an important complementary approach or invaluable counterpart to heuristic global model mining. To take the most from local set pattern mining approaches, a needed step concerns gene expression property encoding (e.g., over-expression). The impact of this preprocessing phase on both the quantity and the quality of the extracted patterns is crucial. In this paper, we study the impact of discretization techniques by a sound comparison between the dendrograms, i.e., trees that are generated by a hierarchical clustering algorithm on raw numerical expression data and its various derived boolean matrices. Thanks to a new similarity measure, we can select the boolean property encoding technique which preserves similarity structures holding in the raw data. The discussion relies on several experimental results for three gene expression data sets. We believe our framework is an interesting direction of work for the many application domains in which (a) local set patterns have been proved useful, and (b) Boolean properties have to be derived from raw numerical data.

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“…In addition to the unrooted analogue of rooted subtree prune and regraft, two other types that have been extensively studied are nearest neighbour interchange (introduced independently in [11] and [13]) and tree bisection and reconnection. We describe these next.…”

Section: Introductionmentioning

confidence: 99%

On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

2005

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Abstract. The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.

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Comparison of labeled trees with valency three

Cited by 187 publications

References 0 publications

Neighborhoods of Trees in Circular Orderings

Neighborhoods of Trees in Circular Orderings

Boolean Property Encoding for Local Set Pattern Discovery: An Application to Gene Expression Data Analysis

On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

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