Computing the Arc-Deletion Distance to Orchard Networks is NP-hard

TL;DR

This paper proves that calculating the minimum number of arc deletions needed to convert any phylogenetic network into an orchard network is NP-hard, highlighting the computational difficulty of this problem.

Contribution

The paper establishes the NP-hardness of computing the arc-deletion distance to orchard networks through a polynomial-time reduction from the Degree-3 Vertex Cover problem.

Findings

Computing the arc-deletion distance to orchard networks is NP-hard.

The proof involves a polynomial-time reduction from Degree-3 Vertex Cover.

This result shows the problem's computational intractability.

Abstract

Phylogenetic networks generalize phylogenetic trees by allowing reticulate evolutionary events such as horizontal gene transfer and hybridization. Among the many subclasses of phylogenetic networks, orchard networks have attracted increasing attention due to their structural and algorithmic properties. In this paper, we study the arc-deletion distance to orchard networks, defined as the minimum number of reticulate arcs whose deletion transforms a phylogenetic network into an orchard network. We prove that computing this distance is NP-hard via a polynomial-time reduction from the Degree-3 Vertex Cover problem. Our result establishes the computational intractability of this proximity measure and contributes to the complexity theory of phylogenetic network transformations.