New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees

Master thesis (2020)

Authors

S.J. Borst Electrical Engineering, Mathematics and Computer Science

Contributors

L.J.J. van Iersel Discrete Mathematics and Optimization - EEMCS (mentor)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2020 Sander Borst
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Published Date

16-01-2020

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of t binary trees with n leaves each with a running time of O(5^k*n*m) where k is the minimum temporal hybridization number. We also present the concept of temporal distance, which is a measure for how close a tree-child network is to being temporal. Then we introduce an algorithm for computing a tree-child network with temporal distance at most p and at most k reticulations in O((8k)^p*5^k*n*m). Lastly, we introduce a O(6^k*k!*n) algorithm for computing a minimum temporal hybridization network for a set of two nonbinary trees.