A Tight Kernel for Computing the Tree Bisection and Reconnection Distance between Two Phylogenetic Trees

Kelk, Steven; Linz, Simone

doi:10.1137/18m122724x

Cited by 12 publications

(20 citation statements)

References 32 publications

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“…To this end, they established a linear kernel of size at most 28k. Recently, this result was improved by Kelk and Linz [12] who showed with a new analysis that the following superior bound actually holds.…”

Section: A New Suite Of Reduction Rulesmentioning

confidence: 97%

“…To obtain this bound, we combine the generator approach introduced in [12] with a careful analysis of agreement forests.…”

Section: A New Suite Of Reduction Rulesmentioning

confidence: 99%

“…Recently, in [12], it was shown that the subtree and chain reduction rules actually reduce the instance to size 15 • d TBR (T, T ) − 9, and that there are instances for which this bound is tight. Interestingly, the sharpened analysis does not leverage agreement forests at all, but instead recasts the computation of TBR distance as a phylogenetic network inference problem, where phylogenetic networks are essentially the generalization of phylogenetic trees to graphs.…”

Section: Introductionmentioning

confidence: 99%

“…In the present article, we combine the agreement forest perspective of [1] with the network/generator perspective of [12], to obtain a new suite of five polynomial-time reduction rules. When applied alongside the subtree and chain reduction rules, these reduce the size of the kernel to 11 • d TBR (T, T ) − 9.…”

Section: Introductionmentioning

confidence: 99%

“…Other reduction rules, such as the cluster reduction [3,4], tend to be very effective in practice, but do not yield improved (i.e. smaller) bounds on kernel size [12].…”

Section: Introductionmentioning

confidence: 99%

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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: A New Suite Of Reduction Rulesmentioning

confidence: 97%

“…To obtain this bound, we combine the generator approach introduced in [12] with a careful analysis of agreement forests.…”

Section: A New Suite Of Reduction Rulesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Other reduction rules, such as the cluster reduction [3,4], tend to be very effective in practice, but do not yield improved (i.e. smaller) bounds on kernel size [12].…”

Section: Introductionmentioning

confidence: 99%

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New Reduction Rules for the Tree Bisection and Reconnection Distance

Kelk

Linz

2020

Ann. Comb.

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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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