  The C-Orientation problem asks whether it is possible to orient an undirected
graph to a directed phylogenetic network of a desired class C, and to find such
an orientation if one exists. The problem can arise when visualising
evolutionary data, for example, because popular phylogenetic network
reconstruction methods such as Neighbor-Net are distance-based and thus
inevitably produce undirected graphs. The complexity of C-Orientation remains
open for many classes C, including binary tree-child networks, and practical
methods are still lacking. In this paper, we propose an exponential but
practically efficient FPT algorithm for C-Orientation, which is parameterised
by the reticulation number and the maximum size of minimal basic cycles used in
the computation. We also present a very fast heuristic for Tree-Child
Orientation. To evaluate the empirical performance of the proposed methods, we
compared their accuracy and execution time for Tree-Child Orientation with
those of an exponential time C-orientation algorithm from the literature. Our
experiments show that the proposed exact algorithm is significantly faster than
the state-of-the-art exponential time algorithm. The proposed heuristic runs
even faster but the accuracy decreases as the reticulation number increases.
