Fixed-Parameter Algorithms for Maximum Agreement Forests

Whidden, Chris; Beiko, Robert G.; Zeh, Norbert

doi:10.1137/110845045

Cited by 87 publications

(121 citation statements)

References 34 publications

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“…A second 3-approximation algorithm presented in Rodrigues et al (2007) achieves a running time of O(n 2 ). Recently, Whidden and Zeh (2009), Whidden et al (2011) presented a linear-time approximation algorithm of ratio 3, which is the best known approximation algorithm for the Maximum Agreement Forest problem on two rooted binary phylogenetic trees.…”

Section: Introductionmentioning

confidence: 99%

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Shi

Jie

et al. 2015

J Comb Optim

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Given two rooted binary phylogenetic trees with identical leaf label-set, the maximum agreement forest (MAF) problem asks for a largest common subforest of the two trees. This problem has been studied extensively in the literature, and has been known to be NP-complete and MAX SNP-hard. The previously best ratio of approximation algorithms for this problem is 3. In this paper, we make full use of the special relations among leaves in phylogenetic trees and present an approximation algorithm with ratio 2.5 for the MAF problem on two rooted binary phylogenetic trees.

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Section: Introductionmentioning

confidence: 99%

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Shi

Jie

et al. 2015

J Comb Optim

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“…We may first compute a full cluster reduction (T 1 , T 1 ), ..., (T t , T t ), (T ρ , T ρ ) of T and T in time O(n) by Lemma 3. We then apply the algorithm of [22] …”

Section: Conversely Letmentioning

confidence: 99%

“…Note also that the authors of [22] claim to have an algorithm to solve rSPR Distance in O(2 drSPR(T ,T ) · n) [23]. If this is true, the running time in Corollaries 2 and 4 will reduce to O(2 k · n).…”

Section: Theorem 4 (Theorem 22 Of [16])mentioning

confidence: 99%

On the fixed parameter tractability of agreement-based phylogenetic distances

et al. 2016

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International audienceThree important and related measures for summarizing the dissimilarity in phylogenetic trees are the minimum number of hybridization events required to fit two phylogenetic trees onto a single phylogenetic network (the hybridization number), the (rooted) subtree prune and regraft distance (the rSPR distance) and the tree bisection and reconnection distance (the TBR distance) between two phylogenetic trees. The respective problems of computing these measures are known to be NP-hard, but also fixed-parameter tractable in their respective natural parameters. This means that, while they are hard to compute in general, for cases in which a parameter (here the hybridization number and rSPR/TBR distance, respectively) is small, the problem can be solved efficiently even for large input trees. Here, we present new analyses showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any O(f(p)⋅n) -time algorithm for any of these problems into an O(f(k)⋅n) -time one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic network displaying both trees

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“…The first method [20] compares each pair of trees in a collection using a fixed-parameter algorithm [18] to determine whether their SPR distance is 1. Although the SPR distance is NP-hard, this fixed-parameter algorithm scales exponentially only with the distance computed and linearly with n. This pairwise comparison method thus takes O(n)-time for each pair of trees, for a total of O(m 2 n)-time (O(m 2 n 3 )-time for unrooted trees).…”

Section: Introductionmentioning

confidence: 99%

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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Fixed-Parameter Algorithms for Maximum Agreement Forests

Cited by 87 publications

References 34 publications

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

Improved approximation algorithm for maximum agreement forest of two rooted binary phylogenetic trees

On the fixed parameter tractability of agreement-based phylogenetic distances

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

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