  Phylogenetic networks are increasingly being considered as better suited to
represent the complexity of the evolutionary relationships between species. One
class of phylogenetic networks that has received a lot of attention recently is
the class of orchard networks, which is composed of networks that can be
reduced to a single leaf using cherry reductions. Cherry reductions, also
called cherry-picking operations, remove either a leaf of a simple cherry
(sibling leaves sharing a parent) or a reticulate edge of a reticulate cherry
(two leaves whose parents are connected by a reticulate edge). In this paper,
we present a fixed-parameter tractable algorithm to solve the problem of
finding a maximum agreement cherry-reduced subnetwork (MACRS) between two
rooted binary level-1 networks. This is first exact algorithm proposed to solve
the MACRS problem. As proven in earlier work, there is a direct relationship
between finding an MACRS and calculating a distance based on cherry operations.
As a result, the proposed algorithm also provides a distance that can be used
for the comparison of level-1 networks.
