On the parameterized complexity of the problem of inferring protein–protein interaction directions based on cause–effect pairs

We consider the following problem: given an undirected (mixed) network and a set of ordered source–target pairs, 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 the maximum graph orientation problem, and has applications in understanding interactions in protein–protein interaction networks. Since this problem is NP-hard, we take the parameterized complexity viewpoint and study the parameterized (in)tractability of the problem with respect to various parameters 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. Also, we present an exact algorithm which outperforms the previous algorithms on trees with bounded number of leaves. In the mixed case, we present polynomial-time algorithms for the problem on paths and cycles, and an FPT algorithm with respect to the combined parameter number of arcs and number of pairs on general graphs.