  We consider the following problem: Given an undirected (mixed) network and a
set of ordered source-target, or cause-effect pairs, direct all edges so as to
maximize the number of pairs that admit a directed source-target path. This is
called maximum graph orientation problem, and has applications in understanding
interactions in protein-protein interaction networks and protein-DNA
interaction networks. We have studied the problem on both undirected and mixed
networks. In the undirected case, we determine the parameterized complexity of
the problem (for non-fixed and fixed paths) with respect to the number of
satisfied pairs, which has been an open problem. Also, we present an exact
algorithm which outperforms the previous algorithms on trees with bounded
number of leaves. In addition, we present a parameterized-approximation
algorithm with respect to a parameter named the number of backbones of a tree.
In the mixed case, we present polynomial-time algorithms for the problem on
paths and cycles, and an FPT-algorithm based on the combined parameter the
number of arcs and the number of pairs on general graphs.
