Calculating the Unrooted Subtree Prune-and-Regraft Distance

Whidden, Chris; Matsen, F. A.

doi:10.1109/tcbb.2018.2802911

Cited by 17 publications

(41 citation statements)

References 63 publications

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“…The 28 now improves to 15. Our result implies a similar improvement on the kernel for computing the so-called subtree prune and regraft (SPR) distance [32].…”

Section: Rooted-hybridization-number (Rhn)mentioning

confidence: 52%

“…Many such kernelizations use subtree reductions and variations of chain reductions. The reductions typically have a common core but details differ from case to case depending on the specific combinatorial nature of the problem at hand: there are many subtle differences between TBR distance, SPR distance [4,6,32], hybridization number [7,29,30] and agreement forests [24,31], for example. Other relevant factors include whether the input trees are unrooted or rooted; whether the input trees are binary or non-binary and the number of trees allowed in the input (see earlier references and [28]).…”

Section: Rooted-hybridization-number (Rhn)mentioning

confidence: 99%

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

Kelk

Linz

2019

SIAM J. Discrete Math.

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In 2001 Allen and Steel showed that, if subtree and chain reduction rules have been applied to two unrooted phylogenetic trees, the reduced trees will have at most 28k taxa where k is the TBR (Tree Bisection and Reconnection) distance between the two trees. Here we reanalyse Allen and Steel's kernelization algorithm and prove that the reduced instances will in fact have at most 15k − 9 taxa. Moreover we show, by describing a family of instances which have exactly 15k − 9 taxa after reduction, that this new bound is tight. These instances also have no common clusters, showing that a third commonly-encountered reduction rule, the cluster reduction, cannot further reduce the size of the kernel in the worst case. To achieve these results we introduce and use "unrooted generators" which are analogues of rooted structures that have appeared earlier in the phylogenetic networks literature. Using similar argumentation we show that, for the minimum hybridization problem on two rooted trees, 9k − 2 is a tight bound (when subtree and chain reduction rules have been applied) and 9k − 4 is a tight bound (when, additionally, the cluster reduction has been applied) on the number of taxa, where k is the hybridization number of the two trees.

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“…The 28 now improves to 15. Our result implies a similar improvement on the kernel for computing the so-called subtree prune and regraft (SPR) distance [32].…”

Section: Rooted-hybridization-number (Rhn)mentioning

confidence: 52%

Section: Rooted-hybridization-number (Rhn)mentioning

confidence: 99%

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

Kelk

Linz

2019

SIAM J. Discrete Math.

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“…Thus two rooted trees which differ by a single SPR operation must share a two component rooted MAF ( No general MAF formulation has been identified as equivalent to the unrooted SPR distance and there are reasons to believe that a directly analogous formulation does not exist [19]. However, we prove that two unrooted trees differ by exactly one SPR operation if and only if they share an appropriately defined hybrid two-component MAF.…”

Section: Preliminariesmentioning

confidence: 76%

Efficiently Inferring Pairwise Subtree Prune-and-Regraft Adjacencies between Phylogenetic Trees

Whidden¹,

Matsen²

2018

2018 Proceedings of the Fifteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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We develop a time-optimal O(mn 2 )-time algorithm to construct the subtree prune-regraft (SPR) graph on a collection of m phylogenetic trees with n leaves. This improves on the previous bound of O(mn 3 ). Such graphs are used to better understand the behaviour of phylogenetic methods and recommend parameter choices and diagnostic criteria. The limiting factor in these analyses has been the difficulty in constructing such graphs for large numbers of trees. We also develop the first efficient algorithms for constructing the nearest-neighbor interchange (NNI) and tree bisection-andreconnection (TBR) graphs.These new algorithms are enabled by a change of perspective: rather than focusing on the trees and checking for pairs of adjacencies, we enumerate the potential adjacencies themselves in the form of structures called "agreement forests." Indeed, two trees are adjacent in the graph if, and only if, they share an appropriately defined two-component agreement forest. We prove that this holds even in the case of unrooted trees, the first such result for unrooted SPR. To turn this observation into an efficient algorithm, we develop two tools: SDLNewick, the first unique string representation for agreement forests, and a new AFContainer data structure which efficiently stores tree adjacencies using such strings.

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“…The problem is also NP-hard for unrooted binary trees (Hickey et al 2008). If we take the SPR distance as a parameter, then both rooted (Bordewich and Semple 2005) and unrooted (Whidden and Matsen 2015) versions are FPT.…”

Section: A Review Of Previous Resultsmentioning

confidence: 99%

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

Hasic

Tannier

2019

J Comb Optim

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Phylogenetic trees illustrate the evolutionary history of genes and species. In most cases, although genes evolve along with the species they belong to, a species tree and gene tree are not identical, because of evolutionary events at the gene level like duplication or transfer. These differences are handled by phylogenetic reconciliation, which formally is a mapping between gene tree nodes and species tree nodes and branches. We investigate models of reconciliation with a gene transfer that replaces existing gene, which is a biological important event but never included in reconciliation models. Also the problem is close to a dated version of the classical subtree prune and regraft (SPR) distance problem, where a pruned subtree has to be regrafted only on a branch closer to the root. We prove that the reconciliation problem including transfer and replacement is NP-hard, and that if speciations and transfers with replacement are the only allowed evolutionary events, then it is fixed-parameter tractable (FPT) with respect to the reconciliation's weight. We prove that the results extend to the dated SPR problem.Keywords phylogenetic reconciliation · dated subtree prune and regraft SPR · gene transfer · transfer with replacement (replacing transfer) · NP hard/complete · fixed parameter tractable FPT

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Calculating the Unrooted Subtree Prune-and-Regraft Distance

Cited by 17 publications

References 63 publications

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

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

Efficiently Inferring Pairwise Subtree Prune-and-Regraft Adjacencies between Phylogenetic Trees

Gene tree reconciliation including transfers with replacement is NP-hard and FPT

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