New FPT Algorithms for Finding the Temporal Hybridization Number for Sets of Phylogenetic Trees
Sander Borst (Centrum Wiskunde & Informatica (CWI))
Leo van Iersel (TU Delft - Discrete Mathematics and Optimization)
M.E.L. Jones (Centrum Wiskunde & Informatica (CWI))
Steven Kelk (Maastricht University)
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Abstract
We study the problem of finding a temporal hybridization network containing at most k reticulations, for an input consisting of a set of phylogenetic trees. First, we introduce an FPT algorithm for the problem on an arbitrary set of m binary trees with n leaves each with a running time of O(5 k· n· m). 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 d and at most k reticulations in O((8 k) d5 k· k· n· m) time. Lastly, we introduce an O(6 kk! · k· n2) time algorithm for computing a temporal hybridization network for a set of two nonbinary trees. We also provide an implementation of all algorithms and an experimental analysis on their performance.
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