Approximating Maximum Agreement Forest on Multiple Binary Trees

Chen, Jianer; Shi, Feng; Wang, Jianxin

doi:10.1007/s00453-015-0087-6

Cited by 16 publications

(11 citation statements)

References 24 publications

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“…In Chen et al (2015) an FPT algorithm for rooted SPR, with complexity O(2.344 k · n) is presented, which is an improvement compared to O(2.42 k · n) (Whidden et al 2010). Rooted SPR is investigated also for non binary trees (Whidden et al 2016), and MAF for multiple trees (Chen et al 2016). For a more complete review see Shi et al (2013) and Whidden et al (2016).…”

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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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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“…For the Maximum Agreement Forest problem on multiple rooted binary phylogenetic trees, Chataigner [33] presented a polynomial-time approximation algorithm of ratio 8. Recently, Mukhopadhyay and Bhabak [34] and Chen et al [35], independently, developed two 3-approximation algorithms. The running times of the two algorithms in [34] and [35] are O(n 2 m 2 ) and O(nm log n) respectively, where n denotes the number of leaves in each phylogenetic tree, and m denotes the number of phylogenetic trees in the input instance.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, Mukhopadhyay and Bhabak [34] and Chen et al [35], independently, developed two 3-approximation algorithms. The running times of the two algorithms in [34] and [35] are O(n 2 m 2 ) and O(nm log n) respectively, where n denotes the number of leaves in each phylogenetic tree, and m denotes the number of phylogenetic trees in the input instance. For the Maximum Agreement Forest problem on multiple unrooted binary trees, Chen et al [35] presented a 4-approximation algorithm with running time O(nm log n) .…”

Section: Introductionmentioning

confidence: 99%

A parameterized algorithm for the Maximum Agreement Forest problem on multiple rooted multifurcating trees

Shi

Chen

et al. 2018

Journal of Computer and System Sciences

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“…The problem has attracted a lot of attention, and indeed has become a canonical problem in the field of phylogenetic networks. Many variants of MAF have been studied, including versions where the input consists of more than two trees [6,7], and where the input trees are unrooted [27,26] or non-binary [20,25]. We will concentrate on MAF in its classical form with two rooted binary input trees, and we will be concerned with the worst-case approximability of the problem.…”

Section: Introductionmentioning

confidence: 99%

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

Olver¹,

Schalekamp²,

Ster³

et al. 2018

Preprint

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We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial time.

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Approximating Maximum Agreement Forest on Multiple Binary Trees

Cited by 16 publications

References 24 publications

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

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

A parameterized algorithm for the Maximum Agreement Forest problem on multiple rooted multifurcating trees

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

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