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 ((8 k) d 5 k · k · n · m) time. Lastly, we introduce an O (6 k k ! · 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. [ABSTRACT FROM AUTHOR]