Extremal Distances for Subtree Transfer Operations in Binary Trees

Atkins, Ross; McDiarmid, Colin

doi:10.1007/s00026-018-0410-4

Cited by 14 publications

(11 citation statements)

References 13 publications

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“…The analysis in [1] made heavy use of a powerful abstraction known as an agreement forest, which in a nutshell partitions the two trees into smaller, non-overlapping fragments which do have the same topology in both trees (see e.g. [14,16] for overviews of algorithmic results and [2] for extremal results). Via a different technique, based on bounded search trees, running times of O(4 k • poly(|X|)) [16] and then O (3 k • poly(|X|)) were later obtained [5].…”

Section: Introductionmentioning

confidence: 99%

New Reduction Rules for the Tree Bisection and Reconnection Distance

Kelk

Linz

2020

Ann. Comb.

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Recently it was shown that, if the subtree and chain reduction rules have been applied exhaustively to two unrooted phylogenetic trees, the reduced trees will have at most $$15k-9$$ 15 k - 9 taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees, and that this bound is tight. Here, we propose five new reduction rules and show that these further reduce the bound to $$11k-9$$ 11 k - 9 . The new rules combine the “unrooted generator” approach introduced in Kelk and Linz (SIAM J Discrete Math 33(3):1556–1574, 2019) with a careful analysis of agreement forests to identify (i) situations when chains of length 3 can be further shortened without reducing the TBR distance, and (ii) situations when small subtrees can be identified whose deletion is guaranteed to reduce the TBR distance by 1. To the best of our knowledge these are the first reduction rules that strictly enhance the reductive power of the subtree and chain reduction rules.

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Section: Introductionmentioning

confidence: 99%

New Reduction Rules for the Tree Bisection and Reconnection Distance

Kelk

Linz

2020

Ann. Comb.

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“…They suggest that 50-53 branch moves would be required to convert the trees into one another. Even if this appears to be an overestimate, considering the results of Atkins & McDiarmid (2019), it indicates that at least one of the trees was still very far from reconstructing the true evolutionary history of this small sample of the subfamily.…”

Section: Discussionmentioning

confidence: 93%

“…As stated repeatedly, there remain multiple areas where the available evidence does not yet allow a highly confident decision between alternative phylogenetic hypotheses. A fully resolved phylogenetic tree for the 680 British spider species could contain at most on the order of 650 "mistakes" relative to the true phylogenetic history of the group (the maximum number of branch moves required to transfer the tree into the correct one; Atkins & McDiarmid 2019). The expected number of mistakes in a random tree would be on the order of 600.…”

Section: Discussionmentioning

confidence: 99%

A completely resolved phylogenetic tree of British spiders (Arachnida: Araneae)

Breitling

2021

Ecol. Monten.

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The recent accumulation of increasingly densely sampled phylogenetic analyses of spiders has greatly advanced our understanding of evolutionary relationships within this group. Here, this diverse literature is reviewed and combined with earlier morphological analyses in an attempt to reconstruct the first fully resolved phylogeny for the spider fauna of the British Isles. The resulting tree highlights parts of the group where data are still too limited for a confident assessment of relationships, proposes a number of deviations from previously suggested phylogenetic hypotheses, and can serve as a framework for evolutionary and ecological interpretations of the biology of British spiders, as well as a starting point for future studies on a larger geographical scale.

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“…It is probably relevant that such instances increasingly start to resemble random pairs of trees; the literature on the expected number of components in maximum agreement forests of random pairs of trees is therefore worth exploring (Atkins and McDiarmid 2019).…”

Section: The Quality Of the D Mp Lower Boundmentioning

confidence: 99%

Reflections on kernelizing and computing unrooted agreement forests

et al. 2021

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Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary phylogenetic trees. This problem is better-known in the literature as the maximum agreement forest problem, where the goal is to partition the two trees into a minimum number of common, non-overlapping subtrees. We have implemented two well-known reduction rules, the subtree and chain reduction, and five more recent, theoretically stronger reduction rules, and compare the reduction achieved with and without the stronger rules. We find that the new rules yield smaller reduced instances and thus have clear practical added value. In many cases they also cause the TBR distance to decrease in a controlled fashion, which can further facilitate solving the problem in practice. Next, we compare the achieved reduction to the known worst-case theoretical bounds of $$15k-9$$ 15 k - 9 and $$11k-9$$ 11 k - 9 respectively, on the number of leaves of the two reduced trees, where k is the TBR distance, observing in both cases a far larger reduction in practice. As a by-product of our experimental framework we obtain a number of new insights into the actual computation of TBR distance. We find, for example, that very strong lower bounds on TBR distance can be obtained efficiently by randomly sampling certain carefully constructed partitions of the leaf labels, and identify instances which seem particularly challenging to solve exactly. The reduction rules have been implemented within our new solver Tubro which combines kernelization with an Integer Linear Programming (ILP) approach. Tubro also incorporates a number of additional features, such as a cluster reduction and a practical upper-bounding heuristic, and it can leverage combinatorial insights emerging from the proofs of correctness of the reduction rules to simplify the ILP.

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Extremal Distances for Subtree Transfer Operations in Binary Trees

Cited by 14 publications

References 13 publications

New Reduction Rules for the Tree Bisection and Reconnection Distance

New Reduction Rules for the Tree Bisection and Reconnection Distance

A completely resolved phylogenetic tree of British spiders (Arachnida: Araneae)

Reflections on kernelizing and computing unrooted agreement forests

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