Semi-directed networks provide a graphical structure for describing the evolutionary history of organisms in the presence of hybridization. We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from their complete set of 4-leaf subnetworks, known as quarnets. The sequential algorithm begins with a single quarnet and adds one leaf at a time until the entire network has been reconstructed. The cherry-blob algorithm is a novel approach inspired by cherry-picking techniques on trees
@article{arxiv.1910.00048,
title = {Constructing Semi-Directed Level-1 Phylogenetic Networks from Quarnets},
author = {Sophia Huebler and Rachel Morris and Joseph Rusinko},
journal= {arXiv preprint arXiv:1910.00048},
year = {2025}
}