  We introduce two algorithms for reconstructing semi-directed level-1
phylogenetic networks from their complete set of 4-leaf subnetworks, known as
quarnets. The first algorithm, the sequential method, begins with a single
quarnet and adds on one leaf at a time until all leaves have been placed. The
second algorithm, the cherry-blob method, functions similarly to cherry-picking
algorithms for phylogenetic trees by identifying exterior network structures
from the quarnets.
