Improved Fixed-Parameter Algorithm for the Tree Containment Problem on Unrooted Phylogenetic Network

Phylogenetic trees are unable to represent the evolutionary process for a collection of species if reticulation events happened, and a generalized model named phylogenetic network was introduced consequently. However, the representation of the evolutionary process for one gene is actually a phylogen...

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Bibliographic Details
Published in:IEEE/ACM transactions on computational biology and bioinformatics Vol. 19; no. 6; pp. 3539 - 3552
Main Authors: Shi, Feng, Li, Hangcheng, Rong, Guozhen, Zhang, Zhen, Wang, Jianxin
Format: Journal Article
Language:English
Published: United States IEEE 01.11.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Biological effects
Biological Evolution
Computational modeling
Computer applications
Containment
fixed-parameter algorithm
Models, Genetic
Parameters
phylogenetic network
Phylogenetic tree
Phylogenetics
Phylogeny
Runtime
Sorting
Time complexity
Uncertainty
unrooted tree containment problem
Vegetation
ISSN:1545-5963, 1557-9964, 1557-9964
Online Access:Get full text
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Summary:Phylogenetic trees are unable to represent the evolutionary process for a collection of species if reticulation events happened, and a generalized model named phylogenetic network was introduced consequently. However, the representation of the evolutionary process for one gene is actually a phylogenetic tree that is "contained" in the phylogenetic network for the considered species containing the gene. Thus a fundamental computational problem named Tree Containment problem arises, which asks whether a phylogenetic tree is contained in a phylogenetic network. The previous research on the problem mainly focused on its rooted version of which the considered tree and network are rooted, and several algorithms were proposed when the considered network is binary or structure-restricted. There is almost no algorithm for its unrooted version except the recent fixed-parameter algorithm with runtime <inline-formula><tex-math notation="LaTeX">O(4^kn^2)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn>4</mml:mn><mml:mi>k</mml:mi></mml:msup><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq1-3111660.gif"/> </inline-formula>, where <inline-formula><tex-math notation="LaTeX">k</tex-math> <mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq2-3111660.gif"/> </inline-formula> and <inline-formula><tex-math notation="LaTeX">n</tex-math> <mml:math><mml:mi>n</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq3-3111660.gif"/> </inline-formula> are the reticulation number and size of the considered unrooted binary phylogenetic network <inline-formula><tex-math notation="LaTeX">N</tex-math> <mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq4-3111660.gif"/> </inline-formula>, respectively. As the runtime is a little expensive when considering big values of <inline-formula><tex-math notation="LaTeX">k</tex-math> <mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq5-3111660.gif"/> </inline-formula>, we aim to improve it and successfully propose a fixed-parameter algorithm with runtime <inline-formula><tex-math notation="LaTeX">O(2.594^kn^2)</tex-math> <mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>594</mml:mn><mml:mi>k</mml:mi></mml:msup><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq6-3111660.gif"/> </inline-formula> in the paper. Additionally, we experimentally show its effectiveness on biological data and simulated data.
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ISSN:1545-5963
1557-9964
1557-9964
DOI:10.1109/TCBB.2021.3111660