Improved orientations of physical networks

The orientation of physical networks is a prime task in deciphering the signaling-regulatory circuitry of the cell. One manifestation of this computational task is as a maximum graph orientation problem, where given an undirected graph on n vertices and a collection of vertex pairs, the goal is to orient the edges of the graph so that a maximum number of pairs are connected by a directed path. We develop a novel approximation algorithm for this problem with a performance guarantee of O(logn / loglogn), improving on the current logarithmic approximation. In addition, motivated by interactions whose direction is pre-set, such as protein-DNA interactions, we extend our algorithm to handle mixed graphs, a major open problem posed by earlier work. In this setting, we show that a polylogarithmic approximation ratio is achievable under biologically-motivated assumptions on the sought paths.