Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

Chen, Zhizhong; Wang, Lusheng

doi:10.1109/tcbb.2011.137

Cited by 33 publications

(28 citation statements)

References 14 publications

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“…[19] Suppose that C is a cycle of G F and r 1 , …, r ℓ are the nodes of C . Then, each r j ∈{ r 1 ,…, r ℓ } has two children u j and u’ j in F .…”

Section: Methodsmentioning

confidence: 99%

“…In the supplementary material of [19], an O ( 3 k n )-time algorithm for solving GAF is detailed. The algorithm differs from Whidden et al ’s algorithm for enumerating all MAFs of T 1 and T 2 only in that we start with F 1 (as it is given) and F 2 = T 2 (instead of starting with F 1 = T 1 and F 2 = T 2 ) and then repeatedly modify F 1 and F 2 until either | F 1 |> k + k 0 or F 1 becomes a forest without edges, where k 0 is the original size of F 1 .…”

Section: Methodsmentioning

confidence: 99%

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A fast tool for minimum hybridization networks

2012

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BackgroundDue 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 combine the two phylogenetic trees into a hybridization network with the fewest hybridization events. This leads to three computational problems, namely, the problem of computing the minimum size of a hybridization network, the problem of constructing one minimum hybridization network, and the problem of enumerating a representative set of minimum hybridization networks. The previously best software tools for these problems (namely, Chen and Wang’s HybridNet and Albrecht et al.’s Dendroscope 3) run very slowly for large instances that cannot be reduced to relatively small instances. Indeed, when the minimum size of a hybridization network of two given trees is larger than 23 and the problem for the trees cannot be reduced to relatively smaller independent subproblems, then HybridNet almost always takes longer than 1 day and Dendroscope 3 often fails to complete. Thus, a faster software tool for the problems is in need.ResultsWe develop a software tool in ANSI C, named FastHN, for the following problems: Computing the minimum size of a hybridization network, constructing one minimum hybridization network, and enumerating a representative set of minimum hybridization networks. We obtain FastHN by refining HybridNet with three ideas. The first idea is to preprocess the input trees so that the trees become smaller or the problem becomes to solve two or more relatively smaller independent subproblems. The second idea is to use a fast algorithm for computing the rSPR distance of two given phylognetic trees to cut more branches of the search tree in the exhaustive-search stage of the algorithm. The third idea is that during the exhaustive-search stage of the algorithm, we find two sibling leaves in one of the two forests (obtained from the given trees by cutting some edges) such that they are as far as possible in the other forest. As the result, FastHN always runs much faster than HybridNet. Unlike Dendroscope 3, FastHN is a single-threaded program. Despite this disadvantage, our experimental data shows that FastHN runs substantially faster than the multi-threaded Dendroscope 3 on a PC with multiple cores. Indeed, FastHN can finish within 16 minutes (on average on a Windows-7 (x64) desktop PC with i7-2600 CPU) even if the minimum size of a hybridization network of two given trees is about 25, the trees each have 100 leaves, and the problem for the input trees cannot be reduced to two or more independent subproblems via cluster reductions. It is also worth mentioning that like HybridNet, FastHN does not use much memory (indeed, the amount of memory is at most quadratic in the input size). In contrast, Dendroscope 3 uses a huge amount of memory. Executables of FastHN for Windows XP (x86), Windows 7 (x64), Linux, and Mac OS are available (see the Results and discussion section for details).ConclusionsFor both biological ...

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“…[19] Suppose that C is a cycle of G F and r 1 , …, r ℓ are the nodes of C . Then, each r j ∈{ r 1 ,…, r ℓ } has two children u j and u’ j in F .…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

A fast tool for minimum hybridization networks

2012

Self Cite

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“…4 Mark each side s of G with |X N p (s)| ≤ 2 as finished and each other side as unfinished. 5 while there exists an unfinished side of G do 6 Let s be an unfinished side of G such that there is no unfinished side of G that is below s. 7 Let x + s and x − s be, respectively, the top and bottom leaf on side s in N p . 8 Let X s be the set of all x ∈ X that are not in N p and such that x + s → x, x − s .…”

Section: An Exponential-time Algorithmmentioning

confidence: 99%

“…For the case of multiple binary trees, there exists a kernel with at most 20k 2 leaves [15], various heuristics [7,8,29] and an exact approach without running-time bound [30].…”

Section: Introductionmentioning

confidence: 99%

Kernelizations for the hybridization number problem on multiple nonbinary trees

Iersel

Kelk

Scornavacca

2016

Journal of Computer and System Sciences

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Given a finite set X, a collection T of rooted phylogenetic trees on X and an integer k, the Hybridization Number problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k. We show two kernelization algorithms for Hybridization Number, with kernel sizes 4k(5k) t and 20k 2 ( + − 1) respectively, with t the number of input trees and + their maximum outdegree. Experiments on simulated data demonstrate the practical relevance of our kernelization algorithms. In addition, we present an n f (k) t-time algorithm, with n = |X| and f some computable function of k.

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“…. ‚ T K when K ‡ 3 (Wu, 2010;Park and Nakhleh, 2012;Chen and Wang, 2012). There are no existing methods for the exact computation of the hybridization number or reconstructing parsimonious networks with three or more trees.…”

Section: Wumentioning

confidence: 99%

An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees

2013

Lecture Notes in Computer Science

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A phylogenetic network is a model for reticulate evolution. A hybridization network is one type of phylogenetic network for a set of discordant gene trees and ''displays'' each gene tree. A central computational problem on hybridization networks is: given a set of gene trees, reconstruct the minimum (i.e., most parsimonious) hybridization network that displays each given gene tree. This problem is known to be NP-hard, and existing approaches for this problem are either heuristics or making simplifying assumptions (e.g., work with only two input trees or assume some topological properties).In this article, we develop an exact algorithm (called PIRN C ) for inferring the minimum hybridization networks from multiple gene trees. The PIRN C algorithm does not rely on structural assumptions (e.g., the so-called galled networks). To the best of our knowledge, PIRN C is the first exact algorithm implemented for this formulation. When the number of reticulation events is relatively small (say, four or fewer), PIRN C runs reasonably efficient even for moderately large datasets. For building more complex networks, we also develop a heuristic version of PIRN C called PIRN CH . Simulation shows that PIRN CH usually produces networks with fewer reticulation events than those by an existing method.PIRN C and PIRN CH have been implemented as part of the software package called PIRN and is available online.

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Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

Cited by 33 publications

References 14 publications

A fast tool for minimum hybridization networks

A fast tool for minimum hybridization networks

Kernelizations for the hybridization number problem on multiple nonbinary trees

An Algorithm for Constructing Parsimonious Hybridization Networks with Multiple Phylogenetic Trees

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