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

Shi, Feng; Qi, Feng; Jie, You; Wang, Jianxin

doi:10.1007/s10878-015-9921-7

Cited by 9 publications

(8 citation statements)

References 20 publications

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“…A divide and conquer approach with MAF is used for computing an exact SPR distance in Linz and Semple (2011). A 2.5-approximation algorithm for the MAF problem on two rooted binary phylogenetic trees is presented in Shi et al (2016). 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).…”

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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“…If R = ∅, then κ is normal and we simply write κ = (X, B) instead of κ = (X, B, R); otherwise, it is abnormal. In essence, only normal keys were considered in [10].…”

Section: Keys and Lower Boundsmentioning

confidence: 99%

“…Whidden et al [20] came up with a very simple approximation algorithm that runs in linear time and achieves an approximation ratio of 3. Although the ratio 3 is achieved by a very simple algorithm in [20], no polynomial-time approximation algorithm had been designed to achieve a better ratio than 3 before Shi et al [10] presented a polynomial-time approximation algorithm that achieves a ratio of 2.5. Schalekamp et al [17] presented a polynomial-time 2-approximation algorithm for the same problem.…”

Section: Introductionmentioning

confidence: 99%

A New 2-Approximation Algorithm for rSPR Distance

Chen

Harada

Wang

2017

Bioinformatics Research and Applications

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Due to hybridization events in evolution, studying two different genes of a set of species may yield two related but different phylogenetic trees for the set of species. In this case, we want to measure the dissimilarity of the two trees. The rooted subtree prune and regraft (rSPR) distance of the two trees has been used for this purpose. The problem of computing the rSPR distance of two given trees has many applications but is NP-hard. The previously best approximation algorithm for rSPR distance achieves a ratio of 2 in polynomial time and its analysis is based on the duality theory of linear programming. In this paper, we present a cubic-time approximation algorithm for rSPR distance that achieves a ratio of 2. Our algorithm is based on the notion of key and several structural lemmas; its analysis is purely combinatorial and explicitly uses a search tree for computing rSPR distance exactly.

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“…Whidden et al [29] presented the third 3-approximation algorithm, which runs in linear-time. Shi et al [30] improved the ratio to 2.5, but the algorithm has running time O(n 2 ). Recently, Schalekamp [31] presented a 2-approximation algorithm by LP Duality (the running time is polynomial, but the exact order of the running time is not clear), which is the best known approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees.…”

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

Cited by 9 publications

References 20 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 New 2-Approximation Algorithm for rSPR Distance

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

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