New FPT Algorithms for Finding the Temporal Hybridization Number for Sets of Phylogenetic Trees

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((8k)^d5^ k· k· n· m) time. Lastly, we introduce an O(6^kk!· k· n^2) 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.