A quadratic kernel for computing the hybridization number of multiple trees

Iersel, Leo van; Linz, Simone

doi:10.1016/j.ipl.2013.02.010

Cited by 24 publications

(43 citation statements)

References 16 publications

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“…HN is APX-hard (and thus NP-hard) [6] but FPT in parameter h r (T ) [32]. That is, the question "Is h r (T ) ≤ k?…”

Section: Goal: Minimize R (N )mentioning

confidence: 99%

“…Adding a set of labels L to an edge side (u, v) of an r -generator involves subdividing (u, v) to a path of |L| internal nodes and, for each such internal node w, adding a new leaf w , an edge (w, w ), and labeling w with some taxon from L (such that L bijectively labels the new leaves). On the other hand, adding a label l to a node side v consists of adding a new leaf y, an edge (v, y) and labeling y with l. In [32] it was shown that if G is an r -generator, then G has at most 4r − 1 edge sides and at most r node sides. We will start by showing that the (CPS) reduction rule leaves the hybridization number unchanged:…”

Section: Parameterized Complexity Of Ruhnmentioning

confidence: 99%

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On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems

et al. 2017

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The hybridization number problem requires us to embed a set of binary rooted phylogenetic trees into a binary rooted phylogenetic network such that the number of nodes with indegree two is minimized. However, from a biological point of view accurately inferring the root location in a phylogenetic tree is notoriously difficult and poor root placement can artificially inflate the hybridization number. To this end we study a number of relaxed variants of this problem. We start by showing that the fundamental problem of determining whether an unrooted phylogenetic network displays (i.e. embeds) an unrooted phylogenetic tree, is NP-hard. On the positive side we show that this problem is FPT in reticulation number. In the rooted case the corresponding FPT result is trivial, but here we require more subtle argumentation. Next we show that the hybridization number problem for unrooted networks (when given B Georgios 123Algorithmica two unrooted trees) is equivalent to the problem of computing the tree bisection and reconnect distance of the two unrooted trees. In the third part of the paper we consider the "root uncertain" variant of hybridization number. Here we are free to choose the root location in each of a set of unrooted input trees such that the hybridization number of the resulting rooted trees is minimized. On the negative side we show that this problem is APX-hard. On the positive side, we show that the problem is FPT in the hybridization number, via kernelization, for any number of input trees.

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“…HN is APX-hard (and thus NP-hard) [6] but FPT in parameter h r (T ) [32]. That is, the question "Is h r (T ) ≤ k?…”

Section: Goal: Minimize R (N )mentioning

confidence: 99%

Section: Parameterized Complexity Of Ruhnmentioning

confidence: 99%

On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems

et al. 2017

Self Cite

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“…(See [15].) If N is a binary network with no nontrivial pendant subtrees and with r(N) = k > 0 and if G is its underlying generator, then G has at most 4k − 1 edge sides, at most k vertex sides and at most 5k − 1 sides in total.…”

Section: Lemmamentioning

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%

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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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Combining Networks Using Cherry Picking Sequences

Janssen

Jones

Murakami

2020

Algorithms for Computational Biology

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Phylogenetic networks are important for the study of evolution. The number of methods to find such networks is increasing, but most such methods can only reconstruct small networks. To find bigger networks, one can attempt to combine small networks. In this paper, we study the Network Hybridization problem, a problem of combining networks into another network with low complexity. We characterize this complexity via a restricted problem, Tree-child Network Hybridization, and we present an FPT algorithm to efficiently solve this restricted problem.

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A quadratic kernel for computing the hybridization number of multiple trees

Cited by 24 publications

References 16 publications

On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems

On Unrooted and Root-Uncertain Variants of Several Well-Known Phylogenetic Network Problems

Kernelizations for the hybridization number problem on multiple nonbinary trees

Combining Networks Using Cherry Picking Sequences

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