Improved Practical Algorithms for Rooted Subtree Prune and Regraft (rSPR) Distance and Hybridization Number

Yamada, Kohei; Chen, Zhizhong; Wang, Lusheng

doi:10.1089/cmb.2019.0432

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…Informally this measures the number of times that a subtree must be pruned, and re-attached, to transform one tree into another. Despite the NP-hardness of computing this distance [3], very fast fixed-parameter tractable branching algorithms have been developed which allow the problem to be well solved in practice, as long as the rSPR distance does not become too large [20,21]. A related concept is kernelization: polynomial-time pre-processing rules which reduce the size of the input trees to purely a function of their rSPR distance [8].…”

Section: Introductionmentioning

confidence: 99%

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

Kelk

Linz²,

Meuwese³

2023

Information Processing Letters

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Section: Introductionmentioning

confidence: 99%

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

Kelk

Linz²,

Meuwese³

2023

Information Processing Letters

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“…Informally this measures the number of times that a subtree must be pruned, and re-attached, to transform one tree into another. Despite the NP-hardess of computing this distance [3], very fast fixed-parameter tractable branching algorithms have been developed which allow the problem to be well solved in practice, as long as the rSPR distance does not become too large [19,20]. A related concept is kernelization: polynomial-time pre-processing rules which reduce the size of the input trees to purely a function of their rSPR distance [8].…”

Section: Introductionmentioning

confidence: 99%

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

Kelk¹,

Linz²,

Meuwese³

2022

Preprint

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The rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a well-studied measure of topological dissimilarity that is NP-hard to compute. Here we describe an improved linear kernel for the problem. In particular, we show that if the classical subtree and chain reduction rules are augmented with a modified type of chain reduction rule, the resulting trees have at most 9k − 3 leaves, where k is the rSPR distance; and that this bound is tight. The previous best-known linear kernel had size O(28k). To achieve this improvement we introduce cyclic generators, which can be viewed as cyclic analogues of the generators used in the phylogenetic networks literature. As a corollary to our main result we also give an improved weighted linear kernel for the minimum hybridization problem on two rooted binary phylogenetic trees.

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“…Although this parsimonious approach is faster than the maximum likelihood approach ( Lutteropp et al 2022 ), the parsimonious network inference problem is still NP-hard even for the special case when there are only two input trees ( Bordewich and Semple 2007 ). For the two-tree case, the fastest programs include MCTS-CHN ( Yamada et al 2020 ) and HYBRIDIZATION NUMBER ( Whidden et al 2013 ). For the general case in which there are multiple input trees, HYBROSCALE ( Albrecht 2015 ) and its predecessor ( Albrecht et al 2012 ), PRIN ( Wu 2010 ), and PRINs ( Mirzaei and Wu 2015 ) have been developed.…”

mentioning

confidence: 99%

A fast and scalable method for inferring phylogenetic networks from trees by aligning lineage taxon strings

et al. 2023

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The reconstruction of phylogenetic networks is an important but challenging problem in phylogenetics and genome evolution, as the space of phylogenetic networks is vast and cannot be sampled well. One approach to the problem is to solve the minimum phylogenetic network problem, in which phylogenetic trees are first inferred, then the smallest phylogenetic network that displays all the trees is computed. The approach takes advantage of the fact that the theory of phylogenetic trees is mature and there are excellent tools available for inferring phylogenetic trees from a large number of bio-molecular sequences. A tree-child network is a phylogenetic network satisfying the condition that every non-leaf node has at least one child that is of indegree one. Here, we develop a new method that infers the minimum tree-child network by aligning lineage taxon strings in the phylogenetic trees. This algorithmic innovation enables us to get around the limitations of the existing programs for phylogenetic network inference. Our new program, named ALTS, is fast enough to infer a tree-child network with a large number of reticulations for a set of up to 50 phylogenetic trees with 50 taxa that have only trivial common clusters in about a quarter of an hour on average

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Improved Practical Algorithms for Rooted Subtree Prune and Regraft (rSPR) Distance and Hybridization Number

Cited by 4 publications

References 19 publications

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

A fast and scalable method for inferring phylogenetic networks from trees by aligning lineage taxon strings

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