Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings

Klawitter, Jonathan; Stumpf, Peter

doi:10.1007/978-3-030-68766-3_14

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…For some applications, the definition of an embedding has to be relaxed (allowing, for example, multiple tree arcs embedded into the same network arc) [HMSW16,HLM21]. Other interesting candidate problems for treewidth-based algorithms include phylogenetic network drawing [KS20], orienting phylogenetic networks [HvIJ + 19] and phylogenetic tree inference with duplications [vIJJ + 19].…”

Section: Cf Lemma 10mentioning

confidence: 99%

Embedding phylogenetic trees in networks of low treewidth

van Iersel,

Jones,

Weller

2023

Discrete Mathematics &Amp; Theoretical Computer Science

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Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic inference methods.We present the first algorithm for (rooted) \textsc{Tree Containment} using the treewidth $t$ of the input network $N$ as parameter, showing that the problem can be solved in $2^{O(t^2)}\cdot|N|$ time and space.

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Section: Cf Lemma 10mentioning

confidence: 99%

Embedding phylogenetic trees in networks of low treewidth

van Iersel,

Jones,

Weller

2023

Discrete Mathematics &Amp; Theoretical Computer Science

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“…More generally, visualizations have been studied for various models in phylogenetics, such as rooted phylogenetic trees [2,6,31], in conjunction with a geographic map [27,29], unrooted phylogenetic trees, and split networks [13,23,36]. In recent years, research has been extended from drawings of trees to drawings of phylogenetic networks [19][20][21][22]37], which are more general.…”

Section: Introductionmentioning

confidence: 99%

Visualizing Multispecies Coalescent Trees: Drawing Gene Trees Inside Species Trees

Klawitter¹,

Klesen²,

Moritz³

et al. 2022

Preprint

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We consider the problem of drawing multiple gene trees inside a single species tree in order to visualize multispecies coalescent trees. Specifically, the drawing of the species tree fills a rectangle in which each of its edges is represented by a smaller rectangle, and the gene trees are drawn as rectangular cladograms (that is, orthogonally and downward, with one bend per edge) inside the drawing of the species tree. As an alternative, we also consider a style where the widths of the edges of the species tree are proportional to given effective population sizes. In order to obtain readable visualizations, our aim is to minimize the number of crossings between edges of the gene trees in such drawings. We show that planar instances can be recognized in linear time and that the general problem is NP-hard. Therefore, we introduce two heuristics and give an integer linear programming (ILP) formulation that provides us with exact solutions in exponential time. We use the ILP to measure the quality of the heuristics on real-world instances. The heuristics yield surprisingly good solutions, and the ILP runs surprisingly fast.

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