On the existence of a cherry-picking sequence

TL;DR

This paper investigates the computational complexity of determining cherry-picking sequences in collections of phylogenetic trees, showing NP-completeness for larger collections and polynomial-time solvability under certain constraints.

Contribution

It proves NP-completeness of the cherry-picking sequence decision problem for collections of at least eight trees and offers a polynomial-time solution for bounded cases using automata theory.

Findings

NP-complete for collections with at least eight trees

Polynomial-time algorithm for bounded number of trees and cherries

Automata theory applied to phylogenetic sequence problems

Abstract

Recently, the minimum number of reticulation events that is required to simultaneously embed a collection P of rooted binary phylogenetic trees into a so-called temporal network has been characterized in terms of cherry-picking sequences. Such a sequence is a particular ordering on the leaves of the trees in P. However, it is well-known that not all collections of phylogenetic trees have a cherry-picking sequence. In this paper, we show that the problem of deciding whether or not P has a cherry-picking sequence is NP-complete for when P contains at least eight rooted binary phylogenetic trees. Moreover, we use automata theory to show that the problem can be solved in polynomial time if the number of trees in P and the number of cherries in each such tree are bounded by a constant.