Inferring protein-protein interaction and protein-DNA interaction directions based on cause-effect pairs in undirected and mixed networks

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.