Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable

Bordewich, Magnus; Semple, Charles

doi:10.1109/tcbb.2007.1019

Cited by 63 publications

(98 citation statements)

References 18 publications

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“…It was already known that Hybridization Number is fixed-parameter tractable when parameterized by the hybridization number [5] but our result is stronger as the hybridization level can be small, even 1, for pairs of trees for which the hybridization number is arbitrarily large. On the other hand, it is clear that the hybridization level never exceeds the hybridization number.…”

Section: Hybridization Numbermentioning

confidence: 61%

“…However, in order to define the required parameter, the rSPR level of two rooted binary phylogenetic X-trees, we need to define a cluster reduction, following [5].…”

Section: Hybridization Numbermentioning

confidence: 99%

“…This question, along with the closely related problems of determining the minimum number of subtree prune and regraft, respectively tree bisection and reconnection, operations required to transform one phylogenetic tree into another (the rSPR Distance and TBR Distance problem, respectively) has been considered in a number of papers [1,2,3,5,10,12,17,18]. Key theoretical developments have shown that each of these three problems is NPhard even in the restricted case that the input consists of two binary phylogenetic trees [4,6,12], but also that they are all fixed-parameter tractable in their respective natural parameters [1,4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Key theoretical developments have shown that each of these three problems is NPhard even in the restricted case that the input consists of two binary phylogenetic trees [4,6,12], but also that they are all fixed-parameter tractable in their respective natural parameters [1,4,5]. In essence, this means that there are efficient algorithms for computing the hybridization number and the rSPR/TBR distance on two trees of large size, as long as there have not been too many reticulations in the evolutionary history of the considered taxa.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Hybridization Numbermentioning

confidence: 61%

“…However, in order to define the required parameter, the rSPR level of two rooted binary phylogenetic X-trees, we need to define a cluster reduction, following [5].…”

Section: Hybridization Numbermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the fixed parameter tractability of agreement-based phylogenetic distances

et al. 2016

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“…; T k . Note that our definition of an AAF is the same as those in [4], [18] but is different from that in [16]. With respect to an AF F of T 1 ; .…”

Section: Agreement Forests (Afs)mentioning

confidence: 99%

Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

Chen

Wang

2012

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

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Abstract-A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N [13]; in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate network of the trees. The better way is to define it as the total number of parents of reticulation nodes in N minus the number of reticulation nodes in N [18]; in this case, a reticulate network with the smallest reticulation number is called an optimal type-II reticulate network of the trees. In this paper, we first present a fast fixed-parameter algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal type-II reticulate network of the input trees. To our knowledge, these are the first fixed-parameter algorithms for the problems. We have implemented the algorithms in ANSI C, obtaining programs CMPT and MaafB. Our experimental data show that CMPT can construct optimal type-I reticulate networks rapidly and MaafB can compute better lower bounds for optimal type-II reticulate networks within shorter time than the previously best program PIRN designed by Wu [18].

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Testing Phylogenetic Methods to Identify Horizontal Gene Transfer

Poptsova

2009

Horizontal Gene Transfer

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The subject of this chapter is to describe the methodology for assessing the power of phylogenetic HGT detection methods. Detection power is defined in the framework of hypothesis testing. Rates of false positives and false negatives can be estimated by testing HGT detection methods on HGT-free orthologous sets, and on the same sets with in silico simulated HGT events. The whole process can be divided into three steps: obtaining HGT-free orthologous sets, in silico simulation of HGT events in the same set, and submitting both sets for evaluation by any of the tested methods.Phylogenetic methods of HGT detection can be roughly divided into three types: likelihood-based tests of topologies (Kishino-Hasegawa (KH), Shimodaira-Hasegawa (SH), and Approximately Unbiased (AU) tests), tree distance methods (symmetrical difference of Robinson and Foulds (RF), and Subtree Pruning and Regrafting (SPR) distances), and genome spectral approaches (bipartition and quartet decomposition analysis). Restrictions that are inherent to phylogenetic methods of HGT detection in general and the power and precision of each method are discussed and comparative analyses of different approaches are provided, as well as some examples of assessing the power of phylogenetic HGT detection methods from a case study of orthologous sets from gamma-proteobacteria (Poptsova and Gogarten, BMC Evol Biol 7, 45, 2007) and cyanobacteria (Zhaxybayeva et al., Genome Res 16, 1099-108, 2006).

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Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable

Cited by 63 publications

References 18 publications

On the fixed parameter tractability of agreement-based phylogenetic distances

On the fixed parameter tractability of agreement-based phylogenetic distances

Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

Testing Phylogenetic Methods to Identify Horizontal Gene Transfer

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