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

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 m binary trees with n leaves each with a running time ofwhere 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 d and at most k reticulations in O((8k) time algorithm for computing a minimum 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.

Orchard Networks are Trees with Additional Horizontal Arcs

“…The difference is that in a temporal labelling both arcs entering a reticulation need to be horizontal, which is more natural when reticulations represent hybridization events. This notion has been widely popular in defining network classes, which have been explored in relation to metrics [CLRV08], encodings [CLRV08], and reconstruction methods [BvIJK20]. Another related notion of time-consistency was introduced in [ELR06], which allows bidirectional horizontal arcs as well.…”