Extremal Distances for Subtree Transfer Operations in Binary Trees

Atkins, Ross; McDiarmid, Colin

doi:10.48550/arxiv.1509.00669

Cited by 3 publications

(3 citation statements)

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“…⊓ ⊔ Diameters of move-induced metrics on tree space are well studied. A few relevant bounds are ∆ rSPR 0 = n−Θ( √ n) (Ding et al, 2011;Atkins and McDiarmid, 2015) and ∆ rNNI 0 = Θ(n log(n)) (Li et al, 1996). We extend these results to higher tiers of network space.…”

Section: The Diameter Of Tail and Rspr Movesmentioning

confidence: 64%

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

et al. 2018

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Popular methods for exploring the space of rooted phylogenetic trees use rearrangement moves such as rooted Nearest Neighbour Interchange (rNNI) and rooted Subtree Prune and Regraft (rSPR). Recently, these moves were generalized to rooted phylogenetic networks, which are a more suitable representation of reticulate evolutionary histories, and it was shown that any two rooted phylogenetic networks of the same complexity are connected by a sequence of either rSPR or rNNI moves. Here, we show that this is possible using only tail moves, which are a restricted version of rSPR moves on networks that are more closely related to rSPR moves on trees. The connectedness still holds even when we restrict to distance-1 tail moves (a localized version of tail moves). Moreover, we give bounds on the number of (distance-1) tail moves necessary to turn one network into another, which in turn yield new bounds for rSPR, rNNI and SPR (i.e. the equivalent of rSPR on unrooted networks). The upper bounds are constructive, meaning that we can actually find a sequence with at most this length for any pair of networks. Finally, we show that finding a shortest sequence of tail or rSPR moves is NP-hard.

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Section: The Diameter Of Tail and Rspr Movesmentioning

confidence: 64%

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

et al. 2018

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“…In addition, the SPR distance is a natural measure of distance when analyzing phylogenetic inference methods which typically apply SPR operations to find maximum likelihood trees [24], [25] or estimate Bayesian posterior distributions with SPR-based Metropolis-Hastings random walks [26], [27]. Similar trees can be easily identified using the SPR distance, as random pairs of n-leaf trees differ by by an expected n − Θ(n 2/3 ) SPR moves [28]. This difference approaches the maximum SPR distance of n− 3 − ( √ n − 2 − 1)/2 asymptotically [29].…”

Section: Introductionmentioning

confidence: 99%

Calculating the Unrooted Subtree Prune-and-Regraft Distance

Whidden

Matsen

2019

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…In addition, the SPR distance is a natural measure of distance when analyzing phylogenetic inference methods which typically apply SPR operations to find maximum likelihood trees [39,44] or estimate Bayesian posterior distributions with SPR-based Metropolis-Hastings random walks [41,12]. Similar trees can be easily identified using the SPR distance, as random pairs of n-leaf trees differ by an expected n − Θ(n 2/3 ) SPR moves [2]. This difference approaches the maximum SPR distance of n − 3 − ( √ n − 2 − 1)/2 [19] asymptotically.…”

Section: Introductionmentioning

confidence: 99%

Chain Reduction Preserves the Unrooted Subtree Prune-and-Regraft Distance

Whidden,

Matsen

2016

Preprint

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The subtree prune-and-regraft (SPR) distance metric is a fundamental way of comparing evolutionary trees. It has wide-ranging applications, such as to study lateral genetic transfer, viral recombination, and Markov chain Monte Carlo phylogenetic inference. Although the rooted version of SPR distance can be computed relatively efficiently between rooted trees using fixed-parameter-tractable algorithms, in the unrooted case previous algorithms are unable to compute distances larger than 7. One important tool for efficient computation in the rooted case is called chain reduction, which replaces an arbitrary chain of subtrees identical in both trees with a chain of three leaves. Whether chain reduction preserves SPR distance in the unrooted case has remained an open question since it was conjectured in 2001 by Allen and Steel, and was presented as a challenge question at the 2007 Isaac Newton Institute for Mathematical Sciences program on phylogenetics.In this paper we prove that chain reduction preserves the unrooted SPR distance. We do so by introducing a structure called a socket agreement forest that restricts edge modification to predetermined socket vertices, permitting detailed analysis and modification of SPR move sequences. This new chain reduction theorem reduces the unrooted distance problem to a linear size problem kernel, substantially improving on the previous best quadratic size kernel.

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Extremal Distances for Subtree Transfer Operations in Binary Trees

Cited by 3 publications

References 0 publications

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

Exploring the Tiers of Rooted Phylogenetic Network Space Using Tail Moves

Calculating the Unrooted Subtree Prune-and-Regraft Distance

Chain Reduction Preserves the Unrooted Subtree Prune-and-Regraft Distance

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